The clothing retailer problem. The scatterplot and histogram below show the residuals from the model in Example 28.20 with all explanatory variables, some interaction terms, and quadratic terms. Comment on both plots. Do you see any reason for concern in using this model for inference?

Example 28.20:

Create the following interaction terms and quadratic terms from the potential explanatory variables:

Figure 28.15 shows the multiple regression output using all six explanatory variables provided by the manager and the five new variables. Most of the individual t statistics

FIGURE 28.15:

have P-values greater than 0.2 and only three have P-values less than 0.05. The model is successful at explaining 91.66% of the variation in the purchase amounts, but it is large and unwieldy. Management will have to measure all of these variables to use the model in the future for prediction. This model does set a standard: removing explanatory variables can only reduce R2, so no smaller model that uses some of these variables and no new variables can do better than R₂ = 91.66%. But can a simpler model do almost as well?