Use the data in PNTSPRD.RAW for this exercise.
(i) The variable favwin is a binary variable if the team favored by the Las Vegas point spread wins. A linear probability model to estimate the probability that the favored team wins is
P(favwin = 1 | spread) = β0 + β1spread.
Explain why, if the spread incorporates all relevant information, we expect β0 = .5.
(ii) Estimate the model from part (i) by OLS. Test H0: β0 = .5 against a two-sided alternative. Use both the usual and heteroskedasticity-robust standard errors.
(iii) Is spread statistically significant? What is the estimated probability that the favored team wins when spread = 10?
(iv) Now, estimate a probit model for P( favwin = \\spread). Interpret and test the null hypothesis that the intercept is zero.
(v) Use the probit model to estimate the probability that the favored team wins when spread = 10. Compare this with the LPM estimate from part (iii).
(vi) Add the variables favhome, fav25, and und25 to the probit model and test joint significance of these variables using the likelihood ratio test. (How many df are in the chi-square distribution?) Interpret this result, focusing on the question of whether the spread incorporates all observable information prior to a game.