15.1. A logistic regression model describes how the probability of voting for Candidate X in an election depends on x = voter’s total family income (in thousands of dollars)

in the previous year. The sample prediction equation is

(a) Identify ˆβ and interpret its sign.

(b) Find the estimated probability of voting for the candidate when (i) income = 5000, (ii) income = 10000.

(c) At which income level is the estimated probability of voting for the candidate (i) equal to 0.50? (ii) greater than 0.50?

(d) For the region of x-values for which P(y = 1) is near 0.50, give a linear approximation for the change in the probability for an increase of $1000 in income.

(e) Explain the effect of a $10,000 increase in family income on the odds of voting for the candidate.

P(y = 1) log 1-P(y = 1). 1)] =-2.00 +0.03.x.