Redo exercise 52 using the logit model.

Exercise 52

More and more parole boards are using risk assessment tools when trying to determine an individual's likelihood of returning to crime (The Boston Globe, February 20, 2011). Most of these models are based on a range of character traits and biographical facts about an individual. Many studies have found that older people are less likely to re-offend than younger ones. In addition, once released on parole, women are not likely to re-offend. A sociologist collects data on 20 individuals who were released on parole two years ago. She notes if he/she committed another crime over the last two years (crime equals 1 if crime committed, 0 otherwise), the individual's age at the time of release, and the gender of the individual (gender equals 1 if male, 0 otherwise). The accompanying table shows a portion of the data.

Crime............. Age.......... Gender

1.................... 25................... 1

0.................... 42....................1

â‹®............................. â‹®...........................â‹®

0.................... 30...................1

a. Estimate the linear probability model where crime depends on age and gender.

b. Are the results consistent with the claims of other studies with respect to age and gender?

c. Predict the probability of a 25-year-old male parolee committing another crime; repeat the prediction for a 25-year-old female parolee.

THE LOGIT MODEL

exp(bo t Dix) 1+expDo bability 1.2 A8 0.6 LPM: P bobx 0.4 0.2 exp(bo + b,x) Logit: P-1+explbo + bx) 0.2