Refer to the S.A.T. data given in Table 2-15 on the textbook's Web site. Suppose you want to predict the male math scores on the basis of the female math scores by running the following regression:
Yt = B1 + B2Xt + ut
where Y and X denote the male and female math scores, respectively.
a. Estimate the preceding regression, obtaining the usual summary statistics.
b. Test the hypothesis that there is no relationship between Y and X whatsoever.
c. Suppose the female math score in 2008 is expected to be 490. What is the predicted (average) male math score?
d. Establish a 95% confidence interval for the predicted value in part (c).