**Rebate Redeemers**

A study of 294 consumers was undertaken to determine the correlates of rebate proneness, or the characteristics of consumers who respond favorably to rebate promotions. The predictor variables were four factors related to household shopping attitudes and behaviors, and selected demographic characteristics (sex, age, and income). The dependent variable was the respondent’s degree of rebate proneness, of which three levels were identified. Respondents who reponed no rebate-triggered purchases during the past 12 months were classified as nonusers; those who reponed one or two such purchases as light users and those with more than two purchases, frequent users of rebates. Multiple discriminant analysis was used to analyze the data

Two primary findings emerged. First, consumers’ perception of the effort/value relationship was the most effective variable in discriminating among frequent, light, and nonusers of rebate offers. Clearly, rebate-sensitive consumers associate less effort with fulfilling the requirements of the rebate purchase, and they are willing to accept a relatively smaller refund than other customers. Second, consumers who are aware of.the regular prices of products, so that they recognize bargains, are more likely than others to respond to rebate offers

These findings were utilized by Dell when it offered up to $150 cash rebates on its notebook computers during April 2009. The company felt that this would encourage the rebate-sensitive customers to choose Dell notebooks

The rebate proneness example examined three groups (nonusers, light users, and frequent users of rebates). Significant inter group differences were found using multiple predictor variables. An examination of differences across groups lies at the bean of the basic concept of discriminant analysis

**Basic Concept of Discriminant Analysis**

Discriminant analysis is a technique for analyzing data when the criterion or dependent variable is categorical and the predictor or independent variables are metric, i.e., measured on at least interval scales,” For example, the dependent variable may be the choice of a brand of personal computer (brand A, B, or C) and the independent variables may be ratings of attributes of PCs on a 7-point Likert scale. The objectives of discriminant analysis are as follows:

1. Development of discriminant functions, or linear combinations of the predictor or independent variables, which will best discriminate between the categories of the criterion or dependent variable (groups)

2. Examination of whether significant differences exist among the groups, in terms of the predictor variables

3. Determination of which predictor variables contribute to most of the inter group differences

4. Classification of cases to one of the groups based on the values of the predictor variables

5. Evaluation of the accuracy of classification

Discriminant analysis techniques are described by the number of categories possessed by the criterion variable. When the criterion variable has two categories, the technique is known as two-group discriminant analysis. When three or more categories are involved, the technique is referred to as multiple discriminant analysis. The main distinction is that, in the two-group case, it is possible to derive only one discriminant function. In multiple discriminant analysis, more than one function may be computed

Examples of discriminant analysis abound in marketing research. This technique can be used to answer questions such as

• In terms of demographic characteristics, how do customers who exhibit store loyalty differ from those who do not?

• Do heavy, medium, and light users of soft drinks differ in terms of their consumption of frozen foods?

• What psycho graphic characteristics help differentiate between price-sensitive and non-price-sensitive buyers of groceries?

• Do the various market segments differ in their media consumption habits?

• In terms of lifestyles, what are the differences between heavy patrons of regional department store chains and patrons of national chains?

• What are the distinguishing characteristics of consumers who respond to direct mail solicitations?

**Relationship of Discriminant and Legit Analysis to ANOVA and Regression**

The relationship among discriminant analysis, analysis of variance (ANOVA), and regression analysis is shown in Table 18.1. We explain this relationship with an example in which the researcher is attempting to explain the amount of life insurance purchased in terms of age and income. All three procedures involve a single criterion or dependent variable and multiple predictor or independent variables. However, the nature of these variables differs. In analysis of variance and regression analysis, the dependent variable is metric or interval scaled (amount of life insurance purchased in dollars), whereas in discriminant analysis it is categorical (amount of life insurance purchased classified as high, medium, or low). The independent variables are categorical in the case of analysis of variance (age and income are each classified as high, medium, or low) but metric in the case of regression and discriminant analysis (age in years and income in dollars, i.e., both measured on a ratio scale).

Two-group discriminant analysis, in which the dependent variable has only two categories, is closely related to multiple regression analysis. In this case, multiple regression, in which the dependent variable is coded as a 0 or I dummy variable, results in partial regression coefficients that are proportional to discriminant function coefficients (see the following section on the discriminant analysis model). The nature of dependent and independent variables in the binary logit odel is similar to that discriminant analysis

Members of Glare denoted by 1 and members of G2 by 2. The resultant ellipses encompass some specified percentage of the points (members), say 93 percent in each group. A straight line is drawn through the two points where the ellipses intersect and then projected to a new axis, D. The overlap between the univariate distributions G l’ and G2′, represented by the shaded area in Figure 18.1, is smaller than would be obtained by any other line drawn through the ellipses representing the scatter plots. Thus, the groups differ as much as possible on the D axis. Several statistics are associated with discriminant analysis.

**Statistics Associated with Discriminant Analysis**

The important statistics associated with discriminant analysis include the following.