16.1 In Section 16.1.5w e presenta n exampleo f transportationc hoice.U se the sample data on automobile and public transportation times in transport.dal for the following exercises.

(a) Estimate the linear probability model AUTO : 9r * \yDTIME * e using least squares estimation. What is the estimated marginal effect of an increase in DTIME on the probability of a person choosing automobile transportation given that DTIME :20?

(b) For each sample observation, calculate the predicted probability of choosing automobile transportation P@UTO) : br * bzDTIME. Are all the predicted probabilities plausible?

(c) Using the error variance in equation (1 6.6) compute the feasible generalized least squares estimates of the linear probability model. If a predicted probability was zero or negative, replace it by 0.0 I ; if a predicted probability was greater than or equal to l, replace it by 0.99. Compare these estimates to those from part (a).

(d) Using generalized least squares, as we have done in part (c), cures the basic deficiency of the linear probability model. True or false? Explain your answer.

(e) Foreacho f the2l observations,estimatetheprobabilityocfh oosingautomobile transportation using the generalized least squares estimates of the linear probability model. Predict the choice of transportation mode using the rule[liO :
1 if the predicted probability is 0.5 or larger, otherwise AUTO: 0. Define a successful prediction to be when we predict that a person will choose the automobile @UfO: 1) when they actually did (AUTO -- l), OR when we predict that a person will choose public transportation @UfO : 0) when they did @UfO : 0). Calculate the percentage of correct predictions in the N : 2l cases.
(0 Compare the percentage of correct predictions from the linear probability model to that for the probit model.