The Students data file at the text website shows responses of a class of social science graduate students at the University of Florida to a questionnaire that asked about gender (1 = female, 0 = male), age, hsgpa = high school GPA (on a four-point scale), cogpa = college GPA, dhome = distance (in miles) of the campus from your home town, dres = distance (in miles) of the classroom from your current residence, tv = average number of hours per week that you watch TV,sport = average number of hours per week that you participate in sports or have other physical exercise, news =

number of times a week you read a newspaper, aids = number of people you know who have died from AIDS or who are HIV+, veg = whether you are a vegetarian

(1 = yes, 0 = no), affil = political affiliation (1 = Democrat, 2 = Republican, 3 =

Independent), ideol = political ideology (1 = very liberal, 2 = liberal, 3 = slightly liberal, 4 = moderate, 5 = slightly conservative, 6 = conservative, 7 = very conservative), relig = how often you attend religious services (0 = never, 1 = occasionally, 2 = most weeks, 3 = every week), abor = opinion about whether abortion should be legal in the first three months of pregnancy (1 = yes, 0 = no), affirm = support affirmative action (1 = yes, 0 = no), and life = belief in life after death (1 = yes, 2 = no, 3 = undecided).

a. Show all steps of a model-selection method such as purposeful selection for choosing a model for predicting abor, when the potential explanatory variables are ideol, relig, news, hsgpa, and gender.

b. Using an automated tool such as the stepAIC or bestglm function in R, construct a model to predict abor, selecting from the 14 binary and quantitative variables in the data file as explanatory variables.

c. With y = veg and the 14 binary and quantitative variables in the data file as explanatory variables, show that the likelihood-ratio test of H0: β1 = ··· =

β14 = 0 has P-value < 0.001, yet forward selection using Wald tests with 0.05 criterion selects the null model. Explain how this could happen.