Question 1- Political business cycle: Do economic events affect presidential elections? To test this so-called political business cycle theory, Gary 5rnith²⁰ obtained the following regression results based on the U.S. presidential elections for the four yearly periods from 1928 to 1980 (i.e., the data are for years 1928, 1932, etc.):

Y_t^{^}= 53.10 - 1.70X_t

t = (34.10) (-2.67)             r² = 0.37

where Y is the percentage of the vote received by the incumbent and X is the unemployment rate change-unemployment rate in an election year minus the unemployment rate in the preceding year.

a. A priori, what is the expected sign of X?

b. Do the results support the political business cycle theory? Support your contention with appropriate calculations.

c. Do the results of the 1984 and 1988 presidential elections support the preceding theory?

d. How would you compute the standard errors of b₁ and b₂?

Question 2- 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:

Y_t = B₁ + B₂X_t + u_t

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).

Question 3- Consider the following regression results:²²

Y_t^{^}  = -0.17 + 5.26X_t           R₂^- = 0.10, Durbin-Watson = 2.01

t = (-1.73)(2.71)

where Y= the real return on the stock price index from January of the current year to January of the following year

X = the total dividends in the preceding year divided by the stock price index for July of the preceding year

t = time

Note: On Durbin-Watson statistic, The time period covered by the study was 1926 to 1982.

Note: R₂^- stands for the adjusted coefficient of determination. The Durbin-Watson value is a measure of autocorrelation. Both measures are explained in subsequent chapters.

a. How would you interpret the preceding regression?

b. If the previous results are acceptable to you, does that mean the best investment strategy is to invest in the stock market when the dividend/price ratio is high?

c. If you want to know the answer to part (b), read Shiller's analysis.

Attachment:- table 2-15.rar