Working with the full quadratic regression model EY 0 1X1 2X2 3X2 1 4X2 2 5X1X2 and a three-dimensional

Working with the full quadratic regression model EðYÞ ¼ β0 þ β1X1 þ β2X2 þ β3X2 1 þ β4X2 2 þ β5X1X2 and a three-dimensional graphics program, draw pictures of the regression surface (similar to Figure 17.1 on page 504) for various values of the parameters β1; ... ; β5 and various values of the explanatory variables X1 and X2. You will derive a better impression of the flexibility of this model if you experiment freely, but the following suggestions may prove useful:

& Try both positive and negative values of the parameters.

& Try cases in which there are both positive and negative Xs, as well as cases in which the Xs are all positive.

& Try setting some of the parameters to 0.

Exercises 17.4. Cowles and Davis’s logistic regression of volunteering on sex, neuroticism, extraversion and the product of neuroticism and extraversion is discussed in Section 17.1.
Show that ðaÞ interactions between sex and the other factors and ðbÞ squared terms in neuroticism and extraversion are not required in this model.