Question

A logistic regression model describes how the probability of voting for the Republican candidate in a U.S. presidential election depends on x_1=family income, x_2=number of years of education, and s=sex (1=male, 0 = female), the prediction equation is "logit"[P ̂ (y=1)] = -2.40+0.02(x_1) +0.08(x_2)+0.20s.

For this sample, ranges from 6 to 157 with a standard deviation of 25, and ranges from 7 to 20 with a standard deviation of 3.

1. Interpret the sign of the coefficients of income and years of education.
2. Find the estimated probability of voting Republican for (i) a man with 16 years of education and income 30 thousand dollars, (ii) a woman with 16 years of education and income 30 thousand dollars.

Answer 1

a) The coefficient of income that is x1 here is 0.02 which is positive, therefore as the coeffiicent is positive here, an increase in family income results into an increase in probability of voting for the Republican candidate in a U.S. presidential election

Also as the sign of x2 that is the number of years of education here is positive, therefore as the coeffiicent is positive here, an increase in number of years of education results into an increase in probability of voting for the Republican candidate in a U.S. presidential election

b) (i) The probability here is computed as:

Therefore 0.4207 is the required probability here.

(ii) For woman, the same probability is computed as:

Therefore 0.3729 is the required probability here.