13.56 Many predictors of voting Refer to the previous two exercises. When the explanatory variables are x1 = family income, x2 = number of years of education, and x3 = gender (1 = male, 0 = female), suppose a logistic regression reports Term Coef Constant −2.165 radius 2.585 Term Coef SE Coef Constant −2.40 0.12 income 0.02 0.01 education 0.08 0.05 gender 0.20 0.06 For this sample, x1 ranges from 6 to 157 with a standard deviation of 25, and x2 ranges from 7 to 20 with a standard deviation of 3.

a. Interpret the effects by using the sign of the coefficient for each predictor.

b. Illustrate the gender effect by finding and comparing the estimated probability of voting Republican for (i) a man with 16 years of education and income $40,000 and (ii) a woman with 16 years of education and income $40,000.