A Categorical Regression Analysis

The categorical nature of the variables and the nonlinear relationship between Preference and Package design suggest that regression on optimal scores may perform better than standard regression. The U-shape of the residual plots indicates that a nominal treatment of Package design should be used. All other predictors will be treated at the numerical scaling level.

The response variable warrants special consideration. You want to predict the values of Preference. Thus, recovering as many properties of its categories as possible in the quantifications is desirable. Using an ordinal or nominal scaling level ignores the differences between the response categories. However, linearly transforming the response categories preserves category differences. Consequently, scaling the response numerically is generally preferred and will be employed here.

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