(a) Using each model, calculate the predicted probability of survival for a female child in rst class accommodations. Do these predictions make intuitive sense? (b) Maritime code [the code of the sea) dictates that women and children be saved before adult mates [hence the saying "women and children rst"). Using each output, discuss whether (and by how much) being a child increased the probability of sin'vival (for the probit, you should perform a comparison for a male child in third class accommodations). Again using each output, discuss whether (and by how much) being female increased the probability of survival (for the probit, you should perform a comparison for a female adult in third class accommodations). (c) Maritime code also dictates that the captain go down (perish) along with the ship. Indeed, the Titanic's captain did not survive the voyage. Using the LPM output only, discuss whether the data provides any evidence that the practice of "going down with the ship" was followed by the rest of the crew? How would your answer change if you had used the probit output instead? Justify your answers. (d) Several historians have argued that the practice of saving women and children rst, even if followed by the passengers of the Titanic, did not extend to children in third (the lowest) class accormrlodations. What variable could you add to the probit model above to test this hypothesis? Assuming that the historians' hypothesis is correct, what would you expect to nd? 4. (Empirical Exercise) On the course website you will nd an Excel dataset (pntsprd.xls} containing data on the Las Vegas point spreads for 553 men's college basketball games from the 19941995 season. The variable fa'uwin is a binary variable that equals 1 if the team favored by the Las Vegas spread wins. The variable spread [1101-13le the amount by which the favored team is expected to win. Make sure to include your Stata output with your homework! (a) A linear probabiiity model to estimate the probability that the favored team wins is P (frw'min = 1 I spread) =1? 0 +13 1.9p7'end Explain why, if the spread incorporates all relevant information, we expect D = .5. (b) Estimate the model from part a) by OLS. Test H0 33 0 : .5 against a two-sided alternative. (c) Is the spread statistically signic:mt? What is the estimated probability that the favored team wins when spread = 10? (d) Now estimate a probit model for P (fmrwin = 1 I spread). Interpret and test the null hypothesis that the intercept is zero. (e) Use the probit model to estimate the probability that the favored team wins when 3107'ch = 10. Compare this with the LPM estimate from part c). (f) Repeat only part c) using a. iogit model