From the household budget survey of 1980 of the Dutch Central Bureau of Statistics, J. S. Cramer obtained the following logit model based on a sample of 2820 households. (The results given here are based on the method of maximum likelihood and are after the third iteration.)** The purpose of the logit model was to determine car ownership as a function of (logarithm of) income. Car ownership was a binary variable: Y = 1 if a household owns a car, zero otherwise.
Lˆ i = -2.77231 + 0.347582 ln Income
t = (-3.35) (4.05)
χ 2 (1 df) = 16.681 ( p value = 0.0000)
where Lˆ i = estimated logit and where ln Income is the logarithm of income. The χ 2 measures the goodness of ?t of the model.
a. Interpret the estimated logit model.
b. From the estimated logit model, how would you obtain the expres- sion for the probability of car ownership?
c. What is the probability that a household with an income of 20,000 will own a car? And at an income level of 25,000? What is the rate of change of probability at the income level of 20,000?
d. Comment on the statistical signi?cance of the estimated logit model.