Exercises 11.89 through 11.92 use the PPROMO data set shown in Table 11.7.

Question 11.91

11.91 Residuals and other models.

Refer to the previous exercise. Analyze the residuals from your analysis, and investigate the possibility of using quadratic and interaction terms as predictors. Write a report recommending a final model for this problem with a justification for your recommendation.

ppromo

11.91

The Normal quantile plot shows a slight left-skew in the residuals. The residual plot for promotions looks good (random). The residual plot for Discount shows a slight curve and suggests a possible quadratic model. Investigating a quadratic term for discount and possible interaction terms shows that none of the interaction terms test significant. After removing these, the quadratic term for discount is significant . The equation becomes: . This model has an , which is somewhat better than the 56.62% for the model without the quadratic term. It is possible to leave out the quadratic term to simplify interpretation; otherwise, the model with this term seems to be best in terms of prediction.