Homework assignment, due mardi 13 oct

1. Exercise 5.1: The folder nes contains the survey data of presidential preference and income for the 1992 election analyzed in Section 5.1, along with other variables including sex, ethnicity, education, party identification, and political ideology.

(a) Fit a logistic regression predicting support for Bush given all these inputs. Consider how to include these as regression predictors and also consider possible interactions.

(b) Evaluate and compare the different models you have fit. Consider coefficient estimates and standard errors, residual plots, and deviances.

(c) For your chosen model, discuss and compare the importance of each input variable in the prediction.

2. Exercise 5.2: Without using a computer, sketch the following logistic regression lines:
(a) Pr(y = 1) = invlogit (x)
(b) Pr(y = 1) = invlogit (2 + x)
(c) Pr(y = 1) = invlogit (2x)
(d) Pr(y = 1) = invlogit (2 + 2x)
(e) Pr(y = 1) = invlogit (−2x)

3. Exercise 5.3: You are interested in how well the combined earnings of the parents in a child’s family predicts high school graduation. You are told that the probability a child graduates from high school is 27% for children whose parents earn no income and is 88% for children whose parents earn $60,000. Determine the logistic regression model that is consistent with this information. (For simplicity you may want to assume that income is measured in units of $10,000).