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Regression Analysis and a Data Analysis Overview - Overview of Data Analysis Additional Analysis of Dependence Techniques Two analysis of dependence techniques have been presented in detail, conjoint analysis and regression analysis. Two extensions to regression analysis and two additional techniques will be briefly described before presenting an overview of data analysis. Simultaneous Equation Regression Analysis Consider a regression mode: with price, advertising, and perceived product quality (the three independent variables) influencing sales (the dependent variable). Suppose thai sales also influenced advertising because the advertising budget was in pan: set as a percentage of sales and that advertising (which emphasized quality and price also affected perceived product quality. Instead of a single regression equation, it would then be more appropriate to work simultaneously with three regression equations and three associated dependent variables (sales, advertising, and pr...

Regression Analysis and a Data Analysis Overview - Summary Applications Regression analysis is used (1) to predict the dependent variable, given knowledge of independent variable values, and (2) to gain an understanding of the relationship between trie dependent variable and independent variables. Inputs The model inputs required are the variable values for the dependent variable and the independent variables (although actually only the intervariable correlations are enough). Outputs The regression model will output regression coefficients—and their associated beta coefficient and r-values—that can be used to evaluate the strength of the relationship between the respective independent variable and the dependent variable. The model automatically controls statistically for the other independent variables. Thus, a regression coefficient represents the effect of one independent variable with the other independent variables held constant. Another output is the r2 value, which pr...

Multiple Regression Recall that the error term included the effects on the dependent variable of variables other than the independent variable. It may be desirable to include explicitly some of these variables in the model. In a prediction context, their inclusion will improve the model's ability to predict and will decrease the unexplained variation. In terms of understanding, it will introduce the impact of other variables and therefore elaborate and clarify the relationships. In our example it might be hypothesized that store size will influence store traffic. The larger stores usually will tend to get more customers. Thus, if store size is known, the prediction of store traffic should improve. Also, it might be desirable to include a variable that would be one if the store were located in a suburban area and zero if it were located in an urban area. Such a zero-one variable is termed a dummy variable and is often convenient and useful. Our model now becomes Y = 3o + 61X...

Regression Analysis and a Data Analysis Overview - Prediction The regression model, of course, can be used as a predictive tool. Given advertising expenditure, the model will predict the store traffic that will be generated. For example, if an advertising expenditure level of $200 is proposed, a model-based estimated store traffic would be Y = a + bX = 275 + 0.74(200) = 423 Two cautionary comments. First, prediction using extreme values of the independent variable (such as X = 2000) can be risky. Further, the random sample provided no information about extreme values of advertising. Second, if the market environment changes, such as a competitive chain opening a series of stores, then the model parameters probably will be affected. The data from the random sample were obtained under a set of environmental conditions. If they change then the model may well be affected. How Good Is the Prediction, r2? A natural question is: how well does the model predict? Consider store 8 in...

Regression Analysis and a Data Analysis Overview - Model Parameters Estimating the Parameters The parameters, a and 6, are the characteristics of the relationship between X and Y that are of prime interest. One of the goals of the regression analysis is to determine what they are. The procedure is to obtain a random sample of stores and to use the information from this random sample to estimate a and B. For example, assume that a random sample of 20 stores was selected. For each store in the sample, the number of people entering the store on a given Saturday was determined. Further, for each store the expenditure on advertising for the previous day was recorded. The results are plotted in Figure 20-2. The next step is to obtain a line that has the best "fit" to these points. Of course, a line could be drawn freehand; in practice, however, a computer program is used. The computer program generates a line that has the property that the squared vertical deviations from the...

Regression Model The construction of a regression model usually starts with the specification of the dependent variable and the independent variable or variables. Suppose that our organization, Midwest Stereo, has 200 retail stores that sell hi-fi and related equipment. Our goal is to determine the impact of advertising on store traffic, that is, the number of people who come into the store as a result of the advertising. More specifically, we are concerned with the number of people entering the store on a Saturday as a result of advertising placed the day before. The following regression model might then be hypothesized: Y = a + fiX + e where Y = the number of people entering the store on Saturday X = the amount of money the store spent on advertising on Friday e = an error term a, (3 = model parameters There are several aspects of the model worth emphasizing. First, the hypothesized relationship is linear; it represents a straight line, as shown in Figure 20-1. Such an assu...

Regression Analysis and a Data Analysis Overview In data analysis there is often one or a small number of key variables that become the focus of the study. When a new product or concept is being explored, for example, one of the key variables is usually the respondent's attitude or intentions toward it. Is it something that the respondent would consider buying and/or using? The goal may be to predict the ultimate usage of the product or concept under a variety of conditions. Another goal might be to understand what causes high intentions so that when the product does emerge the marketing program can be adjusted to improve the success probability. Consider the HMO study. In this study, the intention to enroll was one of the variables of interest. One motivation was prediction: to predict the enrollment if the plan were implemented. Thus, the intention question was analyzed to help predict the acceptance of the concept among the sample of respondents. However, it would be desira...

Conjoint Analysis - Summary Applications Conjoint analysis is used to predict the buying or usage of a new product, which still may be in concept form. It also is used to determine the relative importance of various attributes to respondents, based on their making trade-off judgments. Inputs The primary input is a list of attributes describing the concept. For each attribute the various levels need to be described. Respondents make judgments about the concept either by considering two attributes at a time (trade-off approach) or by making an overall judgment of a full profile c:" attributes (full-profile approach). Outputs A value of relative utility is assigned to each level of an attribute. Each respondent will have her or his own set of utilities, although an average respondent can be created by averaging the input judgments. The percentage of respondents that would most prefer one concept from among a defined set of concepts can be determined. Assumptions The b...

Conjoint Analysis - Analysis of Dependence Factor analysis, multidimensional scaling, and cluster analysis, the subjects of Chapters 17 and 18, are termed analysis of interdependence techniques because they analyze the interdependence between questions variables, or objects. The goal is to group or position variables or objects. In contrast, when there is a single variable that is the focus, such as a person s preference for a new concept, the goal is to predict this preference level or :: understand what influences it. Such a variable is termed a dependent variable. The variables that are used to predict or explain the dependent variable are termed independent variables. The techniques employed to help analysts predict or explain are termed analysis of dependence techniques. Conjoint analysis is an analysis of dependence technique. The dependent variable is the preference judgment that a respondent makes about a new concept. The independent variables are the attribute levels that ...

Conjoint Analysis - Application Issues Three areas of application appear especially promising. First, the insights that are gained into how consumers make choices within an existing market, coupled with information on the perceptions of the competitive alternatives, are valuable for guiding communications programs. Second, the analysis can suggest new product or service configurations with significant consumer appeal relative to competitive alternatives. Finally, the utility measurements can be used to develop strategic marketing simulations.12 These are used to evaluate the volume and profit implications of changes in marketing strategies. The following is a typical application, taken from Green and Wind.13 As a case in point, a large-scale study of consumer evaluations of airline services was conducted in which consumer utilities were developed for some 25 different service factors such as on-ground services, in-flight services, decor of cabins and seats, scheduling, routing, and...

Conjoint Analysis - Comparing Data Collection Approaches The arguments in favor of the full-profile approach are that (1) the description of the concepts is more realistic since all aspects are considered at the same time, (2) the concept evaluation task can employ either a ranking or rating scale, and (3) fewer judgments have to be made by the respondent than if the two-attribute trade-off approach were used. Unfortunately, as the number of attributes increases the task of judging the individual profiles becomes very complex and demanding. With more than five or six attributes there is a strong possibility of information overload, which usually leads respondents to ignore variations in the less important factors. To get the flavor of this problem, look back to Figure 19-2 and see how difficult it is to choose one package holiday over another. The pairwise trade-off approach is not a panacea either. Because more judgments are required, the task can be tedious and time consuming. Co...

Conjoint Analysis - Collecting Trade-off Data Respondents can reveal their trade-off judgments by either considering two attributes at a time, or by making an overall judgment of a full profile of attributes. Full-Profile Approach In a full-profile approach respondents are given cards that describe complete product or service configurations. For example, two possible full-profile descriptions of package tour holidays are shown in Figure 19-2. Not all possible combinations of attribute levels have to be presented in order to estimate the utilities. For example, in Figure 19-2, even with six attributes each described at three levels, there are 18 profiles to compare.5 Respondents can be asked either to rank order the profiles in order of preference, or assign each of the 18 cards to a category of a rating scale measuring overall preference or intentions to buy. The advantage of the rating scale is that it can be administered by mail, whereas a ranking task usually entails a perso...

Conjoint Analysis - Overview of Conjoint Analysis Conjoint analysis is an extremely powerful and useful analysis tool. Its acceptance and level of use have been remarkably high since its appearance around 1970. One study concluded that over 1000 conjoint studies were undertaken between 1971 and 1978.4 As the previous examples indicate, a major purpose of conjoint analysis is to help select features to offer on a new or revised product or service, to help set prices, to predict the resulting level of sales or usage, or to try on a new-product concept. Conjoint analysis provides a quantitative measure of the relative importance of one attribute as opposed to another. In Chapter 9, other methods to determine attribute importance weights were introduced. The most direct was simply to ask people which attribute is important. The problem is that respondents usually indicate that all attributes are important. In selecting a car, they want good gas mileage, sport appearance, lots of room, ...

Conjoint Analysis Before beginning an examination of the technique of conjoint analysis, we first will take a look at three examples of the kind of management problems for which conjoint analysis is extremely well suited: 1. Modifying a credit card 2. Identifying land-use attitudes 3. Revamping an industrial product line Modifying a Credit Card A firm wanted to improve the benefits of its credit card to retailers, to get more of them to honor the card. Changes could be made to any of the following attributes: • Discount rate (percentage of billings deducted by credit card company for providing the service); the alternatives were 2.5 percent versus 6 percent • Speed of payment after receipt of week's vouchers (one day versus 10 days) • Whether card authorization was by computer terminal or toll-free billing number • Extent of support payment for local advertising by retailer (either 1.0 percent pr 0.75 percent of billings) • Provision of a rebate of 15 perce...

Multidimensional Scaling and Cluste Analysis - Summary Multidimensional scaling involves identifying dimensions by which objects are perceived and evaluated and positioning those objects and ideal objects with respect to those dimensions. The use of attribute data provides useful diagnostic information; however, it can be difficult to create a relevant and complete attribute list. The alternative is to base the perceptual map on similarity or preference data. Cluster analysis provides a direct approach to grouping variables, objects, or people. The clusters are based on some kind of between-object similarity measure. Either hierarchical or nonhierarchical methods may be used to form clusters of objects on the basis of their between-object similarity.

Multidimensional Scaling and Cluste Analysis - Cluster Analysis All scientific fields have the need to cluster or group similar objects. Botanists group plants, historians group events, and chemists group elements and phenomena. It should be no surprise that when marketing managers attempt to become more scientific they should find a need for procedures that will group objects. Actually, the practical applications in marketing for cluster analysis are far too numerous to describe; however, it is possible to suggest by example the scope of this basic technique. One goal of marketing managers is to identify similar segments so that marketing programs can be developed and tailored to each segment. Thus, it is useful to cluster customers. We might cluster them on the basis of the product benefits they seek. Thus, students could be grouped on the basis of the benefits they seek from a college. We might group customers by their lifestyles. The result could be a group that likes outdoor a...

Multidimensional Scaling and Cluste Analysis - Multidimensional Scaling Multidimensional scaling basically involves two problems. First, the dimensions on which customers perceive or evaluate objects (organizations products, or brands) must be identified. For example, students must evaluate prospective colleges in terms of their quality, cost, distance from home and size. It would be convenient to work with only two dimensions, since the objects could then be portrayed graphically. However, it is not always possible to work with two dimensions, since additional dimensions sometimes are needed to represent customers' perceptions and evaluations. Second, objects need to be positioned with respect to these dimensions. The output of MDS is the location of the objects on the dimensions and is termed a perceptual map. There are several approaches to multidimensional scaling. They differ in the assumptions they employ, the perspective taken, and the input data used. Figure 18-1 provid...

Factor Analysis - Appendix - Additional Perspectives to Factor Analysis In this appendix, two additional perspectives may provide further insight into the somewhat slippery subject of factor analysis. The first is a geometric perspective and the second is an algebraic or "factor model" perspective. A Geometric Perspective It often is helpful to consider a geometric interpretation of factor analysis. Principal components analysis, normally the first step in a factor analysis, will be described from a geometric perspective in the context of an example. Suppose a group of prospective students rated, on a -5 to +5 scale, the importance of "good faculty" and "program reputation" in their decision as to which school to attend. Thus, a -5 rating would mean that the individual does not really care if the school has a good faculty (rather, she or he might be more concerned about the athletic program). The respondents are plotted with respect to their ratings...