Consider the automobile purchase data in Problem 13.5. Fit models using both the probit and complementary log-log functions. Compare these models to the one obtained using the logit.

Data From Problem 13.5

A study was performed to investigate new automobile purchases. A sample f 20 families was selected. Each family was surveyed to determine the age of their oldest vehicle and their total family income. A follow-up survey was conducted 6 months later to determine if they had actually purchased a new vehicle during that time period ( y=1$\mathrm{????}=1$ indicates yes and y=0$\mathrm{????}=0$ indicates no). The data from this study are shown in the following table.

Income, x Age, X2 y Income, x Age, x2 y 45,000 40,000 60,000 50,000 55,000 50,000 35,000 48,000 65,000 53,000 1 2432257222 0 37,000 0 31,000 40,000 1 75,000 0 43,000 1 49,000 1 37,500 100 71,000 34,000 27,000 5742924156 1 1 1 1 0 1 0