Part II. Answer the following. Show your work for all answers. 10 points each. 1. After watching the TV show American Idol, Blake thinks that people prefer younger performers over older performers. Maybe this is because younger singers have a “lighter” voice that sounds more pleasant. Thus, Blake thinks younger voters will receive more votes. To answer his question, he gets super-secret telephone voting data from the show and regresses the log of Votes for the singer on singer Age and obtains the following regression output (standard error in parentheses):

Log Votes = 5.0 - 0.03 Age (0.01)

R-squared=0.25

a. (3pts) Plot the Log Votes on the vertical axis and Age on the horizontal axis. Indicate vertical intercept and slope.

Log Votes 5.0 slope= -0.03

Age

b. (4pts) Interpret the value of the coefficient in the above output. Does the regression coefficient support Kathleen’s hypothesis? Be sure to consider tests of significance. = -0.03, which means that for every one year that Age rises, votes are 3% lower Yes, his hypothesis is supported, since the coefficient is negative, and he expected a negative relationship. The significance is also high, with a t-stat= -0.03/0.01 = 3 (absolute value), which is greater than 2. The R-squared is also somewhat low, however, but this is hard to interpret without comparison to another model specification

c. (3pts) After watching another season of American Idol, Blake now thinks that singing too long can hurt the voice and make the voice sound “harsh.” He believes that singers with too much experience will have damaged voices and will receive fewer votes.