UTILIZATION OF AN EXECUTIVE " 1;; 351].) " DECISION GAME TD TEST BDWMAN'S‘ E .I; j; ; _.; MANAGERIAL GOEEEICIEAI TIIEDRY :1}: ; ;, 9' i,;.;_* , DissertaIIIm Ior the Degree of PII. D.g} ; ’ ' MICHIGAN STATE UNIVERSITY “ . - WILLIAM EDWARD REMUS if ‘ “ I974 .~“ ' ' LIBRAR Y ‘ Michigan State University {7 , This is to certify that the thesis entitled Utilization of an Executive Decision Game to Test Bowman's Managerial Coefficient Theory presented by William Edward Remus has been accepted towards fulfillment of the requirements for Ph. D . Management degree in MM! 4 AAA/“21. Major professor Date WW“ /5 / f 74/ 0-7639 [aunt BINDERY mu. m LIBRARY BINDERS SIRIIIGPOEIT. WW“?! ABSTRACT UTILIZATION OF AN EXECUTIVE DECISION GAME TO TEST BOWMAN'S MANAGERIAL COEFFICIENT THEORY By William Edward Remus Bowman's managerial coefficient theory provides a conceptual framework to analyse repetitive decisions in a stable environment. According to Bowman the decision maker may be treated as a linear decision rule coefficient estimator. We can find the rule repre- senting his behavior by performing a linear regression on a set of historical decision variables. According to this theory the decision maker's rule is unbiased relative to the optimal and heur- istic rules, the latter are defined as concise empirical rules derived from a manager's behavior. Poor decision making is said to be characterized by large variances relative to optimal and heuristic rules. The theory has been extended to include learn- ing effects (Carter, Jenicke and Remus). A review of the literature reveals business gaming situations to be a valid laboratory for studying decision making. In this study three key decision variables in the Executive Game were analyzed over 8 periods of play in an undergraduate introduction to business course. The study reached the following conclusions: William Edward Remus 1. Since linear decision rules had concurrent and predictive validity they may be used to represent the behavior of the subjects. 2. The heuristic rules were significantly different than rules which were allowed to contain all decision variables which entered at .05. The two sets of rules differed little in their ability to predict the decision maker's behavior. 3. The decision rules for the composite, best and worst deci- sion makers had structurally different decision rules although each contained the same variables. The rules for the best subjects better explained their behavior than the composite or worst rules did for composite and worst subjects, respectively. 4. Evidence was found to support the hypothesis of learning occurring as play proceeded. This effect was manifest in terms of reduced bias over time. 5. Strong evidence was found that lower ranked subjects were more biased from heuristic rules. 6. Strong evidence was found that lower ranked subjects were more erratic decision makers than higher ranked subjects. This study supports the general applicability of Bowman's theory to competitive simulation games such as the Executive Game. While it points to the necessity of including learning effects in the theory, it does not support Bowman's assertation of unbiased decision making and variance being the major source of economic inefficiencies. This study demonstrates the value of games such as the Executive Game as a laboratory for exploring decision making behavior. The decision makers' behavior has been represented by linear decision rules which are heuristic rather than necessarily optimal. These rules provide a basis for further exploration of behavior patterns. UTILIZATION OF AN EXECUTIVE DECISION GAME TO TEST BOWMAN'S MANAGERIAL COEFFICIENT THEORY By William Edward Remus A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Management 1974 ACKNOWLEDGMENTS Words cannot express my appreciation for the guidance and direction given me by Dr. Richard Henshaw. And to Dr. Phillip Carter who started me on the publication road to academic fame. And to Dr. Maryellen McSweeney who gave me the research tools to bring coherance to a mountain of data. 11 Chapter II III IV TABLE OF CONTENTS INTRODUCTION LITERATURE REVIEW AND RESEARCH BACKGROUND Review of the Literature on Decision Making in Business Games Review of the Literature on Bowman's Managerial Coefficient Theory The Executive Game Applying Bowman's Theory to the Executive Game THE EXPERIMENTAL DESIGN AND ANALYSIS PLAN Description of the Experimental Environment General Procedure of Data Analysis Finding the Heuristic Models THE RESULTS OF THE ANALYSIS Interrelationships among the Heuristic Price LDR's Interrelationships among the Heuristic Marketing LDR's Interrelationships among the Heuristic Volume LDR's Cross Validation of the Heuristic LDR's Summary of the Interrelationships among Heuristic LDR's Analysis of the Equivalence of Method 2 and 3 LDR's Analysis of the Equivalence of Method 1 and 3 LDR's Bias in Decision Making among Teams of Different Rank Variance in Decision Making among Teams of Different Rank Learning Summary of the Effects of Rank and Time SUMMARY AND CONCLUSIONS Conclusions Need for Further Study Bibliography Appendix Computer Print Outs iii 12 21 23 27 27 30 34 39 39 43 50 54 59 61 61 72 73 75 8O 81 81 83 86 Table 10 11 12 13 14 15 16 17 18 19 20 21 LIST OF TABLES Ten Mbst Commonly Made Claims About Business Games Variables Used in the Executive Game Linear Decision Rules for the Price Decision Tests for Autocorrelation in the Price LDR's Equivalence of the Coefficients of the Price LDR's Linear Decision Rules for the Marketing Decision Tests for Autocorrelation in the Marketing LDR's Equivalence of the Coefficients of the Marketing LDR's Linear Decision Rules for the Volume Decision Tests for Autocorrelation in the Volume LDR's Equivalence of the Coefficients of the Volume LDR's Cross Validation of the Price LDR Cross Validation of the Marketing LDR Cross Validation of the Volume LDR Comparison of Method 2 and 3 Linear Decision Rules Comparison of Method 1 and 3 LDR's on Contribution to Sum Squares Structural Equivalence of Method 1 and 3 LDR's Confidence Intervals on Price LDR Predictions Confidence Intervals on Marketing LDR Predictions Confidence Intervals on Volume LDR Predictions Improvement in the Degree of Confidence of Method 3 over Method 1 LDR's iv Page 31 4O 42 44 45 46 49 51 53 55 57 58 6O 62 64 65 67 68 69 70 Table 22 23 24 25 Significance Levels Final Team Rank Significance Levels Significance Levels Periods Significance Levels Periods for the for the for the for the Tests Tests Tests Tests on Bias Across on MAD Across Rank on MSD Across Time on MAD Across Time 78 79 Figure 1 LIST OF FIGURES Output from the Executive Game vi LDR MSD R & D ROI LIST OF ABBREVIATIONS AND NOMENCLATURE Linear Decision Rule A particular linear decision rule calculated from sample 8 using method m to predict decision variable d. Mean Absolute Deviations Mean Signed Deviations Research and Development Return on Investment vii CHAPTER I INTRODUCTION This dissertation is the outcome of two relatively divergent interests. I have long been interested in business simulation games. As the following sections demonstrate there has been far from unani- mous belief in the value of business games. Decision making models also have been of great interest to me. Many decision models we advocate imply that managerial decision mak- ing is inadequate to the tasks to which the model is applied. It is rather as if the manager should hire a consultant to implement a tech- nique and delegate the decision to him. It was refreshing to encounter Bowman's theory given the above misgivings. Bowman's theory can loosely be construed to say the fol- lowing things. First experienced managers making repetitive deci- sions are effective decision makers. They are able to gain an impli- cit if not explicit feel for the variables which are critical to their decision making; they are able to assign appropriate weights to the critical variables in order to make sound decisions. The decision rules a manager uses usually can be determined by regressing his decision on the set of decision variables. The theory states that the decision rule derived from prior decisions is a useful and effective rule for future use in a stable environment. In fact, in some situations the derived rule may be better than an optimal rule obtained from a simplified model. Thus, Bowman's theory, if correct, gives us faith in the effectiveness of manager's making repetitive decisions. Further the theory provides a way to quantify the manager's decision making approach so that it may be explicitly used in the future. If one incorporates learning then the theory would seem to be applicable to any sort of repetitive decision making, even by inex- perienced decision makers (Carter, Jenicke and Remus). In particular, decision making in business games such as the Executive Game by Hen- shaw and Jackson should be amenable to such analysis. This paper includes a review of the literature which strongly supports the use of a business game as a laboratory to study decision making. Such a study will provide the answers to a number of important research questions. First, such a study would test the validity of using Bowman's theory in a competitive, unstable environment where decisions are made by inexperienced subjects. We could test and verify the premises of Bowman's theory such as where it is only higher variance rather than bias that determines poor economic per- formance. We would find whether linear decision rules characterize the behavior of successful teams as well as the unsuccessful teams. It would be interesting to find if the best and worst teams differed in the structure of their rules. We could address ourselves to whether different industries are characterized by different patterns of behavior, bias and variance. The learning effects could be examined by testing reduction in bias and increases in consistency over time. Lastly, we could test if teams of different rank had different rates of learning. These questions will be discussed in great detail in the fol- lowing sections of this paper. CHAPTER II LITERATURE REVIEW AND RESEARCH BACKGROUND This chapter provides a necessary background to the study. First we will examine the literature on business gaming with the intent of demonstrating the appropriateness of using the gaming situation as a laboratory to study decision making. Then we will review the literature on Bowman's managerial coefficient theory. The third section describes the nature of the Executive Game. The chapter concludes with a discussion of the implications of Bowman's theory when applied to Executive Game. The implications form the basis for the experimental design. Review of the Literature on Decision Making in Business Games Many claims have been made for the benefits of playing business games. A recent study (Schriesheim and Schriesheim) examined the claims for the benefits made by the authors of various business games. The ten major claims they found are presented in table 1. The authors than content analyzed the literature on gaming to find if practitioner opinion agreed with those claims. A random selection of the litera- ture when content analyzed revealed strong support for claims one, three and four. The remaining claims were not supported. It is the first of those that we are concerned with. Table 1 Ten Most Commonly Made Claims About Business Games* Claim: 1. They provide a vehicle for learning and practicing decision-making under risk and uncertainty.** 2. They teach the importance of planning and forecasting and provide a vehicle for learning and practice. 3. They develop a recognition and appreciation of func- tional interrelationships and dependencies in business firms. 4. They produce high interest and motivation in participants. 5. They teach facts and provide a vehicle for the applica- tion of specific techniques. 6. They provide an opportunity for the learning of inter- personal skills. 7. They provide an opportunity for learning to bear decision consequences without actual loss to the participant. 8. They provide an opportunity for the development of organ- izing ability. 9. They aid in the development of communications skills. 10. They provide a means of introduction to the computer in a manner which maximizes appreciation and minimizes fear of it. *Other claims are often made. For example, the claims that business games interest students in the study of business and that they teach business terminology are often made. These claims, however, do not have direct implications for managerial development and have thus been excluded from this listing. **Implied within the claim that games "provide" for learning or prac— tice of some ability or skill is that this is done in an effective manner. Although claims of this nature are not explicitly stated, they must be interpreted in this manner if they are to be evaluated. It is certainly encouraging to know that practitioners see busi— ness games as "a vehicle for learning and practicing decision making under risk and uncertainty". Arguments can easily be constructed to support that viewpoint. The empirical studies on that question, how- ever, are not so unequivocal in their support. While there have been many studies on business gaming, few of these studies were more than anecdotal. Of the remainder, few dealt with decision making. The empirical decision making studies tended to take up the question of whether playing the game improved the prob- lem solving and decision making abilities of the participants. A study on the Carnegie Tech Management Game (Cangelosi) examined sev- eral managerial skills including problem solving using pre and post in-basket tests. His subjects and controls were graduate students. He found no support for improved problem solving skills due to the gaming experience. A similar study (befie and Levin) using graduate students for subjects used the Educational Testing Service's inr basket exercise. Included in the eighteen measures found in the in-basket exercise were measures of problem solving and decision mak- ing ability. Again no support was found for enhanced problem solving or decision making skills for the gaming group. In both studies the authors argued the inadequacy of their design or instruments may have obscured the effect they were looking for. These two studies are the only studies which had an adequate experimental design. Both, however, were subject to a very signifi- cant error. In order to find learning the post measure must be such that the learning acquired by gaming must be easily transferred to it. In both experiments the subjects learn group decision making skills; thus we may not find group learning showing up on a test of indi- vidual learning unless that learning is readily transferable. The two studies could possibly be interpreted under learning theory as finding group learning did not transfer to individual problem solv- ing situations. Almost all experimentors studying group gaming seem to consistently make this mistake and thus leave their findings open to question. Thus we find practitioner support for but no methodlogically adequate studies to demonstrate improved decision making after the gaming experience. Another series of experiments focused on the game environment as a decision making and/or behavior laboratory. The concern in these studies has not been to demonstrate the external validity of claims about the game but instead to study the mechanisms involved in various gaming situations. It is these mechanisms which are now of concern to us. First we shall examine the literature about team.decision making behavior during the play of the game (Norman): 1. Each team developed its own unique pattern of decision making. 2. Differences between teams' decision making behavior cor- respond with differences in their stated beliefs about the environment. 3. The team's focus was changed from the general goal of maximizing ROI to some more concise action objective around which it could model the game in meaningful terms. 4. Each team organized the elements of the game around their model of the game. 5. The team's model tended to persist even when partially contradicted; it was simply modified to reflect the new data. 6. Each team exhibited a style; e.g. ultraconservative, gamblers, etc. This style persisted. An intriguing study by Philippatos and Moscato found that gaming subjects were able to learn the rules and objectives of games that they played given no information about the game. In other words, subjects were able to gain an intuitive if not explicit understanding of the games they played without any external guidance. This would imply that Norman's observations on team models of the game is accur- ate and the team decision models were useful and accurate. Norman's findings are strongly bolstered by a series of studies on a aggregate production scheduling simulation game (Miller and Moskowitz, Carter and Hamner, Carter, Jenicke and Remus). Applying Bowman's managerial coefficient theory to the game they found sta- bility in decision making and that their subjects derived decision rules as effective, if not more so, than the tractable optimal rules for the simulation. Significant learning effects were also found and measured as the simulation proceeded. These studies were made on individual rather than team decisions and will be examined in the next section. Another significant finding was that game performance is, at least for certain games, related to subject matter knowledge (Rohrer, cited by Schriesheim and Schriesheim). While this may be obvious for certain special purpose games the finding that knowledge of marketing practices may enhance game success in a more general decision game is consistent with the behavioral findings to be cited in the coming paragraphs. One area of mixed results in gaming is that of conservatism in decision making. One study suggests that student players become more risk prone as play proceeds (Lewin and Weber). Since a study by Mos- kowitz found students to be more risk conscious than managers when making initial gaming decision, we could argue that the gaming experi- ence was a realistic develOpmental activity. A contrasting study (Babb, et. al.) found businessmen to make more conservative decisions than students when gaming; students behavior was characterized as erratic. The Slovic and Lichenstein review of the literature also arrived at no conclusion due to mixed results. A reasonable explanation of the diversity of results on this issue is simply that subjects learn to play games well and understand intuitively what behavior is needed to win. They build simple but useful models of the game and use them to make decisions. This behavior is noted and measured in many studies (Miller and Moskowitz, Carter, Remus and Jenicke, Babb, et. al., Norman, Philippatos and Moscato, and more). It is not unreasonable to conclude that different gaming experiences elicit differing types of appropriate behavior once the learning effect has died out. This behavior may or may not be conservative depending on the nature of the game played. Thus Babb, et. al.'s assertion of businessmen being more conservative initially than students when playing the farm supply game may not be in cone flict with Lewin and Weber's assertion to the contrary made for a different game. This point is made explicit by a study (Khera and Benson) that found the only differences in terms of decision making among businessmen and students was due to background. If the busi- nessmen initially know more about a simulation of a given industry, 10 then the students rapidly acquire background by gaming which puts them on an equal basis with the businessmen (Babb, et. a1.). Thus we would argue that gaming effectively teaches the players the appropriate behavior to do well on that model. This is not an asser- tion that this learning would be appropriate for or even transfer to the real world. Babb found that businessmen transfer their business methodology to the play of a parallel simulation. This transfer, however, did not necessarily lead to gaming success. Apparently his farm supply and dairy management simulations required different win- ning strategies than their unsimulated counterparts. I have been arguing up to this point that game players effec- tively learn the strategies needed to do well in the simulation game and that different games elicit different strategies. If the players learn appropriate strategies for the game and the game models is a valid version of business then the strategies they learn will be useful outside the game. This is a restrictive way to view the use of games. Often games are used in quantitative methods courses to provide students with experience in using the analytical techniques covered in the course. In this case we would require only that the students be able to practice the techniques on the game that they would use in the non-simulated situation. Hopefully the game would reward the use of the techniques by an improved performance. This is a more powerful use of gaming since the analytical techniques are useful in many varied situations. In this use of the game less restrictive requirements are made of the game model. 11 In either case the decision making behavior of the players should provide an excellent data source for empirical studies. The nature of team behavior has elicited a fair amount of litera- ture suggesting or using the game as a behavioral laboratory. One such study (Rowland and Gardner) measured the subjects on the Fied- ler's Least Preferred Coworker scale and then selected MARKSIM teams to reflect different patterns of managerial behavior. No particular configuration was predictive of game success although each configura— tion may lead to different perceptions of the game. Fiedler's measure is a largely discredited measure of managerial behavior and thus may have obscured the desired effects. More frequently the behavioral phenomenon integral to the game is studied without any particular prestructuring. The results of these studies suggest that team performance generally is unrelated to the subject's intellectual ability, aptitudes, tests and grades (Rowland and Gardner), although there is also evidence to the con- trary (McKenney and D111). In the cases when this does occur, the Rz's are extremely small. Little relationship exists between the team performance and the four personality measures found on the Myer- Briggs test (Babb, Leslie, and Van Slyke) although they did find a relationship between game success and emotional stability and cau- tiousness. The latter affect was not particularly prominent. Another study (Nash and Chentnik) attempted to predict success from the 16 psychological characteristics measured by the California Psychological Inventory. No coherent pattern of relationships emerged from the study. 12 Although research have been unable to predict overall per- formance, one study (Babb, et. al.) found microgame behavior to be correlated to psychological variables. For example, emotion- ally stable individuals showed less fluctuations in their pricing decision. Let us summarize our findings: 1. We found practitioner support but no empirical support for improved decision making skills as a result of gaming. 2. We did find the gaming situation to be a good and pOpular laboratory for studying decision making behavior. 3. Many useful understandings about decision making behavior were available from the literature including the finding that players learned appropriate winning behavior for their particular model. This learning effect explains some apparent inconsistencies in the literature. 4. We found that if the game was a valid simulation of its real counterpart we could generalize our findings to the nonrsimulated situation. 5. We found games to be useful in providing practice in ana- lytical techniques. This use made less restrictive require- ments of the game model. Review of the Literature on Bowman's Managerial Coefficient Theory The managerial coefficient theory (Bowman) is a simple but effec- tive approach to modeling decision making. The theory asserts that a decision maker's behavior may be modeled by a linear decision rule. That is, one can conceptualize the decision maker as a coefficient estimator for linear decision rules although he may not explicitly be involved in such an activity. We may visualize the decision maker as intuitively placing the right weights on the various deci- sion variables available to him. The theory asserts that managers make good decisions implying that on the average appropriate weights 13 are assigned to the decision variables. This is a rather appealing notion since many decision making models appear to imply that mana- gerial decisions are inadequate unless a specialist utilizes a sophisticated model on the manager's behalf. By examining a manager's prior behavior we can find his deci- sion rules. If we know the key decision variables or ask the manager which variables he uses we can use multiple regression on his history of decisions. Stepwise regression may be used to discover this deci- sion rules where the key variables are not already known and the full set of potential decision variables is known. The rule derived from the manager's behavior is, in general, a very good rule. This statement applies to an experienced manager who is no longer learning the nature of the process of which he is making decisions. Another implied assumption is that the rule has been derived from a set of variables which the manager uses for his deci- sion making. An incomplete set would give an inadequate decision rule. Others suggest that a stable environment is also assumed. Certainly if the environment were stable the theory would apply. But if the rule contains variables which reflect critical environ- mental fluctuations then that assumption may be relaxed. If the environmental instability causes the coefficients of the rules to change, we may use the most recent observations to update our rule to reflect those changes (Kunreuther). Naturally, to get an adequate data set for analysis the decision must be recurrent. The theory asserts that economic inefficiency has at its source the variance from the rule rather than bias. This can only occur if 14 the magnitude of the bias is small compared to the magnitude of the variance. Also the cost surfaces must be dish shaped. Convex cost functions such as the quadratic cost function are dish shaped. Bowman defines bias and variance as follows: Departures of the decision making behavior of management from the preferred results, in this sense can be divided or factored into two components, one which in the manner of a grand average departing from some preferred figure, we call bias (which causes a relatively small criteria loss due to the dish shaped bottom of the criteria sur- face), and one which represents individual occurences of experiences departing from the grand average, we call variance (which causes larger criteria losses due to the individual occurences up the sides of the criteria dish shaped surface). It is the latter and more important component which seems to offer the tempting possibility of elimination through the use of decision rules incorp- orating coefficients derived from management's own recur- rent behavior. Bowman here asserts that the erratic decision making relative to a manager's rule is the source of inefficiency. Erratic decision making is often prompted by cues from the business environment. Cues from the environment to the extent that they are not reflected in the pre- dictor variables of the linear decision rule must be considered as irrelevant to the decision at hand. If they were relevant certainly we should have included them in the rule. Thus the rule should be more efficient than actual behavior as the erratic cues are elimi- nated. Let X be a random variable representing the series of decisions made by a manager. Assume that the decision X is associated with the cost Y by the quadratic cost function: Y = a + bx + ch 15 If we further assume that X is normally distributed around mean u with standard deviation 0, we find: E(Y) = a + bE(X) + cE(X2) = a + bu + c(o2 +p2) The minimum cost point is found: dY/dX = b + 2cX = 0 xmin = -b/2c Then the minimum cost is: Yum = a + b(-b/2c) + C(-b/2C)2 =a - b2/4c The cost attributable solely to bias is just the expected cost less the minimum cost with the variance zero: COSTbias = (E(Y) - Y min)'o = O = by + cu2 + b2/4c The cost solely attributable to variance is the expected cost less the minimum cost with the bias at zero: COSTvariance a (E(Y) - Ymin)'bias = 0 (E(Y) - Y min)'u = -b/2c 2 2 2 (a + bu + c(u + o ) - (a — b /4c))lu 2 = co 8 -b/2c 16 If Bowman's assertion that cost attributable to variance is greater than the cost attributable to bias may be stated: bu + cu2 + b2/4c < co2 If A is defined as the difference between i and xmin: A = u + b/2c or in terms of u: u - A - b/2c Placing the latter equation in the equation representing Bowman's assumption, we find: bA - b2/2c + c(A - b/2c)2 + b2/4c < coz cA2 < co2 A < 0 Then Bowman's assumption that the cost attributable to variance is greater than the cost attributable to bias is true if and only if the bias in X is less than one standard deviation. Were there an optimal tractable solution to a given process we would expect that a regression analysis would give us a rule which would be about as efficient as the optimal, given the foregoing assumptions. Bowman does not assert that decision makers would end up with rules that are unbiased relative to the optimal nor does he assert that all managers will have the same insights and thus the 17 same decision rules for a given process. In fact on the first point he asserts that a decision rule may even be better than the optimal rule. However, it might be reasonable to find managers having similar insights and thus identical rules or that their rule might be the same as the optimal. Once a rule has been determined from past behavior, Bowman asserts that the rule will outperform the actual decision maker, given the previous assumptions. The decision maker is subject to irrelevant cues and moods which cause him to be erratic in decision making. The rule is not effected and thus yields better results. The reason why the rule from Bowman's analysis may be superior to an optimal rule found by traditional analysis may not be readily apparent. An optimal rule is derived from some mathematical, tract- able model for a process. The real world process does not necessarily conform with that simplified model of the process and in these instances, the Bowman rule may be better. Now to summarize the theory in Bowman's own words: 1. In their decision making behavior, managers and/or their organizations can be conceived of as decision rule coeffi- cient estimators, (not that they explicitly are coefficient estimators). 2. It is the variance in decision making rather than the bias that hurts (more) due to dish shaped criteria surfaces. 3. A decision rule with mean coefficients estimated from man- agement's behavior should be better than actual performance. 4. It may be better than a rule with coefficients supplied by traditional analysis. The literature thus far has been quite favorable toward the theory. Bowman in his original paper presented support for his theory with studies on ice cream, chocolate, candy and paint plants in the 18 Boston area. A study (Kunreuther) at Recordette Company, a electron- ics firm in the Boston area, found support for the theory and also found certain advantages relative to traditional Operations Research techniques. The study indicated some to the assumptions of the theory may not hold in real world situations. A very interesting study attempted to use linear decision rules distinguish the psychotic from neurotics given the MMPI profile and demographic data (Goldberg). He found the linear rule to be better at recognizing the distinction than the actual clinical judgements of 29 psychologists. The literature review of this study alludes to a separate but parallel lineage for a psychological coefficient theory. A major review in this area (Slovic and Lichtenstein) includes a review and analysis of the use of linear regression to find rules used for clinical judgements. In all reported situations the linear model did a fairly good job of predicting judgements and often performed better than the actual decision maker. The latter supports only one part of the theory and does not examine parts two through four. Two major studies (Miller and MOskowitz, Carter, Jenicke and Remus) have reexamined Bowman's theory as applied to a gaming situa- tion using quadratic costs (Holt, Modigliana, Muth and Simon). In the former case the study was done pencil and paper style using a graduate class in industrial administration as subjects. In the lat- ter case the subjects were undergraduates in a required course on quantitative methods and the game was played via interactive timeshare terminals. Both studies demonstrated the appropriateness of a linear model to represent the subjects' decisions. The Miller and Moskowitz 19 study particularly addressed itself to the appropriateness of linear rules with various forecast horizons and degrees of error. The study found support for Bowman's assertion that the rule would yield better than actual performance and in some cases better than Optimal per- formance. The first study, however, found that poor economic behavior was characterized by both bias and variance. A reanalysis of this data (Carter and Hamner) cross validated the rules demonstrating their appropriateness for future predictions and redemonstrated the finding that poor economic behavior was a function of both bias and variance. The study by Carter, Jenicke and Remus addressed itself to the learning of linear decision rules when the cost coefficients were changed across various conditions of information. Their analysis of the data again demonstrated the usefullness of linear decision rules. Although not reported in that paper additional analysis revealed occasions of better than optimal performance using the derived rule and that the rule performance was better than actual performance. As in the analysis and reanalysis of the Miller and Moskowitz data, this study found rules manifesting both bias and variance. When the cost coefficients changed, in all cases, a learning effect occurred as the subjects reduced their variance and bias simultaneously. The question of whether variance is the sole determinant of poor economic performance was not explicitly addressed. A number of interesting findings additionally arose from the latter study. The various treatment groups of subjects never acquired the optimal rule although they did both as well as and worse than the Optimal performance. All treatment groups used the same rule in each of the three periods of the game, even though that 20 rule differed from period to period. The learning effect may be modeled as a linear decrease in bias and a linear increase in mean absolute deviations (MAD) of the actual from the predicted over time. The learning period for this study and the cross validation earlier referenced was less than 8 decision cycles. The degree of information about the coefficient change did not effect the decision rule used. Both the undergraduates and the graduates in industrial admini- stration made similar estimation errors when making decisions although the graduates were more predictable. That is, they had a higher R2. The major review in this area (Slovic and Lichenshtein) found support for the following theories for multiple cue learning in judgemental tasks: 1. Subjects can learn to use linear cues appropriately. 2. Learning of non-linear functions is slower and less effec- tive than learning linear cues and is especially difficult if subjects are not forewarned of the nonlinearity. 3. Subjects can learn to detect changes in relative cue weights over time but do so slowly. 4. It is easier to discover when to use a cue than to discover a functional relationship. 5. Subjects can learn to use valid cues even when they are not perceived with perfect reliability. The Carter, Jenicke, and Remus study is consistent with the preceeding findings 1, 3 and 5 but does not address 2 and 4. We may summarize our review of the literature on Bowman's theory as follows: 1. There is unanimous support for the utility of linear decision rules in representing decision making. These rules have been found to have both concurrent and cross validity. 21 2. We found support for the assertion that a linear decision rules may perform better than the actual decisions made. We also found instances where the rule performed as the optimal rule. 3. We found support for attributing poor economic performance to variance from the rule, but we also found bias to effect economic performance. 4. The literature revealed the need to include in the theory the role of learning in reducing bias and increasing mean average deviations of the actual from the predicted over time. In general, Bowman's theory is strongly supported. The Executive Game The Executive Game (Henshaw and Jackson) is an descendent of the UCLA Executive Game #2. This game allows up to 9 teams to compete for product sales within each industry. The industry is an oligopoly; thus purely competitive dynamics do not hold. This type of situation is realistic for many major American industries. The firms manufac- ture only one product. Each period represents one quarter of actual time. The firms are required to make 8 decisions for each period; these are the starred variables shown in table 2. To make these decisions they have their results from prior periods of play, an example is in figure 1, and industry wide yearly reports. The latter reports show indi- vidual firms expenditures on marketing and R and'D, their net profit, their sales volume in units, and return on investment. Additionally this report shows for the end of the year the cash assets, inventory on finished goods and raw material, owner's equity and plant replace- ment value. General economic conditions, inflation, and tax situa- tions affect play and decision making. To aid the decision makers EXECUTIVE GAME MODEL 1 PERIOD 1 JAS PRICE INDEX 101.9 FORECAST,ANNUAL CHANGE 6.3 0/0 SEAS.INDEX 95 NEXT QTR. 115 ECON.INDEX 99 FORECASTgNEXT OTR. 94 INFORMATION COMFETITORS PRICE DIVIDEND SALES VOLUME NET PROFIT FIRM 1 S 6.15 3 50000 466000 3 118009 FIRM 2 3 6.25 E 53000 471573 S 27966 FIRM 3 E 6.50 5 100000 350696 5 -121412 FIRM 4 S 6.25 f 23000 464328 3 30525 FIRM 5 3 6.00 3 65000 526122 $ 164746 FIRM 6 3 6.20 i 30000 451500 3 81478 FIRM 7 3 6.22 0 65000 449757 E 42738 FIRM 8 S 6.15 S 70000 646000 $ 149559 FIRM 9 3 6.25 S 48000 453497 $ -21965 FIRM 11 OPERATING STATEMENTS MARKET POTENTIAL 471573 SALES VOLUME 471573 PERCENT SHAPE OF INDUSTRY SALES 11 PRODUCTIONgTHIS QUARTER 525000 INVENTORY,FINISHED GOODS 104427 PLANT CAPACITYgNEXT QUARTER 431889 INCOME STATEMENT RECEIPT3,SALES REVENUE 5 2947333 EXPENSES,MARKETING E 325000 RESEARCH AND DEVELOPMENT 160000 ADMINISTRATION 332800 MAINTENANCE 95000 LABORTCOST/UNIT EX.OVERTIME S 1.43) 830245 MATERIALS CONSUMEDTCOST/UNIT 1.57) 826436 REDUCTIONgFINISHED GOODS INV. -160280 DEPPECIATIONT2.500 0/0) 207500 FINISHED GOODS CAFRYING COSTS 52213 RAH MATERIALS CARRYING COSTS 60000 ORDERING COSTS 50000 SHIFTS CHANGE COSTS 0 PLANT INVESTMENT EXPENSES 33062 FINANCING CHARGES AND PENALTIES 0 SUNDRIES 84700 2896677 PROFIT BEFORE INCOME TAX 50656 INCOME TAX(IN.TX.SR. 0 0/0,SURTAX 0 0/0) 22690 NET PROFIT AFTER INCOME TAX 27966 DIVIDENDS PAID 53000 ADDITION TO OWNERS EQUITY -25034 CASH FLOW RECEIPTS.SALES REVENUE . 3 2947333 DISBURSEMENT59CASM EXPENSE 5 2023021 INCOME TAX 22690 DIVIDENDS PAID 53000 PLANT INVESTMENT 575000 MATERIALS PURCHASED 1300000 3973711 ADDITION TO CASH ASSETS '1026378 FINANCIAL STATEMENT NET ASSETS.CASH S 20622 INV. VALUE,FINISHED GOODS 313280 INVENTORY VALUEgMATERIALS 1673564 PLANT 800K VALUE(REFLACE.VAL.S 9108566) 8667500 OWNERS EQUITY(ECONOMIC EQUITY 11116332) 10674966 Figure 1 Output of the Executive Game 23 the authors provide a pro forma balance sheet and explicit instruc- tions for its use in determining what decisions to make. One of the strongest features of the Executive Game is its underlying model. Over the years the game has been amended such that there remain few, if any, strategies for beating the game. The model manifests numerous effects that we would find in real world oligopolies and punishes erratic behavior. The manual for the game outlines some of the model's functioning explicitly and gives one the FORTRAN program so that the remainder of the model may be found. The model is much too elaborate to be discussed in detail in this paper. Players can find conditionally optimal rules to implement their game plan but the game does not have a full set of global and tractable optimal rules. The Executive Game has been in use for many years and is easily implemented even on relatively small computers. Applying Bowman's Theory to the Executive Game Bowman's theory has been applied to simulation games prior to this study (Miller and Moskowitz; Carter and Hamner; Carter, Jenicke and Remus). The aggregate production simulation involved in the lat- ter studies has the following properties: 1. Each subject plays the game independently; his outcomes are not determined by the play of other subjects. 2. All subjects were given identical production scheduling environments including identical sales forecasts. 3. The underlying scheduling model (Holt, Modigliana, Muth and Simon) had a set of tractable optimal decision rules to guage performance by. 24 The Executive Game does not have the above properties. The subjects are aggregated into industries; the subjects compete for the sales within the industry. This situation is a better analogue of situations to which we would ultimately wish to apply Bowman's theory. In his original paper Bowman cited competitive examples of the application of his theory, e.g. the ice cream company. The Executive Game has no underlying tractable optimal rule although it is a mathematical model of a competitive environment. Thus we need to develop a heuristic model for the subject's decision making before further proceeding with the analysis. This is no bar- rier to testing the theory since many situations, including the ice cream example, to which we want to apply the theory may have no tract- able solution. In fact this lack of need for an optimal rule is one of the advantages of the theory. The optimal rule does, however, provide a benchmark for evaluating a subject's decision making pro- cesses. Thus Bowman's theory would seem applicable to the Executive Game. Now let's review the implications of the theory and frame them in terms of the game: 1. Each subject can be thought of as a decision rule coefficient estimator (not that they explicitly are coefficient estima- tors). 2. To the extent to which we can include the relevant variables upon which a subject makes his decision, we may find his decision model via multiple regression. 3. To the extent that the environment changes and we have inade- quate predictor variables to represent the change, our deci- sion rule will lack high predictive value. Note that to the extent that the set of excluded variables are independent from the included variables the rules based on included vari— ables will be stable. Again the ice cream production sched- uling is such an example. It is the variance in the decision making rather than its bias from optimal that leads to lowered profits due to the dish shaped criteria surfaces. Cues from the environment and measurements of other vari- ables in the environment must either be irrelevant or at some stable level. If this is not true and they are not explicitly accounted for in the decision rule the perform- ance of the rule will be reduced if the manager uses that cue or variable in his decision making. Multiple regres- sion will remove to some extent the effects of managers using irrelevant cues and variables. When the decision was made these irrelevant cues and variables led to larger variances. There is the implication that managers have good insight into their decisions. Thus Bowman would not predict dif- ferences among subsets of managers in their ability to intuit good rules. Further, the amount of bias should be zero for all groups of managers and the amount of variance should be the same for any set of managers. Bowman's theory is said to apply to experienced managers implying that other phenomenon may occur in the case of inexperienced managers. Although not explicitly stated this leaves room within the theory for learning to take place. This is how inexperienced managers become experi- enced. The purpose of this study is to explore the implications of the theory on the Executive Game and to examine some areas where the theory may need to be expanded. This includes the following research questions. 1. Can we find a set of heuristic rules which represent the behavior of the subjects? 2. Will these heuristic models represent equally well the behavior of the best teams, worst teams and overall sample? 3. Will the amount of bias be a function of team rank? 4. Will the best teams exhibit less variance than the worst teams? 5. Will there be any learning effects taking place as the game proceeds? If so, what is the nature of these effects? 26 6. Will there be an interaction between rank and time thus demonstrating differential learning? The sixth question will find whether the rates of learning might explain the differing ranks. CHAPTER III THE EXPERIMENTAL DESIGN AND ANALYSIS PLAN This chapter presents the methodology and approach of this dis- sertation. The first section outlines the experimental environment in which the data was collected. The second section presents the general approach to analyzing the data and third section gives the details of the procedures used to derive models to represent the subject's behavior. Description of the Experimental Environment The data for this paper were collected from the students playing the Executive Game in the Michigan State University Introduction to Business course, Management 101. This course is an elective course open to students both inside and outside of the College of Business. The course is intended to be a survey of the topics involved in busi- ness administration and also to aid undergraduate students selecting their major area in the college. The data was taken during the Winter quarter of 1974 when the class consisted of 107 students. 29% of the class were female, 76% were freshman, 23% were sophomores, and 12 were juniors. The instructor's intent in using the Executive Game was to pro- vide a vicarious business simulation for the students. He tried to 27 28 relate the game situations to real business situations and discuss the interrelationships among the various aspects of the business. All students were required to play the game and were given points toward their overall course grade based on their final rank in their respective industries. The game was no more than 10% of the overall grade. It is relevant to discuss why each firm consisted of only one student rather than organizing them into teams. In the prior quarter the instructor had had difficulty when he organized the stu- dents into teams. They complained that other team members did not aid in decision making or even attend team meetings. Occasionally teams decided to have a different individual make the decision each week so as to reduce work. The instructor attributed the difficulty to the fact that some students were taking this course because it was an easy course to pass and so wanted to do as little as possible to pass. Thus when these people were forced to get involved they rebelled. The instructor felt that by making one man firms these intrateam conflicts would be eliminated and decision making responsi- bility placed firmly on the shoulders of each individual. Also, with this approach a more effective motivation system could be arrived at to gain student involvement. Luckily, the latter occurred concurrently with my plan to invest- igate decision making and thus reinforced the instructor's approach. Since Bowman's managerial coefficient theory applies to individual decision makers this organization of the class was necessary also. 29 Early in the quarter the students received a lecture on the Executive Game and some of the considerations in making decisions for the game; this lecture was given by Dr. Richard Henshaw, a co-author of the Executive Game. The students were then divided into 13 industries of 9 firms each. Each firm consisted of one student. The students made one practice decision and output was received for that decision; then the game began in serious. The cycle of the game went as follows; the students made their decision and punched the decision card before the Thursday meeting, they turned in their decision card at the Thursday meeting, and they received their output the following Tuesday. Figure 1 shows a typical Executive Game output. They then had 2 days in which to make their next decision. All teams began the game at exactly the same financial and marketing position; in other words, their previous history as reflected in the Executive Game history cards was identical. The students played a total of 8 periods of Executive Game following the practice period. The decisions for the seventh and eighth period were turned in at the same class meeting. This was done to try to eliminate the possibilities of "end of game tricks", i.e., so that firms could not shut down in that last period. Then the final ranking would represent standing of on-going firms. When a student incorrectly punched a card, the graduate assis- tant made the necessary correction which the student had no right to contest. Should a student fail to input a decision he would be assigned a very poor decision to be used in the play of Executive 30 Game. All variables were poor choices; in particular the price was set to $7.51 when the average price for all teams averaged $6.25 with only a small dispersion. Once the game had begun in earnest only one subject dropped the course; thus industry seventeen was reduced from nine to eight teams. Industry twenty-two consisted of mostly 1ate admissions to the course. The late admissions had a very poor record of turning in decisions. General Procedure of Data Analysis The data analysis was performed on a set of thirty-three vari— ables per decision per subject. These variables (explained in table 2) were punched into their decision cards each period, on the history cards which were used to make the transition from period to period, and from a program which output a special set of profit and financial parameters. For certain analyses the period 1 data was eliminated; since all subjects had the same period 1 history a regression looking for predictors from the historic variables could not yield meaningful results. In searching for decision rules often period 8 data was ignored since the subjects had no feedback from period seven prior to making decision eight. In all cases, all bogus $7.51 decisions and associated variables were eliminated from the data set. Three general groups of data were formed for the analysis pro- cedures: 1. the composite data set consisting of all non-bogus observations 31 Table 2 Variables Used in the Executive Game 10 11 12 l3 14 15 Industry Number - subjects were divided into 12 nine man indus— tries, only intraindustry competition occurred. Team Number - each team in an industry was uniquely designated by a team number. Period Number - each period of play was designated by a period number, each period represented a quarter of a fiscal year. *Price - subjects decision as to the price their products were to be sold for this period. *Marketing — the expenditure the subjects decided upon for this period. *R & D — the expenditure subjects made for research and develop- ment this period. *Maintenance - the expenditure subjects made for plant mainte- nance, including preventitive maintenance, this period. *Volume - the production volume in units that the subjects decided to schedule for this period. *Plant and Equipment - the expenditures to be made this period to compensate for the aging of equipment and to buy new equipment and plant capacity. *Materials - the dollar value of materials ordered from which to manufacture the product, this order will not be delivered until next period. *Dividend - the subjects declared dividend for this period. If paying the dividend reduces net assets below ten million dollars only the portion which leaves the ten million intact will be paid. +Price Index - the subjects price for his product last period. +Marketing Index - an exponentially smoothed measure of his past marketing expenditures. +R & D Index - an exponentially smoothed measure of the subjects past R & D expenditures. +Maintenance Index - an exponentially smoothed measure of the subject's past maintenance expenditures. 32 Table 2 (cont'd.) 16 17 l8 19 20 21 22 23 24 25 26 27 28 29 30 31 32 +Raw Materials Inventory - dollar value of the raw material inventory at the end of the prior period. +Plant Capacity - measured in units of output capacity at the end of the prior period. +Stock of Finished Goods - remaining at the end of the prior period, in units of product. +Market Potential — the potential units of sales in this firm's market at the end of the prior period. +Sa1es Volume — firm's actual sales in units for the prior period. +Cash on Hand - at the end of the prior period. +Raw Materials Inventory Deflated — as 16 only value is deflated. +Book Value - the value of the plant after assets have been allowed to depreciate. +Standard Cost for a Unit of Product — prior period. Profit — the dollar value of the firm's net profit in this quarter. Inventory of Finished Goods — in dollars at the end of this period. True Dividend - the dividend actually paid out this period. Return on Investment - calculated for this period. Rank - firm rank in the industry based on ROI, this period. Annual Change — forecast for the annual inflation rate for this period. Next Seasonal Index - seasonal index forecast for this period. Next Economic Index — economic index forecast for this period. 33 the best data set consisting only of those subjects who finished first in their respective industry the worst data set consisting only of those subjects who finished last in their respective industry without the bogus decisions The worst group did incur a fair amount of bogus decisions. Only 51 of 72 decisions on the worst teams from period 2 through 7 were made by the subjects. Once the data sets had been prepared the data analysis consists of the following steps: 1. 2. Using the composite data a heuristic model was found which described the subjects behavior for key decisions. Alternative models were found using a stepwise regression computer program to make the best possible prediction. This was done by allowing the computer to do the whole task and also by beginning with the heuristic model and allowing the computer to add variables which significantly improve its predictive ability. This step was performed across the composite, best and worst sets of data. The key decision rules were cross validated on the com- posite data set. The LDR's thus found were compared across data sets and methods of determination. The bias and variance across time, rank and industry were examined particularly looking for linear effects. The effect of the interaction of rank and time on measures of variance and bias were examined. This study uses Bowman's definitions for variance and bias. Bias is defined as the signed difference between the preferred and actual value for a variable. When taken across a data set we would expect the sum of the signed differences to equal zero if the rule is unbiased. 34 Variance is defined as the departures of the actual from the mean decision. In this study mean absolute deviations (MAD) of the actual from the predicted shall be used to examine the propositions about variance and learning. Analysis of variance is used for all of the bias and variance testing. The design appears to be fixed effects model when we are blocking on industry. When we block on rank, or time, the fixed effects is apprOpriate. We will convert the first case to a random effects analysis of variance by using the Cornfield-Tukey bridge arguement. Our testing applies to Michigan State University students tak- ing Management 101, Introduction to Business in Winter of 1974. 76% were freshmen, 23% were soPhomores, and 1% were juniors. 29% Of the class were female. The course was a 4 credit elective. Now generalize the testing to a hypothetical population of simi- lar subjects and assume this population is infinite. The latter pop- ulation is rather restrictive when we try to generalize our results. The restrictions on class level and sex could be safely relaxed to allow us to generalize to business undergraduates. We have now ran- dom effects model when we block on industry. This preceding brief listing of steps will be greatly elaborated in the sections of the paper dealing with each particular topic. Finding the Heuristic Models In many gaming situations the underlying mathematical model may be solved for an Optimal solution. In the case of the Executive Game no global solution has been found, although some conditionally Optimal 35 rules exist. TO perform the hypothesis testing that this paper undertakes it is essential to have some baseline if not Optimal solution. This heuristic model then may be used as a basis of intergroup comparisons. There are a number of approaches to finding this model. I have used the following: 1. Choose the set of criterion variables to be examined. 2. For each criterion variable choose a subset of independent variables which could possibly be thought Of as inducing fluctuations in the criterion variables. 3. Use stepwise regression to regress that set Of criterion variable on the independent variables at an alpha of .05. 4. Examine the included variables for the amount of varia- tion explained by each. Eliminate those which only explain less than 2% of variation. 5. Regress the variables from step 4 and find if the total explained variation is of a reasonable order relative to step 3. If not, add back variables and repeat this step. The derived heuristic rules should, concisely characterize the rule used by the decision maker; the heuristic rule should have face validity also. To choose the criterion variables to be examined, I used these guidelines: 1. The variable must be one that the subjects actually control. 2. The variables should explain more variation in Executive Game profit or ROI than variables not included. 3. The better these criterion variables are explained by allowable independent variables the more useful the results of this paper will be. Guideline 1 limits my choice to the following variables; price, marketing, R & D, maintenance, production volume, dividend, price, 36 plant and equipment expenditures, and materials expenditures. Guide- line 2 was examined by performing a stepwise regression to find which variables best explained profit and ROI. Thirteen variables were used to predict ROI including volume, price, R & D and marketing index (an exponentially smoothed marketing expenditure variable). The twelve variables used to predict profit included volume, price, divi- dend, marketing index, and R & D. This analysis yields the following: 1. Winning the Executive Game requires the subject to give attention to all aspects of his firm. The variables (both decision variables and variables internal to the firm) explain 84% of the variation in ROI, the long term profitability of the firm. The variables (both decision variables and variables internal to the firm) explain 48% of the variation in profit in the current period. The Executive Game decisions (with their subsequent impact on the internal variables) are quite predictive of long term profit. Each period's profit has a much greater unexplained variation. Short term profit varies: a. directly with cash on hand, material inventories, stock of finished goods, the expenditure level for the maintenance program, production volume, and price b. inversely with the expenditures on the marketing program. c. directly with R & D this period but inversely with the R & D overall expenditure program when all variables are considered simultaneously. ROI varies: a. directly with cash on hand, production volume, material inventory, book value of plant and equip— ment, stock of finished goods, dividends paid, price, and dollar volume of sales b. inversely with standard cost per unit, plant capacity, R & D expenditures, and expenditures on the marketing program when all the variables are considered simultaneously. 37 The preceding findings demonstrate that Executive Game is a reasonable and intergrative business simulation; simplistic explanations of pro- fit and ROI, had they occurred, would have indicated to the contrary. Guideline 2 reduces the set of criterion variables from the orig- inal to price, marketing, production volume, and R & D. Maintenance is not included in this subset as it is predictive only of short term profit and even then, the maintenance expenditure does not have an immediate impact on the profits. Dividend paid is "predictive" of only ROI and then it is more likely that it is simply symptomatic of good profits rather than "predictive". Thus it is excluded from con- sideration. Plant and equipment expenditures are not directly pre- dictive of short term profit or ROI although they do reflect themself in plant capacity and book value which are predictive of ROI. Even then there are many other factors influencing book value and capacity. Thus it is also excluded from consideration. Material expenditures are not directly predictive Of profit or ROI although it effects the level Of material inventory which, in turn, predicts profit and ROI. Also material inventory levels is probably more symptomatic of good profits than predictive. Guideline 3 eliminates R & D expenditures from further considera- tion since the explained variance is low (9%). Also the only pre- dictor variable for current R & D is the exponentially smoothed aver- age of previous R & D expenditures called R & D index. The fact that this decision was not characterized well by a linear rule may question the universality Of Bowman's Theory. 38 The variables to be used as criterion variables in the rest of the analyses are price, marketing, and production volume. I then preceded to use the 5 steps listed earlier to find the heuristic models. CHAPTER IV THE RESULTS OF THE ANALYSIS This chapter is composed Of 13 sections. Each section addresses itself to a particular portion of the analysis. It is divided into two broad segments. The first segment demonstrates the utility and interrelationships Of the linear decision rules. The second section examines the issues of bias, variance and learning. The implica- tions Of these findings are explicated in the next chapter. Interrelationships Among the Heuristic Price LDR's The heuristic price LDR uses the price index and the forecast of the next economic index as predictor variables. Regressions were made for price forcing the latter two variables to be the only variables in the equation; this was done for the best, worst, and composite data. The results are reported in table 3. Before beginning to use the LDR's we should evaluate whether the betas found by this least squares analysis are unbiased estimates of the true betas. In particular, when autocorrelation occurs and there is a lagged variable, the betas may be overestimated (Malinvaud). Table 4 contains the tests for the autocorrelation effect. Our preference here is for the Durbin test for a lagged variable (Johnson, p. 313) if the required conditions are met, as this LDR has a lagged variable. If that test is not available then the Von Neumann ratio 39 40 Table 3 Linear Decision Rules for the Price Decision 2 Composite Rule n=600 Rs.3084 Price a 2.71465396 + .0175611 (Next Econ. Index) + .29882493 (Price Index) Coefficient Standard Error Confidence Interval at 90% fig 2.71465396 .23063603 (2.33,§.09) él .01756110 .00108810 ( o ,.035) 62 .29882493 .02459381 (.258,.339) 2 Best Rule n=72 £4.5574 Price = -.05403077 + .02767492 (Next Econ. Index) + .59488454 (Price Index) Coefficient Standard Error Confidence Interval at 90% 60 4.05403077 .81995670 (-1.40, 1.29) él .02767492 .00297038 (.0228,.0325) 62 .59488454 .09263832 (~.442, .747) 2 Worst Rule n=51 R§.2637 Price = 4.04612529 + .00941562 (Next Econ. Index) + .20677078 (Price Index) Coefficient Standard Error Confidence Interval at 90% 30 4.04612529 .50036453 (3.22,4.87) él .00941562 .00304465 (.004,.o14) 32 .20677078 .04971813 (.125,.288) 41 (Thiel, p. 199) may be applicable under restricted circumstance. The table reveals that the price LDR on the composite sample does have statistically significant positive autocorrelation. The LDR's on the best and worst samples do not have statistically significant auto- correlation at the 5%. Even though for the best and worst sample price LDR's we can accept the hypothesis Of zero autocorrelation, the fact that lagged variables exist in the LDR means that the betas will slightly under- estimate the true betas (Johnson, p. 306). The bias is -2/n %, where n is the sample size. Thus the betas are underestimated by 4% in the worst sample and 3% in the best sample. In both cases the correction is so small that it may be ignored. The composite price LDR has statistically significant autocorre- lation. There is no easy way to deal with this as it implies the possibility of underestimation Of the calculated autocorrelation coefficient, .1385 in this case, and an equally large overestimation of the beta of the lagged variable, .0246 for this case. In each table describing a linear decision rule I have reported theR2 for that rule. Since'R'2 may be plagued with measurement and independence problems, the value is reported for descriptive and informational purposes only. Hypothesis 1: Having checked the appropriateness of the LDR's as calculated by least squares, we need now to examine if the LDR's for the best, worst and composite sample are statistically equivalent. 1 b,1 1 H"): LDRc’ -LDR -LDR"” 0 p p P 42 Table 4 Tests for Autocorrelation in the Price LDR's H0: zero autocorrelation H1: non-zero autocorrelation Composite Rule n=600 a =.05 Durbin Test for Lagged Variables. r=.l385 Var(82)=.02462 H=.138S 600 = 4.25 l+600(.0246)2 Reject Ho since 4.25 is greater than 1.86 Best Rule n=72 a=.05 Durbin Test for Lagged Variables r=.l Var(§2)-.09262 H=.l ‘2 72 =1.37 1+72(.o926)2 DO not reject H0 since 1.37 is less than 1.86 WOrst Rule n=51 a=.05 Durbin Test for Lagged Variables r-.16 Var(82)-.O4972 H-.l6 ‘/I 51 =1.222 1+51(.0497)2 DO not reject H since 1.222 is less than 1.86 0 43 Results: This hypothesis was tested by a test of structural equivalence (Huang, p. 108); this tests the equivalence of the three families of betas. The hypothesis is rejected indicating at least one of the three is different than the other LDR's. TO find the nature of this difference table 5 also contains the results of bounding the betas of the composite rule to find if the betas of the worst and best rules fall in that range. The table demonstrates that both best and worst rules are different than the composite. Hypothesis 2: The previous test does not tell us if the LDR's for the best and worst sample are structurally equivalent. Thus we test the following hypothesis on the period 1 through 7 composite data. H(2): b l LDR ’ =LDRW’1 0 p p Results: This hypothesis is also rejected indicating the non- equivalence of the coefficients Of the best and worst LDR's tested as a family. This test is the test of pairwise structural equiva- lence (Huang, p. 108). The test is contained in table 5. Interrelationships among the Heuristic Marketing LDR's The heuristic marketing LDR uses the marketing index (an expo- nentially smoothed marketing expenditure average) and marketing potential as predictor variables. Regressions were made for market- ing forcing these two variables into the equation; this was done on the best, worst and composite data sets. The results are reported in table 6. At this point we again address ourselves to the issue of auto- correlation. In table 7 the Durbin test for lagged variables, the 44 Table 5 Equivalence of the Coefficients of the Price LDR's The Family Test at a=.05 H : LDRC’1=LDRb’1=LDRw’1 O P P P Q1=.962 Q2=.754 Q3=.208 n=123 K=3 J=2 F-.208/4 =7.6 .754/115 Reject HO since 7.6 is greater than .95F4,115=2.45 Individual Coefficient Tests using Confidence Intervals for the Composite Rule at o=.lO Composite Rule é é B . 0 1 .- , 2 i Best ; a Rule 3 Outside Within 2 Outside Betas ' i Worst . 5 Rule E Outside Within 2 Outside Betas ; j l The Family Test for the Equivalence of the Worst and Best Price LDR's on the Composite Sample from Periods 1 thru 5 at a=.05 no: LDRP’1=LDRW’1 p p Q1-37.558 Q2=10.O42 Q3=27.516 n=702 K=3 F- 27.516/8 8237.7 10.042/694 Reject HO as 237.7 is greater than .95F8 694=1°94 45 Table 6 Linear Decision Rule for the Marketing Decision 2 Composite Rule n=600 Rs.5024 Marketing = .77532008-+ 1.005355 (Marketing Index) - .07496595 (Market Potential) Coefficient Standard Error Confidence Interval at 90% 00 .77532008 .11912130 ( .579, .97 ) 01 1.005355 .04438912 (..932,1.078) 62 -.O7496595 .01707401 (-.103,-.04 ) 2 Best Rule n=72 Rs.7501 Marketing = .71053198 +1.18925394 (Marketing Index) - .15391043 (Market Potential) Coefficient Standard Error Confidence Interval at 90% 00 .71053198 .26166915 ( .28 ,1.14 ) B1 1.18925394 .08362376 (1.05 ,1.327) 32 -.15391043 .03584165 (-.213,-.095) 2 Worst Rule n=51 fie.5911 Marketing = .17672373 +1.03799056 (Marketing Index) + .01757419 (Market Potential) Coefficient Standard Error Confidence Interval at 90% 80 .17672373 .34378036 (-.39 , .74 ) 81 1.03799056 .15221942 ( .787,l.288) 02 .01757419 .04216553 (-.05 , .087) 46 Table 7 Tests for Autocorrelation in the Marketing LDR's H : zero autocorrelation 0 H1: non-zero autocorrelation Composite Rule n=600 G=.05 Durbin Test for Lagged Variables nVar(81)=11182 thus this test is not applicable Von Neumann Ratio Test VNR=1.842 K=3 Do not reject H0 as VNR is within the range of 1.84 to 2.16 Durbin Watson Test d=1.66 since tables are not available for n=600, this test cannot be utilized Best Rule n=72 o=.05 Durbin Test for Lagged Variables r=.095 Var(81)=-=.08362 H-.095 ‘ 72 j =1.1z. 1+72 ( . 0836)1 Do not reject H0 since 1.14 is less than 1.86 Worst Rule n=51 0s=.05 Durbin Test for Lagged Variables nVar(81)=l.181 thus this test is not applicable Von Neumann Ratio Test VNR=1.841 K=3 DO not reject H0 as VNR is within the range 1.525 to 2.475 47 Table 7 (continued) Tests for Autocorrelation in the Marketing LDR's Durbin Watson Test d=2.03 K=3 du=1.63 Do not reject HO as d is less than 4-du but greater than du 48 Von Neumann ratio, and Durbin—Watson statistic are reported. Recall that for LDR's with lagged variables the first test is most appropri- ate if available and the latter two useful under certain restrictive assumptions. We find in all cases that the available tests accept the hypothesis of zero autocorrelation. Recall that the betas are slightly underestimated. The amount of underestimation is .4%, 3%, and 4% respectively for the composite, best and worst marketing LDR's. The correction factor will be ignored as it is quite small. Returning to table 6, we again note a significantly higherRm2 for the best sample rule. This again indicates that an LDR with the hypothesized variables is most predictive of the behavior of the first place teams in each industry. Hypothesis 3: Having checked the appropriateness of the LDR's we again examine the structural equivalence Of the LDR's evaluated on the best, worst and composite samples. H63): LDRC’1=LDRb’1 ’1 m m -LDRV m Results: As in the case of the price LDR's we reject the null hypothesis at alpha of .05. Thus at least one Of the three LDR's is significantly different than the others. Table 8 which shows the results Of that test'also contains the results Of bounding the betas on the composite rule. We find some betas from both best and worst rules to be outside the confidence interval; both best and worst LDR's are different than the composite LDR. Hypothesis 4: There remains the possibility that the best and worst rules may be structurally equivalent. we then test on following hypothesis on the period 1 through 7 composite data set: 49 Table 8 Equivalence Of the Coefficients of the Marketing LDR The Family Test at a=.05 ° 91: b21= ,1 Ho. LDR; LDRIn LDRH F= 4.14/4 =3.7 32.21/115 Reject H0 since 3.7 is greater than .95F4,115=2.43 Individual Coefficient Tests using Confidence Intervals for the Composite Rule at o=.lO Composite Rule § 3 3 0 1 2 Best 2 Rule ‘ Within Outside ! Outside F Betas i ; Worst I i Rule 3 Outside 2 Within Outside Betas [ I “ . --..——.-a..— —.— . ... The Family Test for the Equivalence Of the Worst and Best Marketing LDR's on the Composite Sample from Periods ] thru 7 at 0-.05 H : LDRb’1=LDRw’l 0 m m Q1=384.77 Q2=366.4 Q3=l8.37 K=3 n=702 F= 18.37/8 =4.35 366.4/694 Reject HO as 4.35 is greater than =1.94 F .95 8,694 50 H(4): LDRb’1 1 O m =LDRw’ m Results: This test is also rejected indicating the nonequiva- lence of the best and worst sample marketing LDR's when tested as a family. The test may be found in table 8. Interrelationships among the Heuristic Volume LDR's The heuristic production volume LDR uses the market potential, current marketing expenditure and R & D index (an exponentially smoothed R & D average) as predictor variables. Regressions were made for the volume forcing the latter three variables into the equa- tion and allowing no others to enter. This was done on the best, worst and composite samples. The results are reported in table 9. The problem of autocorrelation arises again but since lagged variables are not present we have less to contend with. The appro- priate tests here are either the Von Neumann ratio or the Durbin- Watson statistic. We find, as shown in table 10. that all tests retain the hypothesis of a zero autocorrelation. If autocorrelation did exist we would still have unbiased estimates of the betas, however, the standard deviation Of the errors would be underestimated (Johnson, p. 246). Even though the tests did not support the hypothesis Of autocorrelation the correction factors for the standard deviation of the betas were computed. In no case was the value given in table 9 for each variable more than .1% from the true value. Again the LDR from the best sample has the highest R2. This rule is most appropriate for the first placed teams in each industry. Hypothesis 5: Since the hypothesis of zero autocorrelation was not rejected we can now test the structural equivalence Of the LDR's Table 9 Linear Decision Rules for the Volume Decision Composite Rule 2 n=600 fie.4467 Volume = 1.51751553 + .39804395 (Marketing) + .25942319 (Market Potential) + .55468906 (R and D Index) Coefficient 80 1.51751553 81 .39804395 82 .25942319 83 .55468906 Best Rule n=72 Standard Error .20982065 .04121948 .02365509 .10468355 _2 R=.715O Confidence Interval at 90% (1. (. (. 17,1.86) 33,.466) 22,.298) (.382,.727) Volume 8 1.65821861 + .32567365 (Marketing) + .27161655 (Market Potential) + .69930199 (R and D Index) Coefficient 80 1.65821861 81 .32567365 82 .27161655 8 .69930199 Standard Error .38175701 .06760973 .04597963 .19419633 Confidence Interval at 90% (l. ( 03 ,2.288) .215, .436) .196, .347) .38 ,1.019) Table 9 (continued) 52 Linear Decision Rules for the Volume Decision WOrst Rule n=51 2 Ee.3236 Volume = 2.18782496 9 .32567365 (Marketing) + .24345501 (Market Potential) + .97220350 (R and D Index) Coefficients Standard Error 80 2.18782496 81 -.14096602 82 .24345501 83 .97220350 .65973499 .24921883 .08408995 .41486383 Confidence Interval at 90% (1.10 ,3.27 ) (-.55 , .269) ( .105, .38 ) ( .85 ,1.13 ) 53 Table 10 Tests for Autocorrelation in the Volume LDR's H6: zero autocorrelation H1: non-zero autocorrelation Composite Rule n=600 a =.05 Von Neumann Ratio Test VNR=1.96 K=4 DO not reject HO since VNR is within the range of 1.84 to 2.16 Durbin Watson Test d=l.77 since n=600 no tables are available Best Rule n=72 a=.05 Von Neumann Ratio Test VNRel.946 Ks4 DO not reject H0 since VNR lies in the range of 1.525 to 2.475 Durbin Watson Test d=l.91 K=4 du=l.70 DO not reject H0 since d lies within the range of du to 4-du Worst Rule n=51 a=.OS Von Neumann Ratio Test VNR92.012 K=4 DO not reject H0 since VNR lies in the range Of 1.515 to 2.485 Durbin Watson Test d=1.96 K=4 du=l.67 Do not reject H0 as d lies within the range of du to 4-du 54 as determined on the best, worst and composite samples. H35): c,l b,l 1 LDR =LDR v =LDRw’ V V Results: As was found in the case of the price and marketing LDR's, we find we must reject this hypothesis in favor of the asser- tion that at least one Of the LDR's is different than the others. Table 11 contains that test and the results Of bounding the betas on the composite LDR. We find some of the betas the best and worst rules are outside the confidence interval, thus both the best and worst sample LDR are different than the composite sample LDR. Hypothesis 6: Once again we check the possibility of the worst and best LDR's being structurally equivalent. H36): LDRb’l 1 =LDRw' V V Results: For the third time we reject the structural equivalence of the best and worst sample LDR's as tested on period 1 through 7 composite sample data; this result is shown in table 11. Cross Validation of the Heuristic LDR's The appropriateness of heuristic models for the price, marketing, and volume decisions may be evaluated in yet another way. The tech- nique of cross validation (Hamner) segments time series data and finds appropriate LDR's for that segment of data which was collected earlier in time. Then the derived LDR's are evaluated on the remain- ing Observations. TheR2 for both segments should be statistically equal if the rule is equally predictive of behavior in both periods. However, some shrinkage would not be unexpected. The cross validation should demonstrate the validity of the heuristic models. 55 Table 11 Equivalence of the Coefficients of the Volume LDR's The Family Test at a=.05 . C,1_ b,1= W 1 H0, LDRv —LDRV LDRV’ Q1=95.5 Q2=79.25 Q3=15.75 n=123 J=2 K=4 F= 15.75/5 =4.49 79.25/113 Reject Ho since 4.49 is greater than .95F5,113=2.29 Individual Coefficient Tests using the Confidence Intervals for the Composite Rule at a=.10 Composite Rule 8 8 8 8 0 1 WV 2 3 Best g I Rule i Within Outside Within Within Betas I—-— L Worst ; Rule 1 Outside Outside Within Outside Betas ' The Family Test for the Equivalence Of the Worst and Best Volume LDR's on the Composite Sample from Periods 1 thru 7 at 0-.05 , b,1g w,1 Ho. LDR.v LDRv Q1-974.9O6 QZ=710.724 038264.182 n=702 K-4 F- 264.182/10 =25.72 710.724/692 Reject Ho since 25.72 is greater than .95F10,692-1°83 56 Table 12 shows the LDR for price derived on period 2 through 4 observations on the composite sample. The LDR has an R of .4886. The table also indicates that the betas of the period 2 through 4 LDR are not outside the confidence intervals Of the composite LDR for all periods. When this price LDR is used on period 5 through 7 observa— tions we find a R of .4862. A test utilizing Fisher's r to z and pooling the variances finds no significant differences between the R's. Recall that we earlier found autocorrelation for this LDR, however, the weight of the evidence supports the cross validation of the price LDR in spite Of the autocorrelation. The numerator of the Fisher's r to 2 contains the sum of the reciprocals of the degrees Of freedom for the two correlation coeffi- cients. Should there be a lack of independence in estimating the correlation coefficients we would want to adjust downward the degrees of freedom. This would reduce the size of the test statistic and make acceptance of the null hypothesis more likely. Since I have not adjusted the degrees Of freedom, the tests are more conservative than would be necessary should dependence be a problem. Table 13 shows the LDR for marketing derived on period 2 through 4 observations on the composite sample while allowing only the heuris- tic variables tO enter into the regression. The LDR has a R of .7469. The table also indicates that the betas of the period 2 through 4 are outside the confidence interval of the composite LDR for all periods for marketing. When this LDR is used on period 5 through 7 Observations we find a R of .6803. The test utilizing Fisher's r to z and pooling the variances finds no significant 57 Table 12 Cross Validation of the Price LDR Composite Rule n=305 Periods 2 thru 4 R=.4886 Price = 2.12401974 + .01988191 (Next Econ. Index) + .35990635 (Price Index) Coefficient Standard Error Confidence Interval at 95% 80 2.12401974 .53233557 (1.08 ,3.17 ) 81 .01988191 .00434644 ( .011, .028) 82 .35990635 .03736443 ( .286, .433) Comparison of the Period 2 thru 4 LDR and the Composite LDR using the Confidence Intervals on the Composite LDR CompOSite Rule 0 = .10 B B E 0 1 2 Period 2 thru 4 Within Within Within Betas 4g Correlation Of the Predictions and the Actual Price in Periods 5 thru 7 R=.4862 Testing the Equivalence of the R's using Fisher's r to z and Pooling the Variances at 0-.05 H : p - 0 1 p2 H-: 9 f9 1 2 1 23 5,5343—.5314) =.0354 .j(1/302)+(1/292) DO not reject since 2 is less than 1.86 58 Table 13 Cross Validation of the Marketing LDR Composite Rule n=305 Periods 2 fihru 4 R:.7469 Marketing = .44218993 + 1.34129482 (Marketing Index) - .20485693 (Market Potential) Coefficient Standard Error Confidence Interval at 95% 80 .44218993 .21021730 ( .0284, .856 ) é 1.34129482 .08891652 (1.17 ,1.51 ) 1 § -.20485693 .06204873 (—.326 ,-.08 ) 2 Comparison of the Period 2 thru 4 LDR and the Composite LDR using Confidence Intervals on the Composite LDR Composite Rule 0 = .10 6 6 . 6 Period 0 , 1 2 2 thru 413* i T L Betas ; Outside ‘ Outside i Outside 1..---- -__..... - __-_....__-..-.. ._._ Correlation of the Predictions and the Actual Marketing 2 in Periods 5 thru 7 RP.68032 Testing the Equivalence of the R's using Fisher's r to z and Pooling the Variances at a=.05 H=o=o o 2 1 H=p#o 1 12 2' (.966-.829)7 =l.6748 741/302)+(1/292) Do not reject Ho since 2 is less than 1.86 59 differences between the R's at alpha equals .05. The two preceding results may appear contradictory. The marketing LDR meets the definitional requirements for being cross validated at .05. The confidence intervals are three tests each with an alpha of .10 or a combined probability of a type I error of .30. In order to make the comparison meaningful they must be at the same alpha level. Thus performing confidence intervals at .02 might be much more suitable; the combined alpha is .06. In this case, all betas would fall within the confidence interval on the composite marketing rule. There remains no contradiction. Lastly we test the volume LDR. The period 2 through 4 normative rule of volume is given in table 14; it has an R Of .5747. The betas for this rule are entirely inside the confidence intervals for the composite volume LDR. When this rule is used on period 5 through 7 Observations we find an R of .6194. Again Fisher's r to 2 test with pooled variances finds no significant difference in the R's. Summary Of the Interrelationships among Heuristic LDR's Thus far we have found: 1. The LDR's for each decision variable had statistically different betas in each of the three data samples they were calculated for. 2. The heuristic LDR's always had the highest‘R'2 on best team data sample suggesting the best teams were more consistent. 3. In 8 of 9 cases the null hypothesis Of zero autocorre- lation could be accepted at the .05 level. When correc- tions to the betas were made for the lagged variables the correction was less than 4%. 4. All three rules cross validate. 60 Table 14 Cross Validation of the Volume LDR Composite Rule n=305 Periods 2 thru 4 R=.5747 Volume = 1.70101805 + .32858938 (Marketing) + .27581115 (Market Potential) + .47962004 (R and D Index) Coefficient Standard Error Confidence Interval at 95% 60 1.70101805 .31600816 (1.08 ,2.32 ) 81 .32858938 .05269466 ( .225, .432) 82 .27581115 .06006159 ( .158, .393) 83 .47962004 .16210260 ( .162, .797) Comparison of the Period 2 thru 4 LDR and the Composite LDR using Confidence Intervals on the Composite LDR Composite Rule 0 = .10 8 8 8 “ Period r~-Q-~~e T’ 1 2 3 2 thru 4 i Within 1 Within Within i Within Betas - 1 . Correlations of the Predictions and the Actual Volume in Periods 5 thru 7 R=.6l949 Testing the Equivalence of the R's using Fisher's r to z and Pooling the Variances at 0-.05 HO: 9 =0 1 2 z-(.724-.655) =.8435 H': 979 1 1 2 0/(1/302)+(1/292) DO not reject H0 since 2 is less than 1.86 61 Analysis of the Equivalence of Method 2 and 3 LDR's The research design utilized the development of LDR's by 3 methods. These were: Method 1: Construct a heuristic decision model and then fit those variables to the data. Method 2: Begin with the method 1 variables but allow other variables to enter the equation through the stepwise regression technique. Method 3: Instruct the stepwise regression to program select the variables to be entered and the order in which to enter them. We would expect method 2 and 3 LDR's to be very close, if not identical. The stepwise regression program will construct only a locally optimal LDR; hence, different starting points may yield dif- ferent LDR's. Table 15 summarizes the comparisons between method 2 and 3 LDR's. We conclude: 1. In 5 of 9 cases the LDR's are identical. 2. In 3 of the remaining 4 cases the LDR's are not signifi- cantly different in terms of their coefficient of determi- nation. Since this test (Burr) is also a test for finding variables to enter into regression equations we can confi- dently assert no improvement could be gained from changing from one form of the LDR to the other. 3. In the case Of the marketing decision in the worst sample the two LDR's are significantly different, hence the LDR from method 3 is preferable to the method 2 LDR. The tests thus summarized indicate the statistical equivalence in 8 of the 9 cases under consideration. Then by comparing method 1 and method 3 LDR's we adequately compare method 2 LDR's also. Analysis of the Equivalence of Method 1 and 3 LDR's Now we are prepared to compare method 1 and 3 LDR's; we will pro— ceed with a series of tests which will demonstrate that many of the 62 Table 15 Comparison Of Method 2 and 3 Linear Decision Rules Price LDR Marketing LDR Volume LDR k# _"'”'"" T No significant ! Composite Difference Identical LDR's Identical LDR's ; Data Set F=.62 < ‘ .95F1,59o‘3‘84 Best Identical LDR's Identical LDR's Identical LDR's Data Set No Significant A Significant No Significant Worst Difference Difference Difference IData Set F=2.243 < F=7.6 > F=.868 < .95F1,45="-°8 .951'2,44"’3°23 .95F1,44"*°°8 63 LDR pairs are statistically different. Then we shall then argue that these statistical differences are of no practical significance. First recall that method 2 LDR's are the heuristic variables plus other variables in a LDR. Since in all cases variables were added to the heuristic set we can immediately assert that there is a difference in terms Of'R-2 between method 1 and 2 LDR's. This is because improvement in LDR R2 is the criterion for the admission Of a new variable. Now let's turn to the criteria of adding significantly to the sum squared explained by the regression. In a test analogous to testing for linear and quadratic components in an ANOVA table we test the contribution of the additional variables. These tests are summarized in table 16. In all cases a significant contribution is made to the explained variance of the regression by the new variables. Another test of the differences between method 1 and 3 LDR's is the test of structural equivalence, a family test on the betas of the two LDR's (Huang, p. 108). All the extra variables in the method 3 LDR are assumed to be in the method 1 LDR only at a zero level. The results of these tests are summarized in table 17. Note the method 1 and method 3 LDR's are not structurally different when evaluated on the best and worst samples. The composite sample method 1 and method 3 LDR's are, however, significantly different. The results of this test and the previous tests on the best and worst sample are not con- flicting since they test different aspects Of the relationship between the LDR's. Hence, LDR's from the same structural family may induce significant differences in the explained sum squares or R2. Table 16 64 Comparison Of Method 1 and 3 LDR's on Contribution to Sum Squares Composite Data Set Best Data Set Worst Data Set at... 4...-..“- we Price LDR Marketing LDR Volume LDR ' F=22.2 which is greater than F=l7.3 which is greater than F=10.8 which is greater than —'-- .-—~- .95F7,590‘2-°1 .95F9,588“1'88 .95F8.588'1‘94 F=7.9 which F=9.12 which F=22.9 which is greater than is greater than is greater than .95F4,65"2'S3 .95F4,65=2-53 .95F2,65‘3'15 F=6.86 which is greater than .95F2,46"‘3'22 F=5.878 which is greater than . 95F1 ’47-‘10 . 07 F=7.172 which is greater than .95F2,45"3°22 A Significant Difference was Found in all Tests Table 17 Structural Composite Data Set Best Data Set Worst Data Set 65 Equivalence of Method 1 and 3 LDR's Price Rule Marketing Rule Volume Rule 1 , ; T ! Significant Significant Significant : Difference Difference‘ Difference' i F=l.635 > F=2.76 > F=2.9l > ; NO Significant No Significant NO Significant Difference Difference Difference- F=1.407 < F=l.l7 < F=.735 < t, .95F12,6O=1'83 .95F14,58=1'84 .95F14,58-1’84 No Significant No Significant No Significant Difference Difference Difference F=.51 < F=.7 < F-.49 < .95F10,41‘2-°8 .95F12,39=2-°° .95F8,43‘2-18 66 Having found some evidence of statistical differences among rules, it will be necessary to examine the value of these differences when predicting the criterion. Tables 18 through 20 contain the con— fidence intervals on the predictions for Y at the grand mean.§ and the grand mean Y-at the grand mean Y: At this point we can argue whether these differences are of a practical value. The best way to approach this point is to think of the LDR's in terms of predicting the future. Then we could examine the degree of improvement of method 3 over method 1 LDR's. This approach is embodied in table 21. If we were to predict the future using method 1 LDR we can find a confidence interval within which we would expect the true value of the criterion to be 95% of the time. Now if we were to predict using method 3 LDR's we would have a slight— ly smaller interval. The latter table contains the degree Of confi- dence that the true value would lie outside the method 3 interval but inside the method 1 LDR. In other words this is the degree of con- fidence that method 3 interval would give us useful information above and beyond that of the method 1 LDR's. This is done by using the significance level on the heuristic distribution of the limits of the method 3 confidence interval. Table 21 then tells us that method 3 LDR's give us, at best, a rule which would be more useful than the method 1 rule 7.8% Of the time. In the average case method 3 is more-useful only about 4.4% of the time. That small amount of improvement is not of much practi- cal value except in the most critical of circumstances. Further, the cost of getting the additional information might be relatively large as information on three times as many variables is needed. Table 13 67 Confidence Intervals on Price LDR Predictions Composite Data Set Best Data Set Worst Data Set Method 1 Method 2 Method 3 SSE-.1018, K83 $71.20, 37:. 008 _S_SE=.09_25 , K=ll Y:.18, 37:.007 §SE=.09_2_5 , K=-10 Y_-_I-_. 18 , Y-_i-_. 007 §_SE=.069_,_ K-3 Y:.136, 37:. 016 _S_SE=. 0589, K-7 SSE-.0589, K-7 Y:.116, Y: .013 .Lu_ _s_88=.093_9_, K=3 17:. 188, 57:. 026 _S_SE=.O84_,_ K=5 Y-_i-_.169 , Yi. 024 SSE-.086, K=4 171.172 , 171.024 Average Price is 6.255 KEY 783E 3 Standard Error of the Estimate K - Number of Structural Coefficients Yb+ 1.96 SSE 8 Interval on Y at Y. Y i 1.96 SSE/IE = Interval on Y at Y Table 19 68 Confidence Intervals on Marketing LDR Predictions Composite Data Set Best Data Set Worst Data Set Method 1 Method 2 Method 3 _S_SE=.732_,_ K=3 1711.43, 3735.057 _S_SE=.6567_,_ K=12 Y-_I-_l.287 , Y:. 051 §SE=.6567,_ K-12 Y:1.287, 37:.051 _s_ss=.5137_, K-3 17:1.017 , Y:.12 §88=.409_4, K-7 17:.79, 745.09 §sa=.40_0_4, 1<=7 Y:.79, 171.09 SSE-.539; K-3 Yil.08 , 3735.152 SSE-.514; K34 Yii.03, Yigl46 SSE-.4434, K96 Y:.89, 3715.125 Average Marketing was 3.25 (in hundred thousands) KEY SSE = Standard Error of the Estimate 7‘: II “I + __ 1.96 SSE '4) + Number of Structural Coefficient - Interval on Y at Y 1.96 SSE/fil- - Interval on Y at Y 69 Table 20 Confidence Intervals on the Volume LDR Predictions Method 1 Method 2 Method 3 I... ..__._-__..___.. I Composite _s_SE=1.00;, K=4 SSE=. 937 K=12 SSE=. 937L K=12 f Data Set Y:1.96,‘Y:.079 Y+1. 84, Y+. O74 Y+1. 84, Y+. 074 g 1 Best SSE=. 569, __I(=4 _S_SE=.4444_, K=6 SSE=.444_4_, K-6 Data Set Y+1. 126, Y+. 13 ‘Y:.876, Y1.103 Y:.876, Y:.103 ._._. -- -_._._,_--_._- _ Worst SSE=1.1LKF4 SSE=. 981L K96 SSE=. 978L K95 Data Set Y+2. 2, Y+. 31 Yil. 97, Y+. 277 Y+1. 96, Y+. 277 Average Volume is 5.35 (in hundreds of thousands) KEY SSE - Standard Error of the Estimate K a Number of Structural Coefficients -_-t 1.96 SSE = Interval on Y at Y Y i_1.96 SSE/IE - Interval on Y'at Y 70 Table 21 Improvement in the Degree of Confidence of Method 3 over Method 1 LDR's Price LDR Marketing LDR Volume LDR l“. I M I Composite ; .045 E .03 .0158 - Data Set L_“LL_L ' ; Best Data .043 .078 .0786 F Set g - Worst .0218 .0512 .0318 Data Set 71 When we consider the predictions on the grand mean Y'at Y, the percent of the time when method 3 is more useful than method 1 LDR's is identical with Y at Y which we just discussed. However if we return to the confidence intervals contained in tables 18 through 21, we find that the value Of that difference in intervals is very small. For example, the difference for the composite price LDR's is .20. On the marketing LDR it is $1200 and on the volume LDR it is 1000 units. These are all quite small when considered in terms of the magnitude of the mean of these variables. Thus for predicting the grand mean Y we can additionally argue that the magnitude of the gain in reliability is relatively small. Our findings in comparing method 1 and 3 LDR's are: 1. There are statistically significant differences in the Rz's and additions to the sums squared explained variance. 2. In the best and worst samples the LDR's are from the same structural family; the LDR's on the composite sample are significantly different. 3. Even though the differences are statistically significant the practical differences are not apparent in terms of improvement in our predictions. Thus we conclude that the heuristic models can be statistically improved upon, however, little practical value can be gained from such an inclusion of new variables. Realizing that my argument for a lack of practical difference among the various methods to obtain LDR's might not be completely accepted the subsequent hypotheses examining bias, variance, and learning were examined for both method 1 and method 3 LDR's. In fact, given the statistically significant differences of the method 1 and 3 rules, we could be criticized if we did not test both. 72 One could argue if bias or variance was demonstrated across rank, time or industry for the method 1 LDR's it was simply because these heuristic rules were inadequate representatives of the subject's behavior. This point could be strenghtened by pointing to the sta- tistically significant differences in method 1 and 3 LDR's. However, if we test method 3 LDR's we test the best possible rule by all cri- teria including that Of statistical significance. Then no criticism such as the foregoing is available. As we will see the bias and variance effects across time, rank and industry are, if anything, even stronger for the method 3 LDR's. Or looked at another way, the method 1 LDR's may obscure the outcome of the tests. The difference in the outcome Of these tests for method 1 and 3 LDR's could result from random effects rather than true differences in the method 1 and 3 rules. However, no test is available to demonstrate that assertion. It is important to note that method 1 LDR's should be tested also since we desire to have our results applicable to rules calcu- lated by both method 1 and 3 procedures. Bias in Decision Making among Teams of Different Rank In an earlier discussion we examined Bowman's assertion that due to dish shaped cost surfaces the variance rather than bias was the major source of economic inefficiency. We found that given further assumptions on the model his assertion would hold. Bias must be measured relative to some preferred rule. The Optimal rules would certainly be appropriate, however, they do not exist for the price, marketing and volume rules in the Executive Game. The most appropri- ate available standard would be the rules used by the best team in each industry. 73 If bias is not a determinant of team performance then we would not expect bias to fluctuate across team standings. The latter hypothesis is tested and the results shown in table 22. The first three tests are on the heuristic best price, marketing and volume rules. Only in the case Of the volume do we find signifi- cant fluctuations in bias across rank. A linear equation is a signi— ficant predictor at .05 of those fluctuations; however, it is not clear from the equation that the best teams are more unbiased than the worst teams. The next three tests all show significant fluctuations in bias relative to the method 3 best rules. In all three cases a linear trend based on team rank is apparent at .05. These equations predict that the worse the team the more highly biased it will be to the best team's decision rule. Apparently simplifying the method 3 to the heuristic rule obscured this effect. The conclusions based on the method 3 rules point to the need to re-evaluate the role of bias in Bowman's theory. Variance in Decision Making among Teams of Different Rank Bowman has asserted that variance is the major source of economic inefficiency. Thus we would expect that variance would discriminate the levels of team performance. In particular we would hypothesize that variance should be a direct linear function of final team rank. As earlier discussed, the mean average deviation Of the actual from the predicted value was used to measure the variance. This measure would show the degree to which teams consistently used a decision rule. Thus it is a measure of erratic behavior which 74 Table 22 Significance Levels for the Tests on Bias across Final Team Rank Heuristic LDR's Price LDR Marketing LDR Volume LDR Best Rules on the .242 .621 .009 with Composite Data linear effects Set equation 1 Method 3 LDR's Best Rules on the .033 with .106 with .003 with Composite Data - linear effects linear effects linear effects Set equation 2 equation 3 equation 4 Equation 1: Mban Volume = .173 ~ .041 (Rank) Equation 2: Mean Price - .033 - .009 (Rank)“ Equation 3: Mean Marketing = .0677 - .03 (Rank) Equation 4: Mean Volume - .196 + .064 (Rank) 75 Bowman thinks is the underlying cause of inefficiency. The standards Of performance we shall use to calculate the MAD are the best rules. These results parallel those on bias. The MAD for the best heuristic volume rule has significant fluctuations across rank. These fluctuations are fit at .05 by a linear equation. The equation shows MAD to be a function of rank such that the lower ranked teams had larger MAD's. All method 3 MAD's had significant fluctuations across time which were fitted by a linear equation. Again the lower the rank the larger the MAD. Table 23 summarizes these findings. The results support the contention that variance (as measured by MAD) discriminates the levels of team performance. This finding lends support to Bowman's assertion that variance is a source of economic inefficiency. Learning An earlier study (Carter, Jenicke, and Remus) had indicated the need for including in the theory learning effects. This paper will examine two interrelated measures of learning. In the preceding section we introduced MAD of the actual from the predicted decision as a measure of erratic decision making. In this case however, we used the composite rules which characterize aggregate behavior as the preferred rule. This was done to find how the subjects learned their own rules rather than the Optimal rules. If learning were to take place we would hypothesize that the MAD would decrease over time. 76 Table 23 Significance Level for the Tests on MAD Across Rank Heuristic LDR's Price LDR Marketing LDR Volume LDR Best Rules on the .745 .051 .0005 with Composite Data linear effects Set equation 1 Method 3 LDR's Best Rules ' on the .033 with .0005 with .0005 with Composite Data linear effects linear effects linear effects Set equation 2 equation 3 equation 4 Equation 1: Volume MAD = .453 +.05 (Rank) Equation 2: Price MAD = .10 + .01 (Rank) Equation 3: Marketing MAD = .36 + .03 (Rank) Equation 4: Volume MAD - .515 + .083 (Rank) 77 Another measure of interest evaluates the average propensity to use a LDR. A decision maker could be behaving erratically while, on the average, be using the composite LDR. The measure is the mean signed deviations (MSD) of the actual from the predicted decision. We would hypothesize that if learning occurred as time progressed, the decision makers would get closer to the rule characterizing their aggregate behavior, thus reducing the MSD. Table 24 contains the results of the tests of learning using MSD. Both the heuristic price and volume LDR's yield linear trends in MSD over time. As predicted, MSD is reduced as play proceeds. This table also shows that all three method 3 LDR's manifested linear trends to their MSD. Again, MSD was reduced as time progressed. Table 25 contains the results of the tests Of learning using MAD. These results are mixed. We find the heuristic price and volume LDR's have significant fluctuations in MAD over time. The MAD for the price LDR is reduced as time proceeds, however, the volume LDR shows the opposite effect. The linear trend in the latter case explains only 9% of the variance in all means. This may be a type II error. The method 3 price and volume rules also show significant fluctu- ations in MAD's. The price rule, as in the heuristic rule, has a linear trend in the predicted direction. The volume rule shows no linear trend again suggesting that the heuristic volume rule trend was a type II error. We conclude that the learning effect has been demonstrated in terms of mean signed deviations Of the actual from the predicted decisions. The learning effect in mean absolute deviations was only Table 24 78 Significance Levels for the Tests on MSD across Time Periods Heuristic LDR's Composite Rules on the Composite Data Set Method 3 LDR's Composite Rules on the Composite Data Set Equation Equation Equation Equation Equation Price LDR Marketing LDR Volume LDR .0005 with .777 .0005 with linear.effects linear effects equation 1 equation 2 F.ii-n .0005 with .037 with .0005 with linear effects equation 3 linear effects equation 4 linear effects equation 5 Mean Price = Mean Price = .174 - .0332 (Period Number) Mean Volume = .173 - .041 (Period Number) -.26 + .049 (Period Number) Mean Marketing = .14 - .02 (Period Number) Mean Volume = .59 - .112 (Period Number) Table 25 79 Significance Levels for the Tests on MAD across Time Periods Heuristic LDR's Composite Rules on the Composite Data Set Method 3 LDR's Composite Rules on the Composite Data Set Price LDR Marketing LDR Volume LDR .0005 with .322 .0005 with linear effects linear effects equation 1 equation 2 .0005 with .920 .0005 with no linear effects equation 3 linear effects Equation 1: Price MAD . .10 - .022 (Period Number) Equation 2: Volume MAD = .384 + .066 (Period Number) Equation 3: Price MAD = .28 - .04 (Period Number) 80 manifest in 1 of 3 cases and therefore not well supported. Both of these learning effects relative to the Optimal rule were found by Carter, Jenicke, and Remus. We interpret these results as indicating an increased propensity to use the composite rules and weak support for a reduction of erratic behavior as play proceeds. Summary of the Effects of Rank and Time The findings of our tests in the preceding three sections are: 1. We found that bias relative to the best rule was a linear function of rank. The lowest ranked teams had the largest bias. We found that variance (defined in terms of MAD) relative to the best rule was a linear function of rank. The lowest ranked teams had the largest variance. The degree Of support for the findings on bias and variance were equally strong. Learning was manifest as play proceeded by an increased average propensity to use the linear decision rule char- acterizing aggregate behavior. Weak support was found for reduced erratic behavior rela- tive to composite rules as play progressed. CHAPTER V SUMMARY AND CONCLUSIONS In the prior chapter we evaluated a number of significant research questions. It is the intent of this chapter to integrate those results into existing theoretical frameworks. This includes restating Bowman's theory in the light Of this and other studies. This chapter also includes a plan for research projects which will expand and elaborate this area of study. Conclusions The results of this study have implications for Bowman's mana- gerial coefficient theory. Even in competitive business simulation games we can conceptua- lize the decision maker as a decision rule coefficient estimator. The heuristic models found have concurrent and cross validity. Once a heuristic model is found according to the guidelines, little practi- cal improvement seems to be gained from the addition Of more variable. Significant levels of bias occurred over the ranks of the teams. It often had a linear trend such that we can assert that the poorer ranked teams were more biased relative to the best rules than the better teams. SO we could argue that, at least with environments in which the manager is not fully experienced in decision making, we can distinguish the better firms from the poorer firms on the degree 81 82 of bias they have from industry leaders. Thus, using the industry leaders as a bench mark to examine 3 firms decisions seems to be a good idea. Thus we note that, with the exception of fully experienced mana- gers in stable environments decision making may be biased relative to industry leaders. In particular, Bowman's theory should include stip- ulations as to poorer teams being more biased than better teams at least while learning is going on. The variance is asserted to be the cause of the poorer economic performance of some firms since the cost surface is postulated to be dish shaped. We found that the degree of variance (as measured by MAD) did distinguish the better from the poorer teams. The degree of support for both bias and variance discriminating team performance is equally strong. Thus variance may not be the major source of ineffi- ciency. We examined learning in terms of increased propensity to use the composite rules and reduced erratic behavior relative to the composite LDR's. Strong support was found for the former indicating that the subjects in the aggregate tend to get closer to the composite rules as play proceeds. Weaker support was found for the reduction of aggre- gate erratic behavior over time relative to the composite rules. Thus we would suggest the following additions to Bowman's theory: 1. Linear decision rules may be appropriate for unstable, com- petitive environments. They have both concurrent and cross validity. 2. The linear decision rules used by the best, worst and the aggregate industry may be significantly different. That is, different managers may have different insights into similar decision making situations. 83 3. Bias from the first place teams' rule discriminates levels of team performance. The lower the rank the larger the bias. 4. Variance (as measured by MAD) discriminates the levels of team performance. The lower rank teams have a larger MAD relative to the best teams' rules. 5. Both of the preceding effects are equally strong. Thus economic inefficiency may not be solely attributable to variance. 6. Learning was manifest as both increased propensity to use the composite rules and reduced erratic behavior relative to the composite rule as play progresses. All of the foregoing must be qualified by the obvious fact that the data from which the conclusions were drawn came from inexperience young decision makers. The results are also confounded by the fact that all subjects had the same classroom influences while they were playing this game; this is a business game rather than the business world. We might point out in support of the preceding that the learning effects also appeared in an earlier piece of empirical research (Carter, Jenicke and Remus) done with a aggregate production scheduling game. The other questions were not addressed by the latter study. Need for Further Study This section reliably appears in all dissertation and alludes to studies that need to be performed but seldom are performed. For a change of pace I shall use this section to outline my direction for future study in this topic area. It is now clear that the Executive Game being played singly by inexperienced decision makers, yields results which are consistent with the literature and which allow us to examine new and interesting 84 hypotheses. Further this source of data is readily available in quite large quantities, at a low price. In Management 101 this source Of data is fully institutionalized. The first need is to replicate the major findings of this study on the data generated by play in the Spring of 1974. Particularly of concern is that these derived rules may have been idiosyncratic to the winter version of Management 101. The autocorrelation on the price LDR needs further examination and perhaps even a non-lagged rule selected. Then I will be able to return to the data which has been used for this study. There are many questions which can be asked of these data not examined in the hundred plus tests in this paper. Extension of this analysis to other variables in the Executive Game could aid us to understand the mechanisms which lead to game success. I need to examine the interrelationship of bias and variance in each indus- try to see if idiosyncratic patterns of covariation occur within each industry. The game play then could be selectively replicated using the linear decision rules to assert that rules in this competitive environment give better results than actual behavior. Ultimately we could devise a linear model based on our derived rules which would actually compete with live decision makers period by period. An analysis of the individual decision rules has yet to be made. I can then address myself to the equivalence of various individual rules to the composite and examine the effects of non-composite rule behavior. 85 Data has been collected on student grades and national test scores. Also a questionnaire has been filled out by all partici- pants which examines the decision making behavior and their Opinions about the benefits of the game and the real managerial world. The latter data can be used to try to develop behavioral and attitudinal correlates of decision making parameters such as bias and variance, learning effects, and the variance not examined by the decision rules. Bowman claims his theory applies also to group decision making. Fortunately all the hypothesis of this paper are amenable to the data from Executive Game when played by teams in Management 409 and 833. This is virgin territory. These studies are bootstrapped into the Carter, Jenicke and Remus studies on aggregate production scheduling which is now insti- tutionalized in Management 306. Thus cross fertilization will undoubtedly occur. The aim of my future work will be to add more rigor to the field. BIBLIOGRAPHY BIBLIOGRAPHY Baab, E. M., Leslie, M. A., and Van Slyke, M. D. The Potential of Business Gaming Methods in Research, Journal of Business, 1966, 465-472 Bowman, E. H. Consistency and Optimality in Managerial Decision Making, Management Science, 1963, 9 (2), 310-321 Cangelosi, V. E. The Carnegie Tech Management Game: A Learning Experience in Production Management, Academy Of Management Journal, 1965, 8, 133-138 Carter, P. L. and Hamner, C. W. Consistency and Bias in Organiza- tional Decision Making, Proceedings, Fifth National Meeting, American Institute of Decision Sciences, 1973 Carter, P. L., Jenicke, L. 0., and Remus, W. E. Learning in Manage- ment Coefficient Models, presented at the Midwest Academy Of Manage- ment, April, 1974 Durbin, J. and Watson, G. Testing for Serial Correlation in Least Squares Regression II, Biometrika, 1952, 159-178 Fleming, J. E. Managers as Subjects in Business Decision Research, Academy of Manggement Journal, 1969, 12, 59-66 Class, C. and Stanley, J. C. Statistical Methods in Education and Psychology, Prentice-Hall, Englewood Cliffs, N.J., 1970 Goldberg, L. R. Man versus Models of Man, Psychological Bulletin, 1970, 73 (6), 422-432 Hamner, C. W. The Importance of Sample Size, Cut Off Technique and Cross Validation in Multiple Regression Analysis, Proceediggs of the Fourth Annual Midwest Regional Conference of the American Institute of Decision Sciences, 1973, 814-817 Henshaw, R. C. Testing Single Equation Least Squares Regression MOdels for Auto Correlated Disturbances, Econometrics, 1966, 34 (3), 646-660 Henshaw, R. C. and Jackson, J. R. The Executive Game, Irwin, Homewood, 111., 1972 86 87 Holt, C. C., Modigliana, F., Muth, J. F., and Simon, H. A. Planning Production, Inventories, and Work Force, Prentice-Hall, Englewood Cliffs, N.J., 1960 Huang, D. S. Regression and Econometric Models, Wiley, New York, 1970 Johnston, J. Econometric Methods, McGraw-Hill, New York, 1972 Khera, I. P. and Benson, J. D. Are Students Really Poor Substitutes for Businessmen in Behavioral Research?, Journal of Marketing Research, 1970, 7, 529-532 Kunreuther, H. Extensions of Bowman's Theory of Managerial Decision Making, Management Science, 1963, 9 (2), 310-321 Land, K. C. Principles of Path Analysis from Sociological Methodology, edited by E. F. Borgatta, Jossey-Bass, San Francisco, Calif., 1968 Lewin, A. Y. and Weber, W. L. Management Game Teams in Education and Organizational Research: An Experiment on Risk Taking, Academy of Manggement Journal, 1969, 12, 49-58 Malinvaud, E. Statistical Methods of Econometrics, American Elsevier, New York, 1970 McKenney, J. I. and Dill, W. R. Influences on Learning in Simulation Games, American Behavioral Scientist, 1966, 10 (2), 28-32 MOffie, D. J. and Levin, R. J. Experimental Evaluation of a Computer- ized Management Game, Atlanta Economic Review, 1968, 18 (11), 7-11 Moskowitz, H. Managers as Partners in Business Decision Research, Academy of Management Journal, 1971, 14, 317-325 Moskowitz, H. and Miller, J. G. Information and Decision Systems for Production Planning, Purdue University: Krannert Graduate School, Working Paper No. 373, November, 1972 Mbod, A. M. Partitioning Variance in Multiple Regression Analysis, American Education Research Journal, 1971, 8 (2), 191-202 Nash, M. N. and Chetnik, C. G. The Influence of Personality Factors on Group Decision Making, presented at the Western Meeting of the American Institute of Decision Sciences, March, 1974 Norman, R. A. A Experiment in Phenomenological Approach to the Study of Business Decision Makipg, Unpublished Dissertation, Michigan State University, 1966 Philippatos, G. C. and Moscato, D. R. Experimental Learning Aspects of Business Game Playing with Incomplete Information About the Rules, Ppycholochal Bulletin, 1969, 25, 479-486 as Rohrer, J. R. Selected Ability and Interest Dimensions as Predictors of Success of Collgge Students in Business Management Decision Gaming, Unpublished Dissertation, Kent State University, 1967 Rowland, K. M. and Gardner, L. M. The Uses of Business Gaming in Education and Laboratory Research, Decision Sciences, 1973, 4, 268-283 Schriesheim, C. and Schriesheim, J. Divergence of Practitioner Opin- ion and Empiracle Evidence: The Case of Business Simulation Games, paper presented at the National Academy of Management, August, 1974 Slovic, P. and Lichtenstein, 8. Comparison of Bayesian and Regression Approaches to the Study of Information Processing in Judgement, Organ- izational Behavior and Human Performance, 1971, 6, 649-744 Thiel, H. Principles of Econometrics, Wiley, New York, 1971 APPENDIX COMPUTER PRINTOUTS The following nine computer printous are the outputs for LDR's found on the composite data set. The first three are the heuristic price, marketing and volume rules. The three method 2 rules then follow in the latter order. The method 3 rules for price, marketing and volume are the last three printouts in this section. zoummUVa-LIUI JJ‘fl‘I‘)Q Nanak )n‘v.‘ Ufluflv‘n. 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A I.J ‘ICNL"L"‘I 00L“ J'C‘J"'I )Y‘IIC.” DIQI ”EU SIG 82.8623 (0.0005 65650651 STANDARD ERROR OF ESTIMATE MEAN SQUARE 35.71805137 .63105318 MKTG 11 589 OF FREEDOM 599 DEG AOV FOR OVERALL REGRESSION MULTIPLE DEPENDENT VARIARLE-X(5) SUM OF SQUARES 392.89856536 253.05927131 646.35783637 MEAN) MEAN) (AOOUT SSTON TOTAL (ANOUT REGRE ERROR mamncoaoomtoaomm NIKOwuNsCCMDO’ ONO") PNII‘NLDOCIDNMQO‘O Nmoma‘hma‘oc‘ooOIO «Jonmmmmomoomo “1.0.0.0000... ID JILHOU‘flOU‘NNNO‘NO «unamcowammam: HOU‘U‘ONJHU‘O‘U‘WMN I‘Cv-IPTO'NU‘U‘CLDU‘C-Tn m Gov-INWHOHOOHFI (“00.000.00.00 O-M I I I I I I O O mmmmm In In QMOODOOO‘OQQOA Hmaoooomoamco mOOOOOQQOOQOO .0.......... DOOOO ’3 D V V V V V V V WOOU‘NONNIDU‘NC‘ Gdomhhwshmo: m~3rco~mo~wnnno« lLNtDlhdMIk Nnrmmn ............ wnm:n:mm:~.4 om:d.4 .4 .4.4 J DMQOJJU‘MNQOQ omoet: DHF‘DDOM Bmm—IOddemdo Q-ffiwowoa‘lomm h0....0...000 045MMNPNNMM N I I I I I I II) 0’ OMONO‘Mdme‘U‘U‘NO do «a o-vaafiv-I‘T‘G‘VMOFI o’t—Oln OJNMQ‘ONNHN UIMOM3MF‘I $JNMNMM moo'aaoaoooomo . .0.......... 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I—OZSHQuQCdQL ZZHJO’ FZ>H 2 «H OLL-JOLIJ o H O ( (DUO 3 2w.- VOLUME AOV FOR OVERALL REGRESSION DEPENDENT VARIABLE-XI8) SIG 59.0626 <0.0005 MEAN SQUARE 52.05287006 DEG OF FREEDOM ES SUM OF SQUAR 11 588 899 SSION (AOOUT MEAN) REGR 572.50157500 510.21595715 1090.79750219 .88131967 ERROR TOTAL (ABOUT MEAN) 5 STANDARD ERROR 0F ESTIMATE 093078628 EFS BAR 2 .516J O (:0! I! f! O 0 w .J m CL 4' 0.4 N I-Q'IN- _; 0 D 1: 0‘ J NN 0m . (K c: u: o (f- \0 .1 o mo:o‘o~ocmmo~«aom wco‘mrewos NO‘NINOSN 0—0mommbmorsco‘o‘ NwNowcHoaodcndu mammcmmmmmmmmm M000.00000.00 m JILNNU‘vIMNMV-IJNC‘N dumJM3¢c~omHm~DNo Hommm~o«omonc¢ PUQO‘JMO‘NO‘chdou 0: CDv-IHv-Iq-Iv-Iflv-Iv-Idv-Iv-I 4&000.00..000. an: I I I O 0 mm as snow ONOOC-IOMQDOIDQH Hdcocccoocoofl mooaoraooooaoo ............ MdQMIDC‘JIDOJ’NM mmemJO‘QQQON mmd‘mdeKdG‘U‘KM ua30M3cmmasoa‘: .0.......... MO‘HJQJNHBIDO Nkv-IN N.4N O‘NncnmmOHN”N ONMMU‘NKOJMv-IO MJNLOJK ”£0683", CNOO‘MO‘O‘O‘VIQNOU‘ I-00000000000. JQMSNJJJNNN I I I OMDQNHOU‘IO3NU‘KM n’¢.J:N.4ro.1.r,mm¢ru~m (rt- ‘IdeO‘OmHO‘m‘ad UIIII'SmMMJMMMW‘IV‘M (DOOOQOOGOGOQO . ............ Duo I—O U) oM‘Oooamo 00151.00 than 0.4mm JMQJB—N I—c’mo mNC-HDOJLI‘OU‘ druadeChN‘mfi/‘mk FOONNv-INclv-IHHHDU mo—I...00.0.0000 (two I I I I womoswo30m3rso F—C‘NM JmeICuoNJM mzmtmoroo “HE‘QNlh-O 0 U'MMNJ'JKNQ’ Jhlfim OHC‘HLDH‘N.nI~Q‘Nm.-¢m QQHM-JI’)N‘C‘NI\.\D€C~TJ “HWMSH'IC‘CNNJ'DOO ulumaaodo‘3r0~33m'wo LL00000000000. .UJV DO I-U (I) IL 0 (DOV-108010.11) )Nhk(v ZFKO mend-4.43.: 3&0" OZQO‘CONNNC!NMU\U‘ HI: O‘filfil’T‘U-G‘OWC’OJF m mHNv-I.DNI\I-P' de‘Cm mumwmmkrmMNch-c uchoxoerxONM'JHmud 0 ILLI‘v'II’JV IDLATMNQ'J') LSD 0.0.0....000- 1111.! H I I (YO I O OmanNfl .0mnm.4.4 .4 «Mo-I «ha-0P6! <1 FL“XHUMIICDLL'HI Zkh' .101: .JC V hwxoacHoozmq ZIPS-2 HOV‘>H C.) «no Hr-LICL *- FO Yb V‘h X (I) DILII— LLJL‘lu 20- <2o mom >04 «0.x00u4mqau<> thozwamo .msmc.m0. Nd mozH mUHm. wwmswkms. mm H m xmz as Mcsms.- p2 pmzo“ mthHoHuumoo was onmmuaouy wk mmmao .zqmt Enema. nape» xoamm .z¢mz.p:ocs. onmmmmomm 0A/01/7I 2.2A8- ELAPSED MKTG DEPENDENT VARIABLE-X(5) REGRESSION AOV FOR OVERALL SIG MEAN SQUARE 107.5807 <0.0005 28.39287352 DEG OF FREEDOM SUM OF SQUARES 56.78090705 18.21033507 7A.99528212 REGRESSION (AOOUT MEAN) ERROR .26391790 69 71 SAN) (ABOUT M TOTAL ' S STANDARD ERROR OF ESTIMATE .51372960 cz MULEIPLE CORR CO .8702 R2 .7572 CASES 72 U'IMMO‘ IAIN-7N b.4105) NMMJG‘ (14800 W 0 0 0 mm (900:: Hoes: mono . . . VV MOO ”Clo comm: ALTON-f 0 . . NNO OMN mama) hock <1]?me buoo‘m IUD-I 0 0 0 mmro I the!” ZI-O‘U‘J OZV'IMI) Huw‘md WHU‘NO‘ WL‘FJU‘M UIHv-Icm Q khflfl ULL 0 . 0 hilt) "I I 'O U VOLUME AOV FOR OVERALL REGRESSION DEPENDEAT VARIABLEr-XIBI SUM OF SQUARES SIG MEAN SQUARE 60.3773 <0.0005 DEG OF FREEDOM 19.60676901 58.82030703 22.08216267 83.902AA969 EAN) REGRESSION (AROUT M ERROR .32673739 68 71 TOTAL (ABOUT MEAN) ' S STANDARD ERROR OF ESTIMATE .56985736 MULTIPLE CORR .8527 2 271 (IN 72 CASES MNNQC) Luna‘s»: I—v-IMLDLD NLUU‘M '95 GJOOUMD LU 0 . 0 0 U) .ntsauoo (NONI... HOIDJNC) humour): 3 3mm: 4“ 0 . 0 . C VVV mama: NF’IIDN QIDDO‘ID ALONOO‘ 0 0 0 . QMJN .4NM.4 Dana MK“ Jv-IOO GMOOHD .— . . 0 0 4’31“” (I) o: OUIOOHOM dqucfitom mI—nmmm tall-000000 manor: . O . . . Duo I-O In 00.7“] UIUmuN PQNMON (IO-4' DC) I-LDUMU‘M ILIH 0 0 0 . (but: MHII‘U‘O‘ ZI—WOUV‘J‘ OZ‘T‘(’)\DH HILIVINd" WHNLDG", monomv-«o‘ UJHU‘NNO‘ Q’LLIDMNO LDLL 0 0 0 . IIHHH 0’0 0 PRICE DEPENDENT VARIABLE-X(A) AOV FOR OVERALL REGRESSION SIG DEC 0? FREEDOM MEAN SQUARE 2605050 (0.0005 SQUARES SUM OF .0910h892 .5A629351 AN) - '- ‘ (ABOUT M REGRESSION ERROR .003A3529 65 .22329399 .76958750 71 AN) TOTAL (ABOUT M 5 STANDARD ERROR OF ESTIMATE .05861136 0 (ON N04 “(KO ILCO mm . CO MULTIPLE CORR .SHZS F2 .7099 CASES 72 (DMJLDLDdHDd UO‘O‘NOLDMO‘ hQHMoMO‘d NmocMJU‘JJO‘ KJNN¢OO~DID w 0 . 0 0 0 0 0 V) JILQIDNO‘OS’N F-UU‘NO‘NDJJ C mocanw (« . 0 . 0 . . 0 0.0: I I I I O 0 «now 60600.43”) 0mnocmum33 m¢mnaacmua . . . . . O . ecu: V V V seasoned snmnmnoa' muommw~a ILNOQv-«DON . . . . O . . mv-IJNO‘J' 60.4.4 QU‘U‘4U‘Nv-I MOJNv-Iv-IO mOHDIOan-«D QJNONIDOQ I- 0 . 0 . . 0 . I O‘NMMMN I I I U) I! oakmncuwuou (rdcn4crumno dI-nosmmmo wmommpoavs (madwumadc . . . . . . . . OUJJ PO U) ONJIONvad UTOMDv-IOLJv-IN I-UJNJOCG (Ivarsccmdro hunmumnmwod tut-I . 0 0 0 0 0 . mumn4 I II I WMQMQQCN I—mfa v-ILDv-IUM 2'01? mmO‘P‘d Q'txlkc‘f‘fflkkfl OHv-INNP-t’NM (C0 JNMN'Jv-Ifl ofHNnOMNHr-v MILLNLJ’WUL‘O'D u. 0 0 0 0 0 0 0 0“] DO P0 (I) LI. 0 UT’Dv-II'UNMKN ZI-NLJNNIK‘LDN OZM'Q‘H'fi‘Dv—IU‘ U)Hr_)M(')0-IMC‘Q (1)0!fo QNHMN 1.0.4!on :rsrm: Q‘LLMcufv-Icunu 01L 0 0 . . 0 0 0 MN!) I I I I (1'0 0 '-)NNQ~3®.4 Mv-IrIv-I N VAR I-ILHQXHII CLLLII‘EU') I-LUZOODd Z HMZJU 4.- HO r—xm > (IMHO O 22H ( O 0: M MKTG DEPENDENT VARIABLE-X(5) AOV FOR OVERALL REGRESSION SUM OF SQUARES SIG MEAN SQUARE 67.1157 <0.0005 10.76207628 DEG OF FREEDOM 60.572A5767 10.A2282“Ak 7k.99528212 MEAN) (ABOUT REGRESSION ERROR .16035115 65 71 AN) - p -. TOTAL (ABOUT M 1.20 . . CASES MULTIPLE CORP UL?~D-f¢Mc.-a UNLONNMQO‘ I-QO‘U‘NNON NW3300‘dJ: «400005500000 w 0 0 0 0 0 . . D (I) JILNJQOU‘HO de-IIDU‘MMU‘ID Homdmmo‘rfln FQDNQNOOO‘ K NOLDIDIDMN (a 0 0 0 . . 0 . O.“ I I I O I.) «wanna uOocooNO I-Iv-IOOODv-Iv-I maoooooc . . . . . . . coco v v v v v-IdU‘QmNO‘ «000.4413 mMIDNDIDNv'In umomnnoa . . . . . . . IDII‘MNNOO :nmm .4 .00063869 STANDARD ERROR OF ESTIMATE 3hflFOONDd mound.««o unoaw¢u~s mdmn\0hMM: p.000... Nummncmnl «I II BAR 9210 (h or OMODMJJNln NN Edna'mmskc o mr—ovx «00:0: mMLJO‘DQOJLO monocooo . . . . . . . Chan (I: I-0 m cameraman WOJNv-Iuv'nn I—on-IfomtJ (Itadhfsomo I-LDOCDJJMHv-I IIIH 0 . 0 . 0 0 0 come: I I I I .9279 2 .8610 (DNLDNNLDCOFI I-J‘LDCMONJ (1327\th 30""! (Y'LJO‘anJ 1&9 fk OHv-INHw—ILDCJN QQHHN- I"):nu_, Gin—unmar’oaom LuLLLhDQJN-JN LL 0 . 0 0 0 0 . (”CNHKDMB '0 ZI-HQU‘IUNC‘QN CZU‘HvflhM'YN HHH‘JWIHLDO‘N'L mFIF‘QU\mL)U‘v-i UTQILCUMJLDNO IJJHLDQJU‘QHN O LLMO‘NJCULD OIL 0 0 0 0 0 . 0 (1)")1-4 I I I O'O I) 72 23")00 JHN 21’ HH .4M V XI—LIIXHQ UIZILU Z I-OLdDOWd ZZI-JZ Z UW'U‘IU'V 70‘SW CLHTJEU VOLUME AOV FOR OVERALL REGRESSION OEPENDENT VARIABLE-XI8) SIG MEAN SQUARE 13.57506618 68.7755 <0.0005 DEG OF FREEDOM SUM OF SQUARES EAN) 67.87523091 REGRESSION (ABOUT M ERROR .19730210‘ 66 13.02721878 80.902Ak969 71 MEAN) (AROUT TOTAL MUUTIPLE CORR CASES STANDARD ERROR 0F ESTIMATE 0“““27706 - .9160 8390 72 MQNNv-ILDO‘ Luv-IMONLDQ I-olDLON3H NUHO‘NNLDO‘ (24050th LU 0 0 0 0 0 . (II .IIuLV'Iv-IIONDMLO CULI‘IDII‘QNLD HOU‘v-IQNNU‘ PUCLDOOLUN C neuron: (M 0 . 0 . 0 0 CC! I I O 0 mm mm owmnawcma hmuaovmu: mcmraocma ...... acaiao vv *vv TomUWwHo thko-IMM MNU‘QNO‘ mawammn .- . 0 . . 0 0 MJQNLOJ I I U) (r omomsmsm QidomNONQ (XI-om mrsu'w: wmeomanun meooooo . . O . . O . DLLO II-O m (300me UTC’HLUISJ’LI‘ I-VJNC’LDQLD dILJNthr-IF‘O I—LDDNJNJN IUD-I 0 . . . . . OJIUO I Z maomowovo I-O‘NQLAO‘LO mzxmamma Q IAIJLDIKJO‘N OHJLDMHLDN LLOxDHNNQLD «Hmmm:.-mo LNLL 1.40023: 11.. . 0 0 0 0 0 0111.4 00 I-Q (1) LL 0 mnmmmc‘: ZI—HFIHHIDN OZHJMHO‘r-w HUTNNQ-Iv-IH’J‘ WHJHONNv-I (00.4.470an uJHJJ'LONmm 0'0..de «0.4 cu. . 0 0 0 0 . IN'HU‘ O’OI I O osmmma O.’ .4 .4m.4 <1 ) xot-Hx LIN-Z Ll) I—OleuO 221:.— 2 4H OI—H I- 0.x mo uJZ 2< I-ZH CI! :2 <1 I\ 3' 1' II. . I u .. A null I A III II .. I I SIG 26.50k0 €0.0005 S STANDARD ERROR OF ESTIMATE .05861136 b'va vvvhl'vw o0910b692 .003h3529 MEAN SQUARE CC FRI 65 DEG 0F FREEDOM 71 oBhZS AOV FOR OVERALL REGRESSION MULTIPLE CORR DEPENDENT VARIABLE-X(b) .5u629351 .22329399 .76958750 .7099 SUM OF SQUARES SSION (AROUT MEAN) TOTAL (ABOUT MEAN) 4532 noon p - MM4~0.0:\D« WO‘O‘NOU‘MO‘ PQdMOMC‘o NWOCMJmOO‘ xgmuu:¢umoo g o o o o o o 0 U) JILJ‘DKO’HDJN ‘UJO‘NCv-IC‘ID HOOHCNMO‘N I’CU‘NU‘NQJ: m ONO-34M“! <1: 0 o o o o o 0 am I I I I O O Imam iaocmmadcr: Hmooooc: Viacooaoa' O O O O I O O can: vvv KOmU‘COv-I swummo: (vacuum—0N1 lLNmC‘v-IQON O O O O 0 O O Inc-0.70104 (mo-0.4 countmo-a ma-dev-ID monommv-uo mskwhmoo I— o o o o o o o IC‘NMMMN I I I m d Othoca‘mkl‘d n d'fiv-IU‘HU‘LD‘J oft-om fommm wwommhm—ux m-nduoodo O O O O O O O 0 Che h-O U'I ONJMNH-I WULDFIQ'JHN POINJOQD dxc'hcc‘ddo bocNO‘NMMv-o uJ-I o o o o o o o (INDv-I I I I 3 UTMOMOCCDN I-Cfiv-«nv-dnf") MZKDC‘U‘LI‘O‘Mv-I (ILLINO‘ 36‘th OHHNNNC‘HMM (1L) IGIMN Jv-flv-I O’HN JnMNdCJ wuhcvcovjoo IL. 0 o o o o o o ouJ DO I-Q 0') I1 0 U‘KHNNW‘F Ix ZI—K aan‘DU‘h OZMtnv-nna v4!!- khflpr ”\OHU: MHCr-MMv-IMOCK‘ mcc Nva-IN‘N IJ‘HMIMLGJNMH muf’cuov-coog L'U. o o o o o o o mml I I I (YO nmmmsmd 0’ MHv-Iv-I o.- d > HHIUX'IIT CU wit!- v—chch Z HMZJU CI— HO P )fll' > mwu O 27H ( SIG 67.1157 <0o0005 63/2917“ MEAN SQUARE 10.76207628 .16035115 MKTG DEG OF FREEDOM 65 71 ADV FOR OVERALL REGRESSION DEPENDENT VARIABLE°-X(5) SUM OF SQUARES 6k.572&5767 IJoAZZBZAQA 7».99523212 SSION (aqour MEAN) TOTAL (annur MEAN) ‘sr AVALYSlS RD? REGD go .- q C. XGAH If; U) L) S ROR OF ESTIMATE oh00k3869 STANDARD ER MULTIPLE CORR .9279 8510 72 £0.20"):de wmmnmmco I-CO‘NNOHDK Nw33d0‘034' x—IQU‘ONNQO u o o o o o o o O (I) JLLNJU‘QOv-IQ «Luv-ammmmo‘m HOU‘HO‘U‘MMM PUcmoNooa‘ I! NCIfid‘U‘MN (I o o o o o o 0 at! I I I o . Q tmmmn uncooowo I-IdOOOOv-Iv-I mooooooo O O O O O O O cacao V V V V «dmcmwo‘ v-«DHO‘O‘JQ (Drunk «MD—on ILU‘IONv-ILDLOv-I O O O O O O O mmwmmoo :NMM .4 :NU‘QOoc-A “‘O‘HMMHQ MONKO‘NK QJUNQNU‘J I- o o o o o o o NNJLI‘U‘NN v-I I I I II! o! owoossnmm (Yd 113G V‘km (Yb—“3'0“”: [ULIIC'NDLC‘CG‘JO mooooooo . I O O O O C O cur: F-O m GU‘NM‘Ju-Id) WuJanNM® I-(DMNNHLDC) (Ioduthw o—or—aaom::«« NH 0 o o o o o 0 CALL“: I I I 3 msmmkmra I—JJ‘C‘MO‘NJ VZKLDQJU‘M 1' O'ldO‘OxOJNéN OHHN SHHCvN O'UHH"‘" '(\‘ nu) O'HLOCOJG,‘ tL-M mama-4 Ju-aN IL. 0 o O O o o o STD. OF COL V‘C‘N‘M\OHI\\D 2hr“! ~OO"DI'JN CZOw-wxnra .JN Hmmarmv-Hxn mhh‘xnmmo‘w UNA-Oran ’MN 3 u'Ha.¢¢rJ\:HI\ (YLLMOHPJNCJU‘ cu. o o o o o o o LHLIv-I I I I O O O OMRG‘M'IN PK «.4 «M a > xxtm—Ho uJuI)‘2 Z kCLZLLA/Tq 772.»- 2 VOLUME AOV FOR OVERALL REGRESSION DEPENDENT VARIABLE-X(8) SIG <0.0005 MEAN SQUARE 13.57506618 DEG OF FREEDOM "S p ‘ OF SQUAR 67.87523091 13.02721878 SUM 66.7755 SSIDN (AWOUT MEAN) REG? .19738210 66 71 ERROR 80.902Ab969 TOTAL (AROUT MEAN) S R0 l. .‘I MULTIPLE CORR II' m C.‘ STIMATE E 06 OF 77 R 5 STANDARD ER .9160 6390 .72 (flQdNJ‘O‘N luv-INQU‘CM hONsDJv-Im NIUHNNQO‘O‘ Ohfinc¢nqsh III 0 o o o o 0 U) JLC-IQOMOV-I CulU‘QlDNOsD HOU‘NCDva-I bQCDQON‘D a "NONMMIJ (M o o o o o 0 (LC! I I O O mtmnm UdNoooc HCv-IO'DOO moooO-ao O O O O O O coco v v v v \DMJ‘HQO‘ .flmmnc.-. O‘HOJOOK ILCOIDU‘NQ O o O O O O dOOoO‘N v-I \DMv-Iv-I exam-com mdNMMN MUFMNO‘N meflmMN .- o o o o o o MNQIAJIJ I I U) a! omomskm'n O dnrmfx-nm (Yb—orxmmmm mmormNuun C‘CD'D’J’D'JD O O O O O O 0 Duo 0—0 m ('mOG‘QJ WLJNOJth-I Hometown (ICINUKHION I-LO'.)NJ’JNN hnH o o o o o o C‘UJ': I I (DC‘NO‘O‘CID I—O‘LP'C‘WHDN (P7NMv-‘d‘v4‘f3 (rm: 38 TN 0 0H3v-4MLOk-D auohkc-DH wHO‘va-urm um :Q'1r33-4 ll. 0 o o o o o oLLv-I OD F—U V) n. O M'DNNO‘JO‘ dewamm—O OZHv-IMO‘Jd! Plqu-Irdo-tmk (III-IJNCINv-Iv-I (I‘Cv-IHC (\‘d‘v-I b'HJNsDO I0: 0 I1 flHJt.3fi\L LOU o o o o o o unuu. N (YC I I 0 "MI“ (\103 0' v-I Mv—v-I d > I-LEHXY 2'" l1 LL. FUJX'LLC. O 2”: :7 <10 I—HH he )1 The following nine computer printouts are the outputs for LDR's found on the worst data set. The first three are the heuristic price, marketing and volume rules. The next three are the method 2 price, marketing and volume rules. The last three are the method 3 price, marketing and volume rules. PRICE DEPENDENT VARIABLE'-X(A) AOV FOR OVERALL REGRESSION SUM OF SQUARES SIG MEAN SQUARE 909535 <0.0005 DEG OF FREEDOM .08776h75 .175529A9 .h2323913 .59876863 IAN) REGRESSION (Aqout an ERROR .006817h6 A8 50 AN) .- '- 5. TOTAL (ABOUT M ‘ S STANDARD ERROR OF ESTIMATE .093901h5 N's (onto IL‘N mm 0 CO R MULTIPLE GORP CASES 51 MNNm IAIN”: I-O‘NO NUJOU‘M Edodo U o o 0 CI m In {Dana Hooo Moo 0 O 0 v v «Ow-0 0000‘ unmN o o 0 “‘0‘75 0 VII 3mm «DNQ 00““ macs-I I— . o o and OMOO‘O «43:4 (XI-oar. muonn mac-4.4 O O O 0 Duo I-O MMU‘M I-Lnst-I (11233:!) O’ulchc-o OHMC‘N Q U' "’30‘ TYI-H'HD: mum-Jo IL 0 o O (Amman ZI—NLON 02;!”an thNv'IK WHNJN (DUOO‘NC UJHJQCJ a'chncJN OIL o o o 11"“! 0'0 0 UV! UA'IV GOUV‘ bbfl' all-U MKTG DEPENDENT VARIABLE--XIS) AOV FOR OVERALL REGRESSION SUM OF SQUARES SIG 37.1331 <0.0005 MEAN SQUARE DEG OF FREEDOM 10.821A6912 21.68293825 13.9883k509 35.63128333 MEAN) REGRESSION (ADOUT ERROR .291h2306 98 50 MEAN) TOTAL (ABOUT ‘ S STANDARD ERROR OF ESTIMATE .53963666 R BAR .7688 ("M0 ILdlI'I LNG) 0 CO .779“ MULTIPLE CORP R2 .607» CASES 51. «on JUNO v-Iv-Iv-I 0330.1 .- o o o OMOIDO «Comm O'I—ooc NLUOv-Iv-I (Dav-«4 Duo 13:" mOdO' I-on d IKJLD 3 I-LDDNC) NH O O . (mamas ZF-va-I 0 2M ('3‘? Huvn! TN ersO‘m muonn UJHNMv-I mm d 0’0 0 OAIO117A 3.609 ELAPSED VOLUME AOV FOR OVERALL REGRESSION OF SQUARES 3h.58369753 57.1A85572A 91.73225977 AT VARIABLE-X(8) C. DEFEND SIG MEAN SQUARE 9.k000 (0.0005 11.52789910 DEG OF FREEDOM SUM AN) REGRESSION (ABOUT M ERROR 1.21592675 #7 50 MEAN) TOTAL (ABOUT CASES ' S STANDARD ERROR F ESTIMATE 1.102 069 MULTIPLE CORP O 69 .61AG R2 .3770 51 (fiche—o wNNO‘N I-v-cmm: NmmNCO QJN'ONM m o o o a II) .IILIAMQII‘ ‘WNOJ HOWNO‘M I-UMmmN a: 89")” (U o o o 0 $0! I 061.10", HokoN (Damon O O O O flown» howUA maw«om ILO‘MM-t O O O O o «no DIDv-IO‘ mammal I—Dhubv-I (IQQON honor)": [HH 0 o o o CUluOI (Nah-In zr-o'un-am OZJLOlnM HIA'N'J‘UNH (flo—«DO‘JN WLWIJMN (10H033N 0.lLv-Iw4NO" OIL. o o o 0 (”MN I 0’0 0 9mm: (Y «.4 I‘IIIIIIIIIAIII. III I ll I‘lIlI' IIIIIII! .IIJL‘III I] \Illl‘ I .|.11 uwrvgv v v W07G7 :LHT'JLU PRICE NOENT VARIABLE-X(A) DEPE AOV FOR OVERALL REGRESSION SIG DEG OF FREEDOM MEAN SQUARE 9.6221 <0.0005 OF SQUARES SUM .06819160 .00700701 .27276638 AN) SSION (ABOUT ME REGRE A6 50 .32600225 .59876863 AN) - h . TOTAL (ABOUT M .08h18535 ‘ S STANDARD ERROR OF ESTIMATE 2 82 mm: 6:: .1. R MULEIPLE CORR CO .6749 N 0." .h555 ES 51 CAS MOU‘O‘ON UJO‘OIAH I-QU‘IDQO‘ NMMv-IQJK KJSJNMM In 0 o o o o O I (I) .III-IIMDON: ‘NMONO Hone-sauna POOH-HBO!“ C NNU‘JT’I (fl 0 o o o 0 DOWN): mom v-Iv-IM I—OM :O‘N (I: J") 000‘ l-LDonMN Odo-I o o o o o mvnc: I 3 (1300‘ch I-Jm (JUNO 0)szka O (umm "'56? OH'DO‘MO‘O UGKNDBJ «HMOJNID mu. Jouc.3 u. o o o o o MFROMU‘F’! (PMNQJU OZMSw-mlc-a HHTNHKG‘ 3 (hf-MD: (N’): mormnomx uvHM'JNNM Qumumufi cu. o o o o 0 him: . 0'0 0 tWN :H (Y rod—0d VA meo OuJZ I—lUZDHJ 2 H20 <0- HH I-xw > MLUQOH ZZH H D N A IKT P0 PRICE DEPENDENT VARIABLE-X(A) RALL REGRESSION AOV FOR OV SIG MEAN SQUARE DEG OF FREEDOM SUM OF SQUARES In D a I: 0 a V s I». m .0 0 d .4 na‘ NIB on N: 0: MN 0° oo .0 Mb. 3 cm ml!" c3)» .00 or 06‘ :4 NM .0 A Z d 'm l: p. :3 O C“ < up 2 O H U‘ 0‘ IIIEY (KC 00? wt! O'm .59876663 TOTAL (ABOUT MEAN) S ROR OF ESTIMATE .00625860 STANDARD ER or MULéIPLE CORR co .suue 2 .A160 CASES 51 MNMNM when-«O 6.8.ka NMMOOO QJNNNN IL) 0 Q 0 O m .JILQQv-IN ‘LIJNNQ HOOO‘MD hUde-IJ own: (C 0 o o o NMJN NQO‘M Nthd‘: GONG: I— o o o o IDMJM d I Qweréo 0 d Orw'jn (KI—OMMN LUUJ'Dv-INN taro-4v. OILO 'DOOO V1433") kCnQSv-I 13:90:)“: boomm: Luv-I o o O 0 (two a 2 OHNNUVD QL‘UOADLM (xv-0.4m fN Tummocna II. o o o o MUM-5.7: thmxcrn" CZNmNm “[pmv-INAI MHNMNH MCU‘L‘IQO‘ ILHf‘ONO‘d) o umfidu LCD» 0 o o . mm: I at DANA? O“ fifld C'xlx ffluzo ZCHZ (H H MHUD 2CH< 41'77'Ilul‘ ‘I..lll‘l 03/29/7“ '7'3.6A3 ELARSED MKTG DEPENDENT VAFIABLE-X(5) REGRESSION DEG OF FREEDOM AOV FOR OVERALL SIG 27.2“16 (0.0005 MEAN SQUARE S 26.78279915 SUM OF SQUAR 5.35655993 SSION (ABOUT MEAN) REGR. .19663296 AS 50 8.8“8A8Q19 35.63128333 ERROR TOTAL (ABOUT MEAN) S STANDARD ERROR OF ESTIMATE .hh3h3316 .0670 MULEIPLE CORR CO RZ .7517 IDHNJOth IUNxONMKID humkcom NwOv-Imv-IO‘N KJNJONIDN HOO‘OMMMM roommaawv a: {NJI‘QJV’ (a o o o o o o 0.x I I O O In UJOchk HOOOv-ION mccoooo C O 0 O O O O v MJQOOd NJJoco mmowxnmu‘ ILDCLOOC‘N O 0 O O Q C och-«0.4m out .4 NIflCOOo omommro ocdmmd‘ GOCJJMN fi— Q o o O o O MNMNMN I I If) (Y omonmsm: 03¢: )0.“th Mbn3HI~Mo wUIoO‘rO‘Cr mooooco C O 0 O O O 0 Duo 0—0 m cmocycom MLJNMISNO‘ #00500: «I 43h MN‘O I—L" :NNNNd NH 0 o o o o o mun-r I 3 MKU‘U‘O‘v-I‘h I—CN ACE-G3 (nZv-oh‘mhcrk aha—7066mm OHhcascn-NN QCUU‘w-I I‘JOWN «Hva-«npm wILC‘v-IONOJ IL 0 o o o o o oulN 00 0-0 M n. O U‘CON mmcr thmmc \rc‘ OZJMNO (TN HIN’T‘H" OMN (fir-or F' nmmm (DURING Oar-.1 I: HG‘K4ONDC.‘ (Immune (MC‘ L'IL o o o o o o In '11ch I O’C‘ I U PIMAINIOK 0' and VA XH'UC’O In: (:(7 pCmZQq 22 H 2 cHI— u: I» 76' >- (0wa 2 zr-zw H N ‘ U‘l'hJUIW ’UJU' U—U l-hn' VOLUME AOV FOR OVERALL REGRESSION DEPENDENT VARIABLE-'X(8) SIG MEAN SQUARE 12.6322 <0.0005 11.91317267 DEG OF FREEDOM SUM OF SQUARES “7.65269068 “3.07956609 91.73225677 MEAN) REGRESSION (ABOUT 59902 .95825139 “6 50 TOTAL (ABOUT MEAN) S ROR OF ESTIMATE 7890316 STANDARD ER (\lk k EFS BAR .67 R MULTIPLE CORR cc .7207 R2 .5195 r: 51 CAS U) JmOhO—IG‘ (UO‘QIDNO HOJLDMNID hOOO‘ONO‘ a: JNU‘JN «a o o o o 0 an: I In In coach-I H0300: 01:39:66 0 O O O 0 VV mmomn enema QSANON ILv-IJLON: O O O O O :Jma-t v-I v-Iv-I .nov-«mn con-3N \Oomoo Inseam”. .— 0 o O o o MNMMN I TI) (2 OMOG‘IDNJ Q’C'CJC'Dv-IN") xI-OKOIDN DJUJON‘H'DN fide-IH—I O O C O O . OILO I—O TIT OC‘v-I'Dv-I ULJQNJN hoaoa‘oh (Iomem I—LDQNJ'MN UH o o o o o cum I (1)020de #0130") (0241‘ ("Ohm ammo: NO‘ OHU‘U‘G‘NN (1:0quer O’HONOOO‘ wumootoa IL 0 o o o o UUKC-O‘IVO' Zv—howdmm OZNMNO‘J Hlp “NIH—I") WHHOE'ALON U,()C‘:|DNN lLHf'nDMJv-I (luv-17400.1 on. o g o o o 'U‘uN I 74 0'0 0 flaw-4am O.“ «Na PIC'J 2’09?» I—uquat ZbUCI «:0 H I—O > ZFC --n The following three computer printouts are the outputs for LDR's found on the period 2 through 4 portion of the composite data set. They are the heuristic price, marketing and volume rules. 3-29-7u VERSTON alas MSU STAT SYSTEM PRICE DEPENDENT VARIABLE-°X(A) ADV FDR OVERALL REGRESSION SIG MEAN SQUARE 67.3671 <0.0005 OF FREEDOM DEG SUM OF SQUARES 037M5769’ 000791129 .7A91539A 2.36921030 SSIDN (ABOJT MEAN) RE RES 302 ERROR 304 3.13836393 TOTAL (ABOUT MEAN) S STANDARD ERROR OF ESTIMATE .OBBQASQA O U03 MULTIPLE CORR .4886 2 .2387 (O'DIDN ELDU‘CD I—GJU‘J‘ mwoeo “Jdv-IO u] o o o O Immn (DOC—3° HOOD (”COD 0 O 0 COO V V V «Nb 9.1.. «Human ILO‘O‘N O O 0 man: v-INO OHM O‘NM CDO‘UHO h- o o o ”10‘ UIII'CHOUN mar: 3 O O O 0 Duo .--0 (I) “‘3 3'") U)'.3(‘JN has: d'IHJJv-I v—ovumm ’UH o o o (I'LLJCJ UJHm ZI—NO‘I") C76 HO hula-I'D?) mHtfiCZO anfi‘o‘ IIIHNV'IU‘ O lLv-IOM ("LI 0 o 0 “HM“! U 'jmnv 0’ ma UMIUIIIQ 2.331 ELAPSEU MKTG DEPENDENT VARIABLE‘-X(5) AOV FOR OVERALL REGRESSION SIG MEAM SQUARE 87.3666A357 190.5106 (0.0005 DEG OF FREEDOM SUM OF SQUARES 175.7332871h 139.287218b1 315.0205055A ssION (anon? MEAD) RE RES .96121595 302 30k ERROR TOTAL (AROJT MEAN) S ROR OF ESTIMATE 7912062 6 STANDARD ER R BAR O7QM9 O Ch! MULTIPLE CORR .7h69 78 “It? C. In In In H (h M I.) MFG“? uwuoo hwmsd NuNNVJ «.mwmn U¢Mmd hwnao moor: O I 0 FdfiN 3PM: CRMWB RQMWF 00. 3F“: N'I WOU\ MJv-I .Tna CHIC)", 5‘... “I DMN umec; FONT“) (IJO'U‘ FOOCH LLJH o o o QUIO I 3' 005V") I-MUnE MTFHEO OWUHrdf OHFIO‘H OCJJCRJ Q’Hv-Id IL} IIILLNO'D LI. 0 o o MVWUM Zhnewv ozurac Hh'mmlf‘ Whhflwm V(“UHJ Int-414’") ‘ZUJVmJ ('0. o o o [All] HI ()0 U‘VIUOI'W JOIJ‘ -h‘Rr JbU p .- - VOLUM DEPENDENT VAFIABLE-X(8) EGRESSION EDOM AOV FOR OVERALL R SIG “905308 (000005 MEAN SQUARE 33.1%2572b0 .: .— DEG OF FR ES SUM OF SQUAR 99.h2771719 201.61199790 301.03961508 SSION (awour MEAN) REGR .66960697 301 30% TOTAL (ABOUT MEAN) OF ESTIMATE 1736 6“ S STANDARD ERROR .61 5? cup 7 .3236 CO R CORR .57A7 MULTIPlE R 2 303 um CASES 335 Uhmooc: WQNF‘O I—mnmo NLLJxDJCvI «ANNNM U o o o o C) In JILMQOv-I HOOQU‘Q mums coach Hooao mcooo 0 O I O on: v v v OMKN 8.18.? ENC-I'm ILO‘C‘OK O O O O (10.40 NMN CNv-IN NIFNO ("‘Id‘m mnNmO‘ F- o o o 0 I303“) (I) 0’ OMOHOQ {it . )C" r? .4 (thank—4 um'omzmn Income 0 O O Q 0 on o I—O m OMHN UILJ'MC 3 I-OxDth-I (IQMOJN I—OQMN—I LI..H o o o 0 (Stud 3 U)\O~OU‘O v-v-qu-o U‘Zcr 3.4m o moO‘O 3 OHerfld LKLLDN'JN Q'Hv-IU‘ADLD Manon-4 LL 0 o n o mmxm 3 Zt-ram—In OZCO‘HC’ Hth-Iff‘an ch‘u‘cr D (f)(‘v-(’T‘U'VO‘ IIIHORINIV 0U NPWVJ L'LL o o o o (“LUV-I 0’0 G ”"3"" VAR (DI—X )NSTA 0 [Al The following three printouts show the analysis of variance on bias relative to the best heuristic LDR's across team final rank. They are as follows: 1. Best price LDR on the composite sample 2. Best marketing LDR on the composite sample 3. Best volume LDR 0n the composite sample The next three printouts cover in the same-ordertthecthree=ana1ysia ( of variancesifor bias relative to the best method 3 LDR's across final team rank. UMIUDII“ (COUUD ELRVDCU E G O R Y C A E A C H F O R S T A T I S T‘I C 5 BP FRANK unnd film: «“3! DFI (”flu IfldI HP IL) ow: DC) U D u; U) 2 DC) m». (P' Gd: 2 (3' kn) VKD U) u) M a D 0' (D m, OT 2 «I 3 k» m d *0 O p. 2 u) 2 ul m (J 2 p. I u) 2 .3 fl .1 u) d .L > I 3 2 FI X < Z 2 d u) I k In N. h- d \D o C! I w a' u_ I u) D T J 3 q (n > I D t H 2 PI 2 A .4 J <’ m u: > C) V 31.050499 .21061305 37.5582636 .09635130 701 6705M2261 ochstQUHrc dWhflDOfiNWSW ovuu~oomwn¢ unronhaaqu:« :CHGOONNJCnO (VJUKmanhim .OOOOOCOO Ionmunrnocwuu Juflflchdflfidflh .300mvravunc (”sfivflrmvflo3 ouoaoxova1m bficofiflvcflhod fidumrnrmcu~¢ Okaodkauflhfin .«vnnuumouum OGWJAOCWMVH IDONth33¢Mnh Inounomuuhsm .30rmV%M6MDm tadNanNvflum Iv0h4133FHvM NOWDQrkflDHvI 00.00.... Ionvnm::UM:: OJWHVJJMvac «ocmrocmm «NmNmJNNm v"°N"L3NUVGO Numaanrot cacaocogo 0.00.0... cowmdkaownmc muuawaunhhdn .«snanxmdh4d nwwvvowunaq ounn.n~wdhom IDNNHWHQvMfim Nano®¢na¢0ns (JOCRJDdVMDd 000...... ~910MOFKF3540 QGMDQINH\NU\ Inwfiukth¢UMO FJOBOW\MUVOK :mam©:cmu mimc‘d‘quno («mnuquvwnm MGMM~NMHL30 I O 0 O O O 0 I O \OOUWMDQCM\¢ TH )rfifi'DOO 3') ’3 Crmficxjfi;uao r.rfir ) WQ’jrfir-‘Cj >000200fi00 QCMDQuLDQ;M3U acrfififiijfi‘wjfi u«-......... IUHAHOJUMONaxh p, d L} (ALLONS A SEPARATE MEAN FOR EACH CATEGORY) T A B L E F V A R I A N C E O A M A L Y S I S RP FRANK F STATISTIC MEAN SQUARE SUM OF SQUARES .262 1.29623 .05730366 .A5693065 30.5920682A 31.050A9910 'THEEN CATEGORIES .OHA20819 692 700 CATEGORIES THIN ITAL MULTIPLE CDRREL .121507 i lull-III) \Illlll \Ill. 366.376102 UV’V’IIW LLOB‘V c A 1 E c o R v “”"rJL" 3.5129 SUM OF SQUARES 366.393u278 .723u6202 E A C H MEAN INCREMENT O F MAXIMUM VALUE- MEAN ’.00A67577 -A.1A9576 S T A T I S T I C S FREQ 701 UM -3.277713 MINIMUM VALUE- (OVERALL) auomw:oou Nswwmmocm ONQONJMwm onuqxdmso bamwommon owdmomowo 0.0.0.... hmOmeMQN NNJSOIOMd «memmnhm OGQHJOmsa OmNOWNOdQ MCQJJSKWJ m33000m4~ md3N¢MOMM NWDJCONHQ WMNNQNOF: 000000.00 monommnmn contoomm: BN¢3quHm mwmonmcmw Mamh:mmmu MohNomoo: DMNNNNOON 000...... omommmrcm NN::O:0Md mnwmmmwom OJMOJmWJM mosmddde moommnmmm MMNCDJtoJ 000000700 2 0.00.0... OJHNm0303 :NOGdMomd ashomamoo JODNNMNNm NNJmJDmsk MQHKJfiCMM gmwnnm333 DO DOD Jv-I'DO 0.0.0.... I I II a:~mmw:~m womcchhhm «cm3mmmom ucnmmhmmw NJMOdDmNm monmm73~o Mwnmhmoo: ONm3000N: 000...... MNN0040 N I I Id I anfiocfinw OOfiGOwPOo ijmmqfiOw >Oufizdon0fi dfluOuJucoo Ooononhfififl Qooooooooo UHNM1mONCO- p d C .621 R .77965 .09b513 F STATISTIC MULTIPLE CORR (ALLOHS A SEPARATE MEAN FOR EACH CATEGORY) BM FRANK MEAN SQUARE .AG909696 .52A71666 T A 8 L E 692 700 E V A R I A N C 3.27277588 363.10532609 366.37610197 F SUM OF SQUARES A N A L Y S I S D CATEGORIES YHEEN CATEGORIES [THIN )TAL .‘U U 0' -h.-‘dv 1-. bh' G 0 ° Y A L A C H C O 9 STATIS_TI >y (722 'u'” TL}- IN?" (“0 .9752556h 665.786A97 SUM OF SQUARES 710.7235007 5.SQCB MEAN INCREMENT WAXIHUH VALUE- «can .25315795 -9.311512 7L1 SUM 177.B8h’58 VAL”;- "IAI‘A'W FALL) ("V > V O C“ L" uoonuumsmna wnommokmm O‘JdIONNNNO :OHMMODNN \COU‘NJ~OVJU\~D JMHOMQOQN O O O O O 0 O O O accomacunu mnmmmmsw: H “\JMCDO‘NJMO ntwnd‘Fh-Dmfl‘ LDKO‘O‘DmCHhM HQO‘DO‘NU‘DLO O‘O‘NN30 ct 3‘0 NNKU‘UMDKU‘: dJJJ\I\OH’)v—I© mLDFflCMv-IOHQ 0 O O 0 O I O O O «av-0'4 NNM-«OO‘DNO \fsCLhNNv-«firufi moNr’MDO’ (\JN‘O Mv—IO‘OMdv-im’n hm70MN¢rm HO‘ 13"”:QO \DO‘NU‘HHJU‘U‘ O O O O O O O O O :JMNrmJJ’N mmommncwm “'4 '4 mmd‘nO‘v-JMO‘N Namf’KT‘JMxO-d U‘LDO UMP" :v-un dNMMWMNHfi HLC fiQOOuhIkN Nwocnuour0v4 O O O O O O O O O «ca'JJxr‘vhv-cwus AJNU‘IflLerI—I)‘, (ij‘d‘d‘rr‘ahm «J (MU‘c‘IMN‘DLJ \CthflJkLfistON '4 J7‘CI‘C DLJJQ. J’T‘ f‘fifihfofil") ouNH—UNOJL“: O O O O O I O O O 3.1mmr oar tr m¢cmck~nm amounc'r’nCnc 'LMv-omt- ho-ao r‘ (\JG’K :JNC 1" lrl.’ 1)er .‘I‘H‘ {\rr U‘r:!’"")L"d CRT dxf tlxrxdkr-rx O O O O O O O O 0 MN'- mu r-z4110 (\mer-am (’.‘C.'¢’. k-)(->' ‘L“"‘)") ..)'_)"_-1‘~ JP‘f'."‘fl' )"9 (\r\ “,(“M'fif 3') ‘C '3 )("")(.'(-rf) QT.) fig’k ~_)&JL. C) rfi-‘w- J'flrfi’f’) -fimcx . O O 0 o o o O o Luv-INMJURWNCU‘ .— d O EGOPY) ACH CAT . b h- HéAN FOR ‘ C ‘EOAQAT S 0V E T A R L E (ALLOWS A “RANK V A R I A N C or V A L Y S I S V- XX VL" HH £11..) I'L') IJHJ “1" CL) F STATISTIC PEAN SQUARE SUM OF SQUARES C Cu: (‘ AN OH :0; C O‘DJ 03(3 000 o o o CMON NJQ 06‘0" th-IN LOOK v-‘IMC‘ dN 10.13560251 1u.~zu?uq"5 .935A66‘1 692 7u0 6h6.65080A72 395.756A972h CATEGWDIES :TYHIN ’OTAL A din MULTIPLE CORREL 14.033.93.903 .169533 REGRESSION SUM OF SQUARES .05652“20’X(51)l o31§6183h+ STRICTEO TO A LINEAR TERM'ONLY,[Y(~3)=- p ,. R IF WI- Dd ZI- <0) HIL HIL 20 H> U»- H 0.1 XH m C0 0 Odd r3 (LG 0 0.0 0 «UK c O. V w H m 6‘ '3 IL 0 m N \O 0“ k C!‘ an I— o M (Y a.) Q a) I: N (I H LL] m 3 C V4 0. 0 <1 0 C‘ 2 d y. W I-J'ID ZMN Illu‘J Hv-(N (\Ul". h‘ono LLv4U lL')|'3 03].. CI L) Mod (1 (0 > y 7 ya 70' cu ‘— (I) Z O U LYSIS s r A r I s f I c s I r! 111 COMPOSITE AH PHAS C A T E G O R Y E A C H F O R S S MAXIMUM VALUE- .8599 -.677932 I MINIMUM VALU (OVERALL) MEAN INCREMENT SUM OF SQUARES FREQ MEAN SUM 5B.15%956 .21250717 31.611507 35.795727C .07725885 701 \DMONIOMv-IOM NOMNNO330 NOMOU‘NKKA "nurmcwnuu: CNLDOQCJOHN lawnmnflmnwh O O O 0 O O O O O NMMNMMU‘JN 'NQxDOO‘HxDO‘v-I huancanJQ NUMI')I\MU\\DN Homtfld‘t’lfillfl tNO‘V‘LOO‘uADLD whommmmmxo Baryfiorvt 5 ("am FIHNv-INNNNN O O O O O I I O O HOMU‘NU‘JNQ OOJK‘OIDLDO‘O‘ NO‘G‘G‘NL‘OC)H nonmmommm O‘COOQJHOLD om 3NN\OL'JU‘I.D O‘va-«DQv-«OM O O C O C O O O I NMMMMMOJ: :Nosmmmcd CJNC‘Jv-‘UJU‘NO Jva-I-JLONNQ 6‘1NH00‘DO‘N onOv-INc‘flVQO‘ Quuouomoo O O O O O O O O C I I I I I “‘3601’3d'fik :mqnnmnmn :NomHONM’XjO‘ “HMQHNNJH KNUlenanv-I chpLDC‘IOert-a \DxflJtO fwfi‘nfs o-DOLjoov-Inv-I O O I O O O O O O ~1‘ J NMM O‘ J’h-lb QCNDQHWq\NU\ .Tfifi‘fiv-IMflm,.g b'\U'J‘f\JO"Jf’)rOf\ fiHv-IH 1"“Kkm mvrwnm fIOr-smqp (Tc-:1: nvnNu‘)‘ 3m \CmNJmLOerrsm O O O O O I O O . IF-U‘J'Mf‘ .3 \L‘thC" OCDLJ'JLJUIJ'JL’) L-)'J(_J'_)'..J‘J'.J--)'_J I')1)"‘)v ) Jh')"'3 )n-ar'vficvfi'. )r‘) 1:7) 'Y'v'wr‘s-a'sfinc-v‘a OQQLJrQIJUQCJLJ Q o o o o o o o o o (Ht-INVOJ’C‘ROKQO‘ .— q 0 AN FOR EACH CATEGORY) ME V A R I A N C E T A B L E (ALLOWS A SEPARAI O F A N A L Y S I S LB AN as- LAC-I mun F STATISTIC MEAN SQUARE -C C.) SUM OF SQUAR '03!» Mr": 00”) O O O \DHN M00 331‘ ~JH” HUM-I o o o NOv-I QQN HtJO (xv-ND 3N6) mhc.) MOM") O‘Nm 000-.) O O O v-IN .75077725 «no 0.4 .4-0 mm n1-» ma kn MM 0 O LGOPIES N CAT EAR R o0AA596A3 692 70 30.36072966 31.61150685 CATEGORIES THIN ITAL 0 MULTIPLE CORREL .15ui11 06926“73‘X(51)l .033010160 AR TERM ONLY,[X(55)=+ O TO A LINE ESTRICTE IF R p- p- - REGR CORRELATICN \ ,- 90 SSION SUM OF SQUARES .37972106 5 J SIMFL .1 .00“ F8 8.h966 TB 2.9152 RROR .06317605 STANDARD FQANK CONSTANT 0h/09/7A PAL”: C A T E C 0 R Y E A C H F O R sranstcs ANALYSIS .- .- b- III composxt PHAS “A \DH mm .75772538 “01.903022 SUM OF SQUARES h06.3068220 3.3585 MEAN INCREMENT MAXIMUM VALUE- MEAN -.07925653 -A.187759 FREQ 701 .- - SUM -55.553823 MINIMUM VALU (OVERALL) socmomcom mONO‘Nh\NQd :JJLDMNOMO IOO‘NNv-Iocuc O O O O 0 O O I 0 (0303056400 «NMMB mums... ecummasormo O‘O‘HfimeJQ DNONKNJMN ”MIDNU‘IH‘I‘U‘O‘ JNLDJMJJNN \DQMLONUHJJUN :Jh3'rrmmmm :mooc‘aoacom O O O O O O O O O vI 40001.1()de Nmommmd‘rxm No.3'ngouv-omm NHJONOQNO‘ omo‘u-«mmmN QQNNO‘JNMN mommdmamm O O O O O O O O I Oink JO‘KU‘JMO v-INMMNanCOv-i v-Iv'Iv-IO'UQMOG‘U‘ NomNerqu.) O‘ummO‘HO‘O‘O QIDLflouHMO‘O‘J moat-4:10.40 Ofl'JOH-DIGNC’ I O O 0 O O O O O MIND tMNO‘JIt) NMLO om'oQHm mJNm'DCONt—I erJCmNuCNIC NNONonNw 11631.4( NS‘VT‘M OJNW‘HO!NNH‘~O O'JOQUDv-INH I O O 0 O O O O O :3mmmmqsm poncmNKNm v-INMH'V‘thfl‘h- \DNNwfi‘v-«o‘nc O‘lr'r‘M-FNG‘NM ramwmsmrsr-N O‘DTOI‘JHT'fijv-I rs HO‘HNUNOQ O O O O O O O Q 0 HNO NILMTOU‘ I I I v-INI I I C)¢3I_H’J~.)CN_')€J'2 I...) .JL) I.) J!) )I) CJ'3(3C11_)C)'T)F')'.J >61 C""_"‘)")”) '1-11") Q’q'flfififi’J'fifiQ OQDQOUL‘JOUJ L9 0 o o o o o o o o IIIHNMJU‘LONG‘IO‘ .- <1 0 AN FOR EACH CATEGORYI F STATISTIC LBM FRANK (ALLOHS A SEPARATE M SQUARE T A B L E MEAN C E V A R I A N SUM OF SQUARES O A N A L Y S I S \DNN rIQU‘ v-IDU‘. o o o a”!!! #0") mom: m1: LCM-n O O O as» MN") KOO v-II’Ora O‘OLD LhMO mung 30:0 O‘HJ‘ v-IN 7.54873331 NO‘ 0" Mn cm W") (Jr) CKC‘ HM o 0 3M 'SORIES AT: .007 R .137049 SUM F8 MULTIPLE CORREL 7.3613 REGRESSION .03076973’X(51)l TB -207132 .56937672 .0677007h- ERROR 692 700 .0113h091 STANDARD RM ONLY,IX(56)=I . y. 39A.35h68636 “01.9C3h2188 AR T CORRELATI “01021 L E q IMPL ' D TO A LIN Q b- no ORIES STRICT FRANK CAT IF R CONSTANT ITHIN )TAL ANDLYbl) ALL bUHP‘UDLI '. rnu.) sransr'Ics C A T E G O R Y C H In] F O 7.h691 MAXIMUM VALUE- '8.771779 I ¢ “ - - - MINIMUM VALU (OVERALL) SUM OF SQUARES MEAN INCREMEAT AN .503Ah383 FREQ M SU 352.914123 1.21A0h535 1031.73b206 1209.A067227 1 'J 7 mNOOQMJO‘O‘ mOMJNdch‘ Naomm 7.1M: unscammsm “‘O‘HHHMLDLOU‘ NmHNMv-IMNC O O O O O O O O O IDJCMH-SNC'IM :mmohkfidk “V‘Nfl owvxomhk: mmxov-(momom OF‘MUNJF‘LRNCV" O‘JHNCT‘LDMNJ :cwfiJMHmO‘m New-ameo‘m JMHHJC‘N'JU“. NICO‘DJJNNv-I O O O O O O O O O v-Iv-Iv-Iv-IHv-I O'ONO‘MHNNN J‘DNU‘d‘NInO‘N v-I'D'VN’DMQ’IK") «)er ranmmmm mmc‘mmmnmo mNQMJLhJO‘CD 0‘ (fiv-ILHW J Ohm I O O O O O O 0 O nadmkmmo‘m momcawcom'o-J o-Iv-Iv-INdv-I \dekmonMO‘O‘ NO‘HO’INU'MUJw \omawmiomso :NQNHJNOG‘ mommwm1n3N No-Iguoaumm O O 0 O O O 0 O O Nrsm txcdkmm :va-IHU'HD- yo NO‘deVD-arON OJQJN 160‘") N «m «mutmmd QMOHON‘DLDG‘") J JGINJK 3am NMU': SJMJON O O O O O O O O O .4 .1 :NMMU‘ :sm .1) mcmmkhrxm :rr'v‘Nfl‘MJkk (“ON “'0'"! 3'.) gmnmsmmkm (om ffiJ'f‘nv—Ir‘.) (Tuxmm 1' UNION or. {IIU‘NOVrNU O O O O O O I O 0 c:1r¢>a~¢0‘n,f\m NNJMMNMINJ UIJIJ'JlJuJUCNZJ .JIJ'JLJ 3k)') )'_) (J'—"I1'..')' H’.‘ J") J >(.. )(flfiji'I' \»'1!'\ J fry.» rfi. Sr 1"! "5 ‘1"‘7Iffl OQ-JxfifDLJIJLDUi) L9 0 o o O o o o o o hidN-‘OJH‘LONIDG‘ CAT EACH CATEGORY) MEAN FOR . p b V A R I A N C E T A 8 L E (ALLOWS A SEPARAT O F N A L Y S I S A A- NH (Am F STATISTIC MEAN SQUAR ES SUM OF SQUAR MO'D ("Ham Dav-I o o o numb QCM MQN «cow mom I O 0 NNv-I Nmfi URN“ wru~ ~n~~ kqun (VHa 00¢) ana O O O J‘DN HN 33.62191C95 ‘Ch (\le‘ N") «7' ) H ¥ 2 P—d 20’ «u. '- In 2 O Q The following three printouts show the analysis of variance on MAD relative to the best heuristic LDR's across final team rank. The order is: 1. Best price LDR on the composite data set 2. Best marketing LDR on the compoSite data set 3. Best volume LDR on the composite data set The-next three printouts cover in the same order the three analysis of variances for MAD relative to the best method 3 LDR's across final team.rank. -- R E A C H C A T E G O R Y F 0 S T A T I S T I C S ADP RANK .8172 AA Dd 3m MAXIMUM VALUE- .00C092 MINIMUM VALUE- (OVERALL) SUM OF SQUARES MEAN INCREMENT MEAN FREQ SUM 98.30k236 .18h28h9h 23.772659 37.5562836 .1Q023A29 701 ”Ohwcddhw IDJU-INNODNN \DJQJMWOU‘ 0mm°NH00o whmhocoom JOMMOmmm: O O I O O O O O O NNNNNNMNN oscommwmo HdKSv-Immm-fl «wonoMOO mmsmmmnmw nmmodanmo NWOOCdddM fifikfithQH ddddddNHN 0.00.0... omnmoomwa GOOH33®mN M®m®0m43M soamommww Gdnwmkdmm NQNDJJMNM NmQCHHOHfi 0.0.0.... nnmn::m:: NM3Nd3rN: OMONNJCNO amwmcmmoo cmsmWOmJ: dacaoomom ooouuouoo 0.00.0... IIIII OMSUM’ONMv-IO‘N O'DU‘O‘FNCHDC.‘ NHO‘QMKNQN NONU‘IDNIU 20‘ “NOVIMNHMQ NJOMOQOJt NNMMMJIOJN v-Iv-Iv-Iv-Iv-IHr-Iv-Ifl 0 o 0 o o o o o o :JNMMO‘ .fF-U‘ QQCQONNNLD W‘OIDU‘QUNDO‘CI “\MU‘NMJI‘OGG? SO‘JOHJONM NIJNflHMNO‘ \ONLD'DHNGUWH N—de‘Mv-INHID o o o o o 0 o o 0 OIJHIJo-Ide-IO‘ v-Io-Iv-Iv-Iv-Iv‘v-Iv-A manor) )(10'1 'm a") Dances-‘3 C‘fif) 3‘ )Cl ‘011 >rno'3 :3 3000'.) GOODDDQQD3 ofififinn") 'I') U o o o o o o o o o (“div") 3 IRON 00‘ .— q 0 MEAN FOR EACH CATEGORY) T A B L E (ALLOHS A SEPARATE F V A R I A N C E O A N A L Y S I S ox E2 ‘4 AA OH 3m F STATISTIC MEAN SQUARE SUM OF SQUARES .795 .63885 .02178599 .17A2879k 23.59837071 23.77265865 ITHELN CATEGDRIES .U3H10169 692 700 CATEGORIES THIN )TAL MULTIPLE CORREL .085626 -.--o C A T G 0 R Y ABM FRANK b.1h96 E A C H F O R S T A T I S T I C S 1AXIMUM VALLE' .001266 MINIMUM VALUE‘ (OVERALL) SUM OF SQUARES MEAN INCREMENT MEAN FREQ SUM 3Q6.569558 .52786880 195.051632 366.393A278 .69939309 701 JIDNIDIDIDNv-IN “MNNDDIUIUID NO‘U‘VDNMMQQ NO‘U‘O‘NNNNJ v-IO‘O‘va-IIAQID NIB-TJJNDJN o o O o o o o o o "NCU‘JMU‘QUI dds-INMNMv-I NOM03HOD: “JQKHNOMN BM00300mN mmswmamam :cQNJmJNN Omhhaouwnm'u ochmJJM®H :msmmmsan O O O O I. O O O mnuommnwn mammoomm: kmcsdfdam ommonmrww MHCIKJ'V‘U‘mv-I MONNOMQCOJ' onNhthmh O O O O O O O O O omommmsmm NN::OJ®Md adomssmwm QJdmmNoNo JIDDNDJvIN'D Hmdfl¢OJNm QONQHV‘O‘v-IN cv-IJQdQOOv-I O O O O O O O O 0 II I NQQw-IJQQNN OO‘O‘V‘NONJJN WHCCO‘Odbtk HIDQU‘JNO’NUN 00314311):fo NJDJ‘JCJWCONfl H'DV‘O‘OM’OH O JMIDJIDLBLBIDM o o I o o o o o . 33NMMO‘JNLQ CQQ4QQNNNID Chmaomkoh @OMJNmnofi omnamnmom tmmmdmmflm coedohtmh OONdem3N 0.0.0.0.. 3NNHUNM®J MMJJmJJMN Gear-)0 3006 ”7000 3'3'3fl'3 rj )(Jr .0 ,,,, H v >r:v )O'J-‘J'.'JC) 3 a at.) gong-.3301 0'30 DH’U’D'fi DO U o o o o o o o o o UfiNMJAONDO .— d L‘ (ALLOWS A SEPARATE MEAN FOR EACH CATEGORY) T A B L E F V A R I A N C E 0 A N A L Y S I S F STATISTIC MEAN SQUARE SUM OF SQUARES 0051 1.9A093 .53507833 h.28062663 190.77120569 195.05183231 GORIES ITHFEN CAT‘ .27568093 692 EGORIES CAT TTHTN ITAL 750 MULTIPLE CORREL .1h81b2 372.701759 .72967875 6 O R Y 710.7235007 A T F A9 RAN 9.0115 SUM OF SQUARES C O‘HHMOMMQH O‘CONJNNLDN o-zmomomuo coma me-JO <0.0005 F8 21.7939 TS “.6681 E A C H A“ :v-I JU‘. MEAN INCREMENT R O MAXIMUM VALUE- OEQW90975 S C GORY .0C377A .- g. . Dauaswr CAT roan 731 TATIS‘TI 1) S SUM 936.775A31 VALU MINIMUM RALL) p — (0V O‘HDfliWUDMvI ONO‘NJmJMv-I . .00.:0...0 tub OMNJNNIDQO Od .«mnouwnom Zh- d v-I <0) PI- 0 ZUJ H“. III II. HIII A H“. O > 20 Id- 0. L‘) [LN-4 O H>- ILO’: cmmuaocmun¢ (D m»- Iqu) NLJannwafm Ifi hI (I d :JU‘ :NmHHv-I 0- 0_j QC: MLhIMOwOO‘OUMD <1 XH mo (0 \DNNNC'CG‘v-INOJ I.) 0:) mm 2 t 0 mm ONHCJNCO ff." (Yd uoN Cd can v-I )P’mv-IVOTOV‘I I OK no"? HZ: <31) MJU‘HOv-ICNO‘ID 0 00 6'0") I—C’ I: 0......... 11 Tax 0.. dU) c:- uJ O 6C! .1 V‘N VV w G.’ (r [LN O N C). D. Q NR'O‘ O .4 amom L) m z 2 I- on'm N D hnmhmow¢MHO d m "NV: mar: m ¢MMDNQNH3HN‘ (U H hdrd .1 M mnmwommwa r h 00. Q n 2 ~h+ofi~uaama~ q IfiHwI *4 N O fi'nJmMNmm’“ m I— N I— . H .46 .7130.)QO I— V) .1 (I) (DO‘NON-Iv-IJd‘m a '3 I- U‘ 0....o..00 (Y m t A W .3JNHurmnrrn1 d a m RWMDQUVVONU‘ O U U “A H .I’ w h) (I) >¥ X 0! 6’2 0 <1 dd LII C‘NO‘ O v-I a' I! ouuq m N (1‘. IL (1 or: o N 3‘ D ONCO‘ N \O :saunvcwmoc C (3 out: I“ 3 .rmkfimmm'nm .1 (A mix... 0 c3 «\OO‘NmUJO‘N .1 N00 '4 m ‘fi—IM‘H 1.4.4th <1 2 0mm m G TO‘fiv-INOJHNI» V d 0 0 0 . 0 Nv-ICJv-Iv-Iv-Iflv-Iu i] Hv-I 0..0cn.... I d 0 I I At- 4’ u!.1H N :m u . J k F) (D vv M xx m <1 1 UV) 0 0 HOW%%NDHUM\ F khi “D Q (V O P cr- :Nv-«Oc .1 1°: (mu 0“ c: 4 Z MCJuancer mu on IO N n ma \LJfiC mmuwmw J .14 L111; A HN unnmac‘ ’CVOH 'zJ C'ff.‘ cm. db 3 00‘ anIv-«M'nrun .Jc’ dd 1’ 0"!" J'Jrj‘hdo-I ’IN-O ’_) I—JH v LL. N JWFWCKTQN 1% x MCQ .0000.... 76.“! H HUI)", >> v‘ c' Ix m 0 Cup... d [I or. \0 Ln >' (3’! . I— Y I» 3 m _I 3 PH Z)- d cu f0 m 2 ZC m0. : C‘ x f\ o (Du 'Z CC) C h~ to v. H - (.3 U -) ’7‘ o z .— J ibulV‘V'C‘ 3km d “31' J 0: IN (1' < nay¢occrht~t~th L1.— LL . 0 0 u: .1 > ltd O m IN A] I»- 'U (V) fl 'h N N 1' I") m (Y (1 I) a O 0,-41f-lr’0fi'm'f‘m LL m {U L) O on \mnnx ~JM (\no 7 I" v-‘JLL‘v-‘(TL— ”THC C U' "’3 H LIJ'I’I‘» Mn‘r'" wir4v—4 —.(p o’C’ .J .J v-I 301-4th OJT’ENJ (END (1 . «wrnrcrrCuAJ 41 d : .00....00 (f: T\(_'1 H f(nh«h~tUNflJ (J O (n f’.1(f‘..1\(\'.‘rL’ J'J H Nv-I *- . O (I) d 'I O H m >- I- V (1‘ U 4 u: ‘ m H H H 0 fircu: (3')"): '3 a n; n I— NC "Wflr art-Cu 71 f‘ O 'n .r vrrmcv-wr r r. 7 I.‘ I‘) u' >C‘;J "firm’w 1""‘1 u I. l:' 0 QLCrMUMJchD d On p. P nmfi’fir‘"‘ wflrfirfl (\ <1 (r [I c»....:....o uJ? 0Q U H UIHNT'JJU@F‘-Co L.‘<1 QC. 0- IYH 2mm. 4 Ta tail: 2 0 Cd l. I—P r— -I (n) :14C>ZI a F- I- 5.. U! H 0 .01081126 STANDARD ERROR vno 51 FRANK CONSTANT 09/09/76 1 HUI— { ANALYSIS 'III COMPOSIT PHAS STATISTICS CATEGORY E A C H F O R .8599 MAXIMUM VALUE- .000032 I n- ' - - a MINIMUM VALU (OVERALL) SUM OF SQUARES MEAN INCREMENT AN .14567716 ME FREQ SUM 102.119687 .17267163 20.919221 35.7957270 731 damn-oommm mh¢uro¢nmnm QNONQNHU‘N (Du-«O‘QHNO‘v-Id‘ MIONNNO‘anO‘ oucd‘dv-«DNH O O O O O O O 0 I NNv-Iv-INNMNN 'O‘MQNO‘JMO‘LD HmKJONv-IJMM LhUnJOITO‘ONM U‘QG‘U‘U‘JCCNI’I \DMNHQQI‘HC‘ OHoMuNva-I mommmxomtxu HHv-Iv-Iv-Iv-INv-(N O O O O O O O O O VILJTOUWNLHJNQ C3\OJN\C‘\D\CU‘G‘ Nmo‘O‘Nonrav-o DONNWDG‘NO‘ O‘mrvnn:vhou\ \Dmcakksotid‘u‘) O‘mJHOQHQM O O O O O 0 0 0 0 NMNMMMI‘DJ: Mkkdwm'wfiw MJHI$N‘JP~UI\ MNNO‘LJNJ‘IDN oOhNO‘JmNN J v-IvtafijliJCHON)u\ COGJ'JU'DLJUIJ O O O O O O O O O QJNMBLOH:L2‘ .amh-nmthxao :mmmnmmo: JNHC‘UKD twin vomammsoas Inmaomxcmdaooo (jfiJMRIMJ‘mkm v-Iv-IHv-Io-Iv-Idv-Iv-I C O O O O O O O O J-tNMMO‘:r~Ln mmmaommrstsm MYBN 90M fkk ")Hfimk’rxf-Hd O‘H.TK.KC‘TETI"\ QC‘IPIMNv-AHT'W tMU‘MDMO‘Iv-CH QILMHMJ’JNO’ . . . 0 0 0 . 0 . GD' )q-II.)v-‘v-IM")L_\ fidflflv‘vIv-I" LJOQIULJLHDCJLJ LJ-J'JJ- )'.’\_J'-II ’ (v.3! ‘:,'.—)'JL-).,)"J )-r_Hj'_:v3")I N ‘rfirj Narfil‘fif‘firfi'D-‘I OLJt‘JIJO'ULJQ'JLD o O O O O O 0 o o . lIIdNM»1'fl\ONC‘O‘ p. d U MEAN FOR EACH CATEGORY) V A R I A N C E T A B L E (ALLOWS A SEPARATE O F A N A L Y S I S A- :H 011‘ F STATISTIC MEAN SQUARE ES UM OF SQUAR S (Pom v-IC)r‘1 000‘ O O 0 who: cam-3 mono Hmo‘ '0an O O O mood MMO“ de QO‘N «No mm... «no.4 can: 0 O O VIN .545A9877 :00‘ MM mm 0"“) 5n ma (too :0 O O CATEGORIES LINEAR TNEEM OTH£< .029AA180 692 700 20.373722AA 20.91922121 TAL E .161382 MULTIPLE .0102391A‘X(51)l .09677A66I 0 TO A LITEAR TERM ONLY,[X(6A)=+ a - - STRICT p. p — IF R REGRESSION SUM I- Z [LIA F4“! 00'? H5! II. N lLCDN IUIIIRI OLA «.9 Cd . 2 ZC" OU') ORRELATI "\ I i .1A83 SIMPL IL”- 0‘ ZI- <0) 0 Hu. HLL 20 L3 H) (DI- H 0.1 XH In DC!) o 0:"! 0 mm 0 (LO 0 (or O a V (:0 O J’ m d) lg 0 m v-I O v-I C) CD 0‘ r- 0 M 0! N O 0‘ (Z v-I O! B u: l“ N C) c: a: c.) d 0 O 2 d .— U) PLO—7 ZIH IIJJC‘ HNI") LINN Han LLfl‘a 11.66 ”J 0 0 O (2 No.4 d m "> Y Z I—d 70’ -jr'1"‘r.,\r‘)v‘\-1I-L‘v q’,-,P‘Hlfiflqv)I—§rfl CL)OQQ'J~JLJ.JCJ L3 0 o I o o O O o o (JIHN303LDLDNIK3‘ *— d 0 EACH CATEGORY) MEAN FOR I- '- - (ALLOWS A SEPARAT T A 8 L E E p v V A R I A N O F S A N A L Y S I (pa (om ”v XX (DU) HH (A’ll' .J.) C" D dd HH 0 ’1’ dd >> F STATISTIC AN SQUARE - '- M S ,3: \‘- SU1 OF SQUA HR 33.5779163L 0'1) \0'0 03'? (gm 3: 0‘1) om Jr! (A U ( (D I” ow' dw‘ Zluhl (11H?- 1J0 .85833263 692 593.96617628 627.5%“09A62 EGUPIES CAT THIN )TAL 700 MULTIPLE CCRFEL .231316 .06290961‘X(51)l .5150897A+ TERM 0NLY,IX(66)=+ an; 0 TO A LIN ‘ .- u- QESTPICT IF COPPELATI é .22o1 SIHFL' ES 30oh09b7666 REGRESSION SUM OF SQUAR u»- 04 2)— (CD HAL IL. HAL 20 L9 H) (DP- H 0.! XH (D Of!) 0 dd ('9 (LCD 0 (LO 0 (C! C: (L V '3 N O‘ a) m (L o m M M \O \D m 0‘ .- o In (K (D O N 0!. \D a: 0" m :o M D H (1’ <3 <1 0 C1 2 d .— (I) t—JH 2N0 (”C‘U‘ H’OCJ QJO‘ HIDN (.Lfl'!‘ u.'r\r3 LAJQI O 0 Q’fiv-O d (h > Y. Z i-d 7"? (111. .— (I) Z O U The following three printouts show the analysis of variance for .rMSD from the heuristic LDR's across time periods. In each case it is evaluated on the composite data set. They are in the order composite price, marketing and volume LDR's. The subsequent three printouts show the analysis of variance for ' MSD .;.from the method 3 composite LDR's across time periods. They are evaluated on the composite data set and have the same order as the preceding tests . 1Q.501222 o1h393065 A T - G O R Y .5739 SUM OF SQUARES 15.762b619 C t A C H MEAN INCREMENT R O MAXIMUM VALUE- AN .QQZQISQQ L. I. M '.%67935 1 EREQ 79 u -- a S T A T I SIT I SUM 2“.73h310 MINIMUM VALU -L) (OVERA mhmouors: GO‘MCHDN ad'ooncco who‘samm AMQNHAN cmhkomo O O O I O O O NO‘NNO‘NQ Mv—hfiw‘fih’fi \DMrjh O‘C'L" «ammo‘own fitDI‘O'NN”) ofimmmma (70:00th 0 CODOOv-(fi O O O O O O O O‘mO‘JO‘tjt moxooama :mm whom: d‘NmsOv-H": U‘NQAU‘ 30H \ODCDuC‘J—MV "\U‘NNNMN o o o o o o o 0‘ NH nxJ'nJOth. ode‘ (puma O‘Jan‘N 1' «momma f mN'Pox.) 1N0 Nfinuuow O O O O O O O nmamtorvfm Jam 1 iNN O‘F‘W‘I‘NHPTN 0‘0 \ONJr-N "‘08 1 30”?! nowqu MN U’v—(Hh'fl‘ 16) Nov 3;) ‘cv O O O O O O 0 ammo? nd‘ LA." )O‘C #10“ HHH v4 (Ev-«I‘JMY’H'I .pc Mom K N MOIHNd‘UJ‘ nmmk 1 1““ mu ammmm thfiufhn «4 O O O O O O O 0’“de N N I l I ’3'D(.'(1(JC‘C " ‘3"\(: 3C)() r‘v’jr‘trv"- (C. .8 l V"‘c)‘ V IC“ ) O‘IL‘CDFICJL'JL‘fJ CP‘C‘fi'WfiC'fi Q o o o o o o o LUHNM-TU \DN 5.. <1 L.‘ CORY) — '- - (ALLOWS A SEPARATE MEAN FOR EACH CAT T A 8 L E L L 3 ,— -. 7 IA C VARIA? J N EOE-”Pr. NT VA ATZGOQY V A R I A 1 C n F M A L Y S I S A U PR F STATISTIC MEAN SQUARE SQUARES 7.75702922 QC SUM cu» m? uq ”tr—1 C‘t‘" m> mmm 00".) J'J J 0'30 0 o 0 060 V V V km" 405 (Iv-4.4 than oNv-d O O I mum MHO‘ v-cl") 3.0m SOHO (£31 "3'?“ U‘v-‘v-d (\er J (1‘ch NL)O‘ o o 0 WOW) «m TL!) .1 r" '..'C\ at.“ (Kc: «at. so 0 0 M3 C1T-GORIES qurno OTHQP PETNCEH HTTHIN TOTAL Apopnx. PROSABILI 3.06710u96 (0.0505 R .731Q12 MULTIPLE GRESSION SUM OF SQUARES a p .- o033190h3‘X(3)T R .9097169q .17A13hh2- L., 60 700 :+ 122200 ‘ 'RM ONLY,[X(33) LATI .- .. lko5 .- - CORR C O ’oh6lh SIMPL STRICTEn TO A LINEAR T CURIFS .- .— - CAT IF R F8 189.0542 TB '13.?“97 STANDARD ERROR ham; {£10 HG‘O’ (jv-IN HJM uh") u «C- h! o o (T from <1 -RIDO CONSTANT p: COMPOSITE ANALYSIS PHA SE II R E A C H C A T E G O R Y F O S T A T I S T I C S 3.5310 MAXIMUM VALLE' '“0333131 (OVERALL) MINIMUM VALUEf SUM OF SQUARES MEAN INCREMENT MEAN “.005Q150A FREQ UM S -3.7959A1 .71019058 353.059b59 353.0800138 701 OMMNM‘DW 00Wm3va‘ ONOJWHWHM IDKGMNMGD 'dNB&NMO: :mnmnmnm 0001.000 NGMWNDFO‘ nautsmums smolmomn sadism-.4: TVMNTWNO‘ vaunwnm msuwnmo: OWmD«JCh4 (Dwmwumon mKONkhk O‘v-CQN‘MNDM (Dosuwwrd vuanmnmsm AHMdonN) msuuaswro OCKMDDCLJ 0 O C O I. O NUWWDMANU mnmwumm: (NDNKWJFO NJdkmDUQ MMJWHMDJ OOCMMJHO oooocloo vnomomuao cxnaOWNam ‘fldvA d «JWrOSGMO JCOWNWT: owosmqmun onNCWWfiwm (WO«¢HXFN Numamncn 0...... IOM¢’Fm4d 0 HI 0 30CMT136 ‘DO’D'fifi 3f") wjflCCDvS >firj 3")(')"fi(‘) Q“MJQCNJJJ Otyfifiiivfifi (3001-00.. mrmM03mim. h < O PARATE MEAN FOR EACH CATEGORY) - .- . (ALLOWS A S T A 8 L E F V A R I A N C E O A N A L Y S I S OH PERIOD F STATISTIC MEAN SQUARE p (Jt O to m (DU um E SUM OF SQUARES .777 .5h106 .27397255 1.6A383711 351.A1562155 353.05995867 ITHEEN CATEGORIES THIN )TAL .50636257 69% 700 CATEGORIES HULTIPLE CORREL 0058235 G 0 R Y T A C S S T A T I S T I CC) PERI 5.6773 MAXIMUM VALUE- -9.226249 MINIMUM VALUE- ("VEFALL) SUM OF SQUARES SENT — u - MEAN INCP ERCQ QHM 70370500 .97206378 661.A35590 661.5152117 .01L522‘T2 val macwunsh ckfimwmv« huflwawwxh vfloomnwvc :maooro .smaoumxw O... O. O ofimnsHGU\ omuwnnmo «a dtWMOdJ¢> RQVWJMOm Nnmumnma- JO‘KNCWDN JNNLCMNH kkmhumcd hmmvnmroJ Nhkd‘rsd! O 0 O O O O O Viv-A «HDCHONOO‘ OQJNNON @huummwun J‘ON‘V‘G‘J‘: HMDU‘F‘DOd 06‘3”th {T‘NMU‘O‘HQ o o o o o o o C‘LDNNHH‘N \CLDK (\U‘ ’6‘ d—A m-jo.fr\)cr‘ln r4?» U'J’HM-LY) u‘ «at tho m tNM-ON ‘3 OfiJ'I'th fun UHMQONH O O O O O O O (Dc-OJIV‘CC‘NO‘ 5.5.26 CONN JHDM‘C'JLP>V4 mqhma 1&0 cuo ova-nun rv IQNJLCC‘JQ hodd‘v-H'TMJ C)v-4P'ILJ‘.J(‘JH 0 O O O O O O Hrok‘O‘fsrnm Q")(-:U‘3‘ 30‘ HHH v-J MAP”? (NF—x," V4H'~.)("M('\ LG UtCN)?’)UL’ 3 \."Lf\' -H"' Yl" BUBNUPKIU‘ VNCJMNN . C . C . O O NHNv-(orr HT” K'H A A A rvrlvrhOIJC'c“ t-JC‘tr'"')")L‘Q r‘frc ""wficn >r‘\( ‘r ' 'rjcch .JLJ'DL.)L.Y‘_)’J D'N'TPI-)C‘C‘fi L" o o o o o o o mfiNV.~TU\\DB p. d C. GORY) - .— . EACH CAT SEPARATE MEAN FOR (ALLOWS A C C T A R L E V A R I A N 0L- N A L Y S I S A “A “U XX mm OMH (J'U' C (3‘ t: d L4H F STATISTIC MEAN SQUARE mu. SQUARES 23.970quH2 SUM OF 3? SOURCE OF VARIALV 03H (3N1...) DOC) o o o HHLD mud O‘ON MH—O coo cm: km") 0N6. HUM 6.? n (ANN com 0‘07.) M3") HJ‘ SORIFS :wafu 0172 LTNFAD D'HEP .91353831 690 760 637.A653837J CATEGWOIFS JTTHTN 31.03559012 f 7 TOTAL MULTIPLE CORRELA .190366 .0Au92576’X(3)) + .17299983- TENN ONLY,[Y(37) IF RESTRI'TEn TO A LINEAR A ES 0 5 QU R 7“ 2 GRESSION SUM OF S “.693 RE .— Z (Ila HN (‘0 HU LL .4 LL c35— “HUG, ‘3 ;L 3 LAG 0 fi 25 CW 'LATI f h D “03““? SIMPLE CORD u»- 04' 2h (U) HAL IL HLL 20 LG H)- (I).— H o—J )L'H OC‘ \0 (a 61 DIP O QC) 0 (CY Q 6‘. (h 0‘ CD 0‘ (A. o J H (.0 M C" N t— o N O O N O H -z to 0‘: v4 bJ V) 1‘ C, d x o d o G 2 (I g.— (I. O—P'NO ZG‘N LL01» HOOI (VITO Ht‘lrfi Uh: (1.—4) (1‘ o o O I (v 00") d P r. h F—H 70' CU. o—n (f) I! C) U 5 ANALYSIS III COMPOSIT .- - PHAS' sranstcs CATEGORY A C “J F O R 0.0 DC) .10-4 .3311 '.702036 MAXIMUM VALUE- A MINIMUM VALU (OVERALL) MEAN INCREMENT SUM OF SQUARES -.666A8A13 M~AN NJ (I LL SUM ‘M606U5373 .18603A82 2B.226268 27.32A7854 7G1 cosmonaut) O3NO‘O‘NO onmnmwmva O‘Nmmmoo (00030.11) r~c¢uhrdi 00...... '41-. Nvuflusuno (BROOM—dud NLnuO‘NQJLh O‘a‘to ffxcvo \LHDIJJJ'LCN [\QHDJO‘NM mrnno- 1N cocoa-4d O O O O O O O NO‘HO‘NNM mor~oo~oro :QU‘.«1O‘¢N HNHHDCOM :Nmmeno Nora 1®:m Naova-c: o o O o o O o N .4... N “hasn‘t-(0") “\HWTQNLLH’) U‘flmifiv—OO :NQO‘U‘QKD O‘QLDUHDLO‘D ”0(3-39141...) . O . O O C . mvflDJffNN O‘NOC‘dbiJM 3"").1‘0Jv4 MT’HICJ'C'Jm :«OfWOxON: HWNKNv-ACJ -O'3"."r"!f“v I") -t'Qfiooon O O 0 O O O O «IMMO‘N‘JQ «and: )O‘O‘HQOW «(v-4H d ”nommMKln ‘°~U:~’N' II") mvn—at‘r‘sm -fu‘mk'wfi: (DCJm-Oh-f 0(JN0IUHK\ o o o o o o o 0 o I J A nuL‘LJCJ'DLJ 'Jcl) JEJ'J JILJ 1'): )P‘r') )‘J'J >Pyl‘1'fir‘jc \( S“, (Y'w'jr'wrfirvr‘vfi OLJKJEJJKJLJL) LD 0 o o o o o o IIIHNM flhxok CAT MEAN FOR EACH CATEGORY) (ALLOWS A SEPARATE V A R I A N C E T A B L E O F N A L Y S I S A 0.0 00 .10-0 F STATISTIC SQUARE MEAN (DU) (DH) LULZ OLL SUM OF SQUARES OH) ()4 men C)Oc:: ( )(1‘3) QC!) 0 O 0 COO V V V «NM scam tacos!) NM'D MMv-A O O . torso torus MCON ramm (1‘3“ MN: (0‘ .m cmm “an \OJH on") O o O MON Hm 18.H1317737 '0.)- NJ‘ ITIK NO‘ \O\D 40 mm .0C837621 69A 760 5.813C9Gh6 29.22626733 EGOPIES CAT [THIN ITAL MULTIPLE CORR .871809 .0“9A2675'X(3)) RM ONLY,(X(52) EAR TE 3 TO A LIN STRICT RE IF I ErlT ( ) EF CI ‘EO R2 2 O F ORRELATION C SQUA “ J E R SIMPL REGRESSION SUM6 526 .5316 p A (0.0005 FB 275.3%39 TB 16.5935 ERROR .00297868 STANDARD 291.866A01 .6A571599 G O R Y 292.7059533 SUM OF SQUARES A T 3.135A C E A C H MEAN INCREMEN O R F MAXIMUM VALUE- 003596216 MEAN -3.293729 FREQ 701 .' 7 STATISTICS ANALYSIS SUM b.8539? 9 p -— MINIMUM VALU III COMPOSIT (OVERALL) PHAS mmskons NNNO‘OIO: Henssnw OHmmNMN ONOHNU‘O H¢NIJN~7I~ o o o o o o O o m... "303.1010", 0‘! 70:70.13"): ZI- d 0 4m I-I- un- 0 Zn.) Dd HAL IIJ ZI- Il. HIII (In A HIL C) U > 20 HA HAL 0! “JV: IL 0 OH» Ime: van OIDMCNH: L3 (DI- luVH Z HHNMUNMH Lu H O 0‘ (D CMNI‘NO‘LJ I- 04 OCH H) «mmvuvmda Q x». tum 01 Mb O‘O'I‘HU‘NN U om 2!! o IIIN H U‘JO‘IJMIOH (rd Nor.) 04 (IN 0.1 NFLNO‘NK I (LCD MMN H: (0‘ XH LIMDIIMDQOO Q CLO D'JH I-O 30‘ QC!) O .00.... d dd 00. «(fl C35 QCM u: a J Uhd QC) a kl In CLO o o: (X ILO‘ (fl 0 (Y O o n. II. C) MHO‘ O H H 846‘ Q N I Z )- NHIO H D OADOHQJN d U) U‘IMID QJQN (I) a" NJNIDOFIH ILI H NKN .J (3 lb mHJPfiKMN I I- o o 0 Q M Z 0 0005530 4 NJH H H O m h \ONJmOU‘N hi I- I- o H IL 0 choH—mua h— m J V) J NIDI'I'JI’IION <1 D U) o o o o o o 0 0’ ll. 2 H M] O‘xD-YJII‘G‘M d A (Z M3MJJM: LL '0 0 I.” V IL] (I) I0 X 0’ 00 1» d .MH Iu mnhd m 3 (1’ n’ O‘FACC (D 0" M (I) u] d MON 0‘ D 0‘ “I O. D O‘O‘O‘ H 0‘ ID \DMNonM: O G Nhk m '0 I!) H wHNHwaJ .1 II) U‘HJ N O I- o 0N6) JNMIA .J NLhN H N N chnamh d 2 00's 4' o I HIDIJIOI3IL'0 ' d o o o o o NUOIJQ'JIJ lu H o o o o o o o z: I I I I I I I AA H u] MM M o L." m J M N m vv 0 I! \0 xx LL .3 O m 4 CI. H 0’ In (DU) 0 o o: \D «)NO‘NDO‘J‘ I- HH .0 \O J O I- LL! H LhH'YEFOmHJ‘ Inn; 0‘ '9 § 2 N Cv%FMCH4H um: Oh) \D N u (UA O .4 NmMUIG‘L—‘Q _J_J In"! a HN Q.’ (J .Hnsuxomc: m 0K0 Du. (Hm N) 003 d o \OQO‘HIDIDN <4 I.“ H' O .1mnmnnmra o FflH v IL 5. 2 No'aon-JQ 0 (I x [LO 0 d. o o o o o o 0 Z dd H ”INN-D I'- I I I I >> (I) III N -D 0' O'Lo V) d [1) rs Q I“ > 0.1 o I- II M no '3 .I D H Z)- d (O V) c3 2 23 out: :3 N ID 4 0 CU) U CO C In '0 .1 H 20 If) N c ID I I- I-H-f HMMO‘NL’JCO 4 mm In N In C! ct ZIOO‘ ruwamOWWT QF- u o . . uI A Luna HHH H > ”JG! 0 In ID H I- N HMO" DU 6 O‘ 0 UN") 2' N N 0' {Y Hfi-O T) d O LLJ'N nmvnmmo‘m IL (I) III 0 '1'.‘ LLH" rau1f~HIO NV) 2 H u- o o G‘MMNG‘HH 0 Nfl H (”0’1“ 0 I mHOIIOIDr‘ 1' (7‘3 .1 .J F‘ U mQT')UJ\C"J ONO (L o CDO‘LjHCT‘ICN NO“ 4 7: I o o O o o I 0 U) Hm H 3N") I (MN I U N O U) NI I H (TO I— . O 0" HM D II) (Vt-5M >- I— d (A U) (.3 > .I U) (LI H H H O, UJOQLIULICD <1 C: (L I— O 00:) J 4.4-) O O (I) O rnc:'_).)r)v“1-J 2 C) L!) III F—H >rjl‘1r u )C'J'Wr-fi IL L! l-I Q' 2"): (Yr-)Hryfififi-fi d Oh) #— I— an) Cmuaucnwju L) d d u I—Q L9 0 o o o o o 0 L112 OCH 0 H U7 IIIflnJ'fiJmLON ' (.Jd d 7 P 0+4 Zum: O a DQquZI 0 U 04 LIJHI— S V H L O [THIN )TAL ANALYSIS .— III COMPOSIT. ~ - PHAS STATIST-ICS G O R Y - I— C A T C IAJ F O A- JW vv )( )< (hm qu LLJIAJ 6.76A“ MAXIMUM VALUE- '90961001 MINIMUM VALU (OVERALL) SUM OF SQUARES MEAN INCREMEhT AN 019532583 ME SUM 13?.57Ahh3 .97581120 666.5952“? 681.55B5377 731 UWMQGOHDH \DGéflMDJé tuckhxflso unodmmn~n \odommvso vflfimh+nDH .00.... OKDJJJHuJ m4uwnrds Hvfi +«omduflxo Onwxotmrc 0'0‘040‘U‘Hi) mmh¢u¢3¢ Hdwwnmqvw GMOMNOJ \ONMNO‘LG: FMDNCNMDM O 0 O O O O 0 HH ~p®¢mfiva «QJBrWMNn NOMJNOch mawxmomc wruhdlmm MUVmfiHNfl) Mfihumnmm 0...... tomcarwwm OJUWutHN H HH t\JI~!lIb(3‘F\ Lf\:f uvHuNKPJu (UQ1MUJmL) m30mnmum .om¢muwwh ©HF)M'1L1N . O O O O O O 31mm:HAM‘ OHINNNH BHNDMNMHD 00‘1‘r\Jh~'\J<1)Lr. Uhimeflxh mayoHdwfim HHN'P‘J‘mN cnwaHruuH I O O. O 0. HI I I v4f'3d')(?‘f-c;330 rfimcmWWJm Hrhd H (\IHUHHAIF’) O()I~.v4l:\cj.t\J-_J M1MDMflNHM 3"“Hm'f‘r‘0 KWQHNNH lfld‘di' ‘MIAN o o o o o a o Nrwmxmxn: (T‘ I v4‘v4 v4 H I I 11'-)U:J JtJLJ Jt Iv.)a_)~_‘s._JL) LUIJLH H’! )'.‘J >(‘r'flrtfi’3’fi “ rz'.-)r'sr"'—1'-1- 34-1 OL) JUC‘J'.)\JC) O O O o O O O I.Iv-IT\JF’I.3’LI\\()I\- 6 CAT AN FOR EACH CATEGORY) E M (ALLOHS A SEPARATE T A E V A R I A N 3 0 F S I c~ .J A N A L Y AA JM m vv XX MU) HFI lLJllI JJ '13 C!) (I <1 HI—I (ITINT ¢1W<1 2) 2’ F STATISTIC p- b - SQUAR MEAN ES UM OF SQUAp 3 Ola! m2 f_)<1 QHI SW (D) Inmm cxgo r__‘- 3t.) cmao O O O cyan vvv mow» 3mm: .10M can: mra' 0.. ORM\ 'HQH NOE-«In Ln: ’7‘ mm:- L.)~1’F’) 0H3: \LJLS\~3' IPNH ffiHO o o o \Cu‘N v-IT’5 v4 .8189u528 «m 98.19721533 568.38632677 666.5“529215 ES iGOPIES EGOFI AT CAT H L 0 ITHIN >TAL 700 MULTIPLE CORp .363826 .11195555‘XI3II 059079“22' =9 -AR TERM ONLY,[X(5“) 3 TO A LIN: STRICT? ' \— D IF SIMPLE CORRELATI ESSION SU REGR “.2295 m» Dd. 2h (U) L) H& u HK 20 D H) MP I-i o._I in m Omit: m4 (3 am C) 00 o 1' D I H X <1 2 I d ul 7: '3 \D N C“. (1 J o C‘ u! 0 IL I HI 1‘ I .1 I? q (I > 1 5, H H .J .J 1'! ‘1' [H > C‘ u .107137b1 8.03h897 15.762h619 .16h993h8 741 71.603527 WJNMO‘JH 000.050: OJHOJO‘G NMmmG‘HM HO‘OOHO‘D aommmmmo O I O O O O O H NNJva-«D MRILDKHGM Ookma‘ms HHO‘C’DNO HH0L\\DM\L ONJNNNU" ONDLALALAN J ooooocu-a O O I O O O O UmO‘Jd‘o: «DONorav-amu :MNCflVEN—f rourxor‘r’) 1' «summon-4 ©0000an IDONNNFK O O O O O O O c\ v-IH \DMHHCHTQ PSNUMJF F" JHtUU-‘H‘CC‘J O‘NDMCT‘MJ’ G‘FOV’V)“HF\I v-IC‘ JULJ'CJ'J O O C C O O C I I I I I I NOHOO'WOJO‘ mam: '3‘6‘ C‘UAIX *mmo U‘NHJLDVIY'I :fidJficvfc—IK ch’v-«qu‘cn 'J‘u"\0!\ O'V‘T‘ NL‘ ) )-)-'.3c'.) 0 O O O O O O HV‘MG‘erd‘ L)’._)L O-O‘L 'O" v3r~t~vfir~ryfi r)’)P)'J("L "3 I”! Ptvrv ' 1 >7 lr‘|( a ‘v'~f‘)(—‘ Q .‘D’JCJ’."(. g C“ r,-‘r fi-jf‘fi"!, L“ o o o o o o o *— <1 L GORY) EACH CAT PARATE MEAN FOR (ALLOWS A S E T A B L E N A L Y S I S E V A R I A N A “A “v XX (rm ILHH 'x‘d (“(3 F STATISTIC :EAN SQUARE Q7: 00 mm: L" J (HU— OIL If) SQUARE SUM OF mmm "DOC (JQU C300 0 o 0 can V V V C.,"! \OJO‘ mn'O‘ O‘CTO" NNN O O O and) M :r-a HNH @074 euro :06: man «3‘: year HN‘f.‘ 1'».an Hlf‘ ko26QIC~37 F): a U‘ 0‘3 (30‘ 'IN (\1 J no 0 0 H0! ‘GORIES CAT: 0 N JEA‘ ER F “I H III-b H L 0 :gr .335q33h2 6““ 73 379295 3.77 ECWDIFS CAT IITHTN rOTAL 6.33969719 CORREL R .726Q90 MULTIRLE STRICTFQ TO A LINEAR TERM UNLV,IY(3Q)=+ .191218h9- .02171891‘X(3I) IF P GRESSION SUM RE '1”th O‘L'V'I D CORDELAT -.ucss SIMPLE IL”- 04 2&— «m 0 HI]. IL HI]. 20 L" H) U‘I— H 0.! XH L0 Oil" :3 (id o an: O CO 0 «it c Q V 0" m J m \0 I]. o Is M H M N M C" IN I'- o H H I a: H O N '1 H 0! an u] a '4 D 3 (I u d o D 2 <1 *- J) v—C‘H 710‘ Luci!) HHH (VHF I-‘HH nm'u uH") [1' O O Q I (I (Yon d > C‘ O F‘4 70 (ILL kn U‘ 0 C v'vvv “A." h."‘ C A T E G O R Y E A C H F 0 R S T A T I S I I C S b.3331 MAXIMUM VALLE- .DUCASR MINIMUM VALUE- (OVERALL) MEAN IACREMENT SUM OF SQUARES MEAN FREQ SUM 333.557883 .526935b3 19hg3626€5 353.0800136 .h7583150 701 Nnhkonm cnmocws NODHDHO‘ {av-«O‘ONN NWOQO‘NH O‘QJ’LDO‘ON O O 0 O O O O OONJO‘U‘M dNNNNMM Influence) omcrcmko va-aa‘com NNOomoo O‘NNO‘O‘Nm \DOO‘OCLDO" 3.420; mow: :unflmmmn 093N:~Oh an‘ONOv-I ”etc-«01° 3P¢t0033 CHKO‘No-d: mmaowoms mw3mmwm O O O O o O O mama‘wmo‘ nm::mmm «:omNrm LBN'DO‘O‘v-fl') cmawmwac tho mm: Nv-ION 1000 «0000000 0 O O O O I O I I NO‘NNv-IOO O‘MHMO‘H—I OmNsOMO‘O omNNN 34) Comm: :0 NMNVrJdLJ 'OO‘Noch-I ”3334\me «mmok'am or; omen-90‘ «an v-I QdeO‘Uh Nrwcv-Iv-I—IN okxDv-Ida‘m .43c313—4Jtn moraan: o~~r~3e¢o O O O O O O O WUQOMJ’O‘J MLhJJIme DOOOQC": C‘Q'DOUDG f“ Scfi'3" I *GGD"‘DQ¢“ «33()\3'DD° Ora-weanr—wc o o o o o O 0 0 UHNMJU'MDN .— q C F V A R I A N C E T A 8 L E (ALLOWS A SEPARATE MEAN FOR EACH CATEGORY! A N A L Y S I S F STATISTIC MEAN SQUARE SUM OF SQUARES .322 1.1669“ .32355203 1.9H131219 192.A2135326 19h.362665h5 ZTNELN CATEGORIES .27726h20 Q 0 69 CATEGORIES [THIN )TAL 7U MULTIPLE CORREL o0999k0 09/39/79 1b. (bl CLRV‘ALU e A c H c n r e c o p v F O R r A T I SAT I c s S AA (13M 0 367.378237 S .72hhh879 SUM OF SQUARES 661.5132117 9.2262 MEAN INCREMENT .0C2963 MAXIMUM VALUE- MEAN 701 .6A776030 F"‘ZEQ — '0- ‘- SUM A5th79958 MINIMUM VALU (OVERALL) N313MN©® \DOCHfiOO‘ moomkno .tm—umeo ONHNv-tmm NaO‘uDNJQ O O O O O O O NNOJ’C‘MK‘O MNMMNGN - « NJCJU‘J’ID: 3MKM¢¢T~4 mNO‘NO‘O‘m mMV‘O‘me) Outdoor“); O‘NmmN—IN CJflGDTOO‘MQ-I \C‘mmOJQ-d O O O O O O O v-I “LDGMONGC‘ OCJNNVJIK C‘NNLocfd'h :fofiM‘Y‘UwJ nfibfi—nov-O «ICOJNNNM O‘NMO‘O‘HO O O O O O O O omhjk H‘nk xOmINNU‘JO‘ Hv-I mLDO'HNC‘v-I KNVTL‘OJI‘Jn macxuma N'Udmd‘f") LON 7N':)N3 H14 )1 )fiNC‘U o o o o o o o HLDNNN’OI') N'.'Jv-4(‘JI’)I\M Ln fmrJMr'vv-vl C, (“v-4L w-VOG‘ «unaccukcwrr IOID’VE‘JC’WDC‘) {[30,1P‘r‘lh‘kC' :m-Ou Jmccn flMVTC" N am r‘)'3<"G‘O‘L.2J‘ WHO-I H bm‘r~f\t‘.9Mv-I U'wennjjr. (r. F'Mr‘ "JH'EEINI V) )I,|'f‘f‘;.’ff\ (‘ :C’NILCJC‘ Ov~4r.'fil'}~f.fl; o o o o o o o 6‘ :0. HNKI“ JU' \rJI.’ “hf 03m; nr‘r‘o '3 3'3”?“ 7'3 (.fi"' (If‘fi >P'3'x warn“ C CJCJ'VJULJ JU hrjbcwr—w‘r 3" Cacao... LUVANV)JU\.CPs ‘— <1 L! GORY) p- b . ACH CAT E MEAN FOR .- O- \- EPARAT F STATISTIC (ALLONS A S SQUARE T A B L E MEAN E (N U 'S r. . O F V A R I A N SUM OF SQUAR 16.6179037L N A L Y S I S SOURCE OF VARIANCE mm Gav-I C um Dav-4 o o 0 CO V V N30 C-DC U‘I‘DU‘ Km'j 3MK o o o “‘31-. (HEN) OCK'O‘ 0mm Ln‘mr «‘er "FD"! \D-‘JO Nmrc 0 O O NN \O HU‘ EGQ°IES CAT LINEAD OTH IITHTN TOTAL 9 arrwrsw MULTIPLE COR .212692 .96626932‘X(3)l .50541835 .38966826+ 69A 70J =+ 130.76033666 357.37823716 AR TERM ONLY,IX(36) CORRELATI P .1330 IN: I. STRIFTEO TO A SIMPLE carecoa1r< IF 0. c h - Zv-I REGRESSION SU <0.9005 F3 2ho2277 TB 9222 ERROR o (113‘063‘05 STANDARD 7N") Inf-LO" H\0~D (WLI‘I‘ H10 uamo U ")LJ Ln 0 0 Man Fho ~ an» F0. CONS 5 ANALYSIS III COMPOSIT PHAS sransr'Ics C A T E G O R Y CH In F 0 AA H") ILMC «Zn: «0:: :30-0 OIr-Iu (04: HF- II.) Dull: DO t‘a: 2) 'll. (n 2 oo (IH CI- Dd ZH <> F-IIJ MC) V) IL] QC 4 D C! (I) IL 0 I: D D N (h 0" IS 0 .- Z n] I u] '1. U 2 H I LL! 2 3 cl .J m d 2'. > Z Z) 2': H X 4 Z I 11 Ill I Q Lh H O I'.) D o 0 l1] 0: IL .. M? D t .J :3 <1 (I) > 3' D 5' H H 1'. A .J .1 6 Q.’ IL] > O .15h92605 16.601h56 27.3ZATGSA .12252298 1 70 $5.883612 ‘lk O‘mokkm \ONUUMJUID thuflaq oommmso LOCOMHGOHH NGnO‘mwrx cm: #350“ 0069000 0 O O O O O O NO‘AO‘NNM «consonants 1 ml: UUMDN dNHv-ua‘om 3 Nina? 3x90 N (JD 303m N com; '4: N'OJNJnv-I “O‘LDJJIDN O‘N JJOIJN (13 1'60an MLOLD.O‘O: 1’ ”CM )L‘TO’JQ o o o o o o o cornmlxosm O‘NO‘CrMQO‘ 3 .frnnmmd MNLOCONuDfl :NJOuOJ-M «NO‘LDMO‘LO .o-o'mmnmn JO Joana O O O O O O O HMMufirxtnm or )u. )O‘S‘OO‘ Haw-Id v-I mmmu‘m 3mm IOU m. MQLFC‘ O‘ONHG‘N'D 3'n’J‘flJ-OJ‘N (JINRELD DJ“ @O‘HLRNO‘ 1 o o o o o o o \I‘wikk‘dl u-N“ J (’yorDLJQUt.) L, J I .J .J‘J J r) (fir-‘2 )(J ".l‘ J >'fidv~1ca« )'1CI vrfinfirfim'flcs Ocaocuaochu o o o o c o o o SHNMJHMDN d 0 EACH CATEGORY) MEAN FOP FARATE (ALLOHS A $5 '- p b T A B L O F N A L Y S I S A F STATISTIC Ill Q.’ QUA U) AN II) M ES SUM OF SQUAR Oh} Id? ()d CZH 30f W) mmm O'JC) o):.)«‘) 06):) o o o (DOC) V V V #ON an: :30: NOW; mCDN I O O Mthv-I mom :om HID 13.61135361 ATEGORIES .00A59669 69» 7L3 3.19010265 16.801h5626 {GORIES CAT [THIN )TAL E CORREL p MULTIPL .903072 .0h560356’XI3)l .25372087- AR TERM 0NLY,(X(61)=+ STRICTEQ TO A LINE IF Q REGRESSION SUM CORRELATION IU'YN SIMFL IL”- 04 2&— <0) HIL IL HIL 20 I!) H) (DI- H o—I XH m OLD :3 (1’4 0 OJ!) I3 0.0 I do: o O. V n ID 14 (D H II. 0 ID IO N J N to (I) N .— o 0 v4 I O! v-I O IN (1 M CK 0‘ {LI 3 N C) o 0’ o d o (3 <1 .- ‘1) I—NLO ZQU‘. IJ‘")") HNQ GRID HMC‘V LL”)! (LN'W MIC. O I O 0")!“ q > O O I—H TC? dlfl I—(L V) 2 O U 9’7“ 155.0“5070 .h7063C38 292.7“59533 E G O R Y SUM OF SQUARES C A T 3.2937 E A C H AN INCREHENT F - M F 0 R HAXIMUH VALUE- AN .u4328380 .002733 701 s r A r 1 s T I c 3 ANALYSIS SUM 310.6913?) HINIWUH VALU III COMPOSIT (OVEQALL) PHAS omNdfiMv-O KHCDJ’IDO‘O HOMJHH lbw-IMxOIDU‘M MKv-kO-fv-‘m Noum'omo o o o o o o o 0 l1”- IDNCNLDC)” Qt: v-INdNNNN ZI- (In HIL IL A H“. > 20 1! L9 0 H) ‘NNO‘UNCZNID L9 (IDI- JNO‘mHCDLD Lu H ommhdnm *- a.) CLAMKDNv-Ira d )(H DONTQNU‘ L) DC) O‘uod‘omrs 04 0:60 QNI‘INNLDQ I QC) NOLA {IAJJIDJJ 0 Q0 0‘0“!) 0 o o o o o o d an: 0 o 0 Lu Q at O I]. 0 00"“ H NH") 2 I- NNG QQONOJN d U) M'JO‘ (‘IJNLD'DL‘DH UI H '00?" Qv-IJMNMN I I— . o o \DOVDNNJKO 4 \ON :mvrmh m I- QJ'Do-IHNO t- w NmMrJMLbN d o o o o o o o f! IL ONO-1301‘M <1 ”3'04 100! LL U! m to 00 4 .JH III KG‘N («Y (Y 5.10 m u: d NFOG‘ I G. D NfiN TMF’JO'VIMD O C O3N HINOLHUHVN .1 V) J-JO MLr-nmmaon .J No!) mmamnnm d 2 one NHJOIv-Iv-Id ‘I' d o o o (D'D'chrj') .1 LLI o o o o o o o I I . I AA III N") ° 0 .1 m vv XX IL 4 OZ (III/I O LOAJJN‘OON I- HH on ID If-(Vikka-A m'u NKO‘M‘DR‘D uth L9H) ADNNOOTT) .1... Iu‘l' mo 0 fHML‘) u! (DC?- on. «m NNCDKQNJO‘ <14 kmm n'nmm 9 HH 13'“! ’83 “70’ o o o o o o 0 2 dc! >> (A r: d m \0 P- 0’ \D H 2) d M wt! 3 c-o or CO C .7 2U) m J dmrfifl‘huj‘fi d IULU 4’ nnnc‘c‘nm CL!- LL 0 “TIT. H > IL‘d O CO 3“ 2‘ T TNMR'dIfi [L m «1.212.4er I OH N OFW.“ 3' 3 O -fv-C {fiih'nfflr‘fi‘f‘l m'r NJIC'CJ‘OO‘ CID-f NtvwchJO" .1x0 0 o o o o o o U) h") F-JHLOJNJ (JJ 3.1.1.? 1:.) H (3.: o o m y. m J '1] H L'JLJ’)&J'.)()IJ d 0: ')JJ'JLJ'J" O 1 11-1'J'V‘.‘)")L.V Z (3 >r’fl1-iffii3(“'1h IL IJ' ry._,r3r-vwr1rwfi d O"! *— OOOLNJ‘J'JQ L3 < (3.000... In: 01' inc-HUM :Lmorx ' (‘d dt‘Y .— QH 2mm 1:! DQ’ h'ZI 0 Cd UHF- .963 MULTIPLE CORR .053522 F8 .0022 REGRESSION SUM .0h69 .03C41751’XI3II TB .22276792 ohh155228+ ERROR 69% 750 .00889666 STANDARD 15A.60093323 155.04556983 A? TERM 0NLY,[X(62)=+ COQPELATI .0313 Q TO A LIN SIHDL EU 3 3 VA? 50916 RESTPICT 2100 CAT IF CONSEANT :THIN ITAL K: NIN IMO L5\ 4: no o—m G O R Y A IL) F O E ANALYSIS S T A T I S T I C S III COMPOSIT PHAS >0 ()0 <0 9.0610 .000721 MAXIMUM VALUE- MINIMUM VALU (OVERALL) SUM OF SQUARES MENT .— p. b MEAN IhCR AN .67186010 FREQ SUM ~72.973927 .72222h69 365.125950 681.55k5377 701 mamas-om NHQHO‘QN monumvxm IDOv-IMMJN chomhmm NONK‘NIDN O o O O o O O O‘O‘O‘MNNv-I :HNJva-o v4 o‘cmorsmmm ommmmcd‘ vib‘cmu‘mfl‘ O‘hmkmm 3 .tJ'J—u vhd‘ flNIDU‘NmID nJ-tm‘or (TN 5 :UMOJNIJ \OIDIOQNLAJ ('1:deth NC‘JNO‘ND monocoo 'Dv-IJv-I.?C“M {OWLJMHNM MMPILJIDM'JO C O O O O O O Mommmmm \OJIDNJHN v-I v-IH MNNG‘JMN LDJJI~UVJJN viNMLD'DfiO‘ Hm'11\1)g;o\ O‘IDN'DJ—TM MHH(1H )H O Q O O O O O can-cements NlnkNLO—TU‘. NC‘NVI‘DVIN o-IJ‘TA'NO'Jrh LJOJVOHIJK Mxnflkmmfi -.')r-H'r)N-—4.-¢ «:HDanmN’O o o o o o o o H HMI‘OO‘kn )Q (n J *uroujd‘ Hv-Iv-I v4 ANKJNfiMO' SQJMN- N 30‘ NdNT-f’fifl f‘firnurwr‘-¢ ONUs:'O'Jifi Mv-hDv-‘G‘Nh\ o o o o o o o hfi'd'zWJv-IO‘ (\U‘M‘JJU‘I‘ N .4 G‘J‘LJI‘IL—JOD J'JJ‘J )_"J I ) -)'.J¢ )()C‘ ) >rfi-‘V1‘v \rVW'd (Yrsr‘w-r-fifi fir) L3LJUQIJ()(3I'—J L3 0 o o o o o o IUv-INMth‘nN p. Q I.) EACH CATEGORY) AN FOR ME PARATE C’ (ALLOHS A S P C. T A B L t V A R I A N C F S I S O A N A L Y A- Mi") UV XX mm HH IUUJ F STATISTIC SQUAQE MEAN ~ p-Q -~ SUI OF SOUAR Cw: LL12 ()‘I O'H 30.’ W) m m uO‘o 'JC'D DML: O O O V V HIDN 4’"): MMO‘ NJLD O‘NII‘ 30‘3") runo" Nthfl HIDC) who 35’)“ LDICLn ”Mo-I O O O SID Hm 26.15110223 .A8853633 694 700 333.97h8h749 365.12594972 iGOFIES CAT [THIN JTAL MULTIPLE CORREL .267623 .7170B939- .01138256‘XI3)! RM 0NLY,[X(63)=+ A? TE STRICTEO TO A LINE .- ,_ IF R SSION SUM 6R5 R It“ SIMPLE CORRELATI ‘03- I34 ZI— (U) HIL IL HIL 20 L!) H)- (’30- H 0.! XH 00‘ 3 0’4 0 0C!) 3 (LO 0 <0: 0.. Q m 0‘ (1‘ ID IL 0 v-I J I") (D 'D t- o I (I ID 0 0‘ (I ID 01 J I!) IO M O r! a: C) d o D I’. d .- V) I—JO ZMLD IL'O‘N H31) 01:)” HNc-I LLHv-I ILN'TI LL: I O O I U fl’rn") d > O O I—H 70’ 4'3] t—O. (I) Z O (J TTTTTTT ”'WfiTfiuWfififlifififlifljflfilufim IE 53