In an earlier tutorial, you were introduced to a data set that contains voting information for 173 US election districts. Suppose we have access to 40 observations from that data set. Throughout this assignment, data analysis is conducted on these 40 observations only.

The variables are defined as follows:

voteA = percentage of the vote received by Candidate A

expendA expenditure by Candidate A (in million dollars) expendB expenditure by Candidate B (in million dollars)

prtystrA measure of party strength for candidate A (the fraction of the most recent presidential vote that went to As party, expressed in percent)

A multiple regression generates the following result:

voteA = 80.471 1.276*expendA 2.907*expendB + 0.093*prtystrA

se: (9.223)	(1.466)	(0.540)	(0.081)
t-stat: (8.724)	(-0.870)	(-5.375)	(1.138)
p-val: (0.000)	(0.389)	(0.000)	(0.262)

R² = 0.593; adjusted R² = 0.559; F-statistic = 17.51 (p-val = 0.0001).

(a)(1pt) What is the interpretation of the coefficients? Are the slope coefficients individually significant? (Note: use a significance level of 5 percent).

(b)(1pt) We are interested in conducting a joint significance test on expendA and prtystrA. Write down the null and alternative hypothesis of this test. What are the degrees of freedom associated with this test?

The researcher runs another regression, which generates the following result: voteA = 79.210 3.238*expendB

se: (2.011)	(0.456)
t-stat: (39.37)	(-7.10)
p-val: (0.000)	(0.000)

R² = 0.569; adjusted R² = 0.558; F-statistic = 50.35 (p-val = 0.001).

(c)(1pt) Now, use the relevant information in the above two regressions and the appropriate F-statistic formula to compute the F-statistic for the test in part (b).

(d)(1pt) For the test in part (b), what is the critical value associated with a significance level of 5 percent? (Note: briefly explain how you obtain this result. Use the nearest degrees of freedom in the attached statistical table.) Are expendA and prtystrA jointly significant at the 5 percent level?

(e)(1pt) The researcher computes the squared residuals (denoted as u2) using the sample regression line voteA = 79.210 3.238*expendB. He then regresses the squared residuals on expendB. The estimation result is given as follows:

u2 = 18.334 + 1.166*expendB se: (13.858) (3.144)

t-stat: (1.32) (0.37) p-val: (0.194) (0.713)

R2 = 0.004; F-statistic = 0.14 (p-val: 0.713)

According to the Breusch-Pagan test, is the null hypothesis (i.e., homoskedasticity) rejected? (Note: use a significance level of 5 percent)

The researcher defines the following new variables:

expendA_d if campaign expenditure by A exceeds 5.5 million dollars, otherwise expendB_d if campaign expenditure by B exceeds 5.5 million dollars, otherwise

expendAB_d = expendA_d*expendB_d (i.e., an interaction between expendA_d and expendB_d)

expendb_0 if campaign expenditure by B is less than 5 million dollars, otherwise

expendb_1 if campaign expenditure by B is between 5 and 5.5 million dollars, otherwise

Part (f) and part (g) are based on the following regression result: voteA = 69.22 0.63*expendA_d 11.92*expendB_d

se: (1.83)	(2.17)	(2.17)
t-stat: (37.73)	(-0.29)	(-5.48)
p-val: (0.000)	(0.774)	(0.000)

R² = 0.477; adjusted R² = 0.449; F-statistic = 16.92 (p-val = 0.001).

(f)(1pt) Using the p-values and the F-statistic reported above, briefly explain whether the model is useful. (Note: use a significance level of 1 percent)

(g)(1pt) In the answer booklet, reconstruct the following table and fill in the predicted voteA for each subgroup.

	69.22

(h)(1pt) Suppose the researcher runs another regression, which generates the following result:

voteA = 66.33 0.14*expendA_d + 1.33*expendB_d 0.55*expendAB_d

In the answer booklet, reconstruct the following table and fill in the predicted voteA for each subgroup.

	66.33

Part (i) and part (j) are based on the following regression: voteA = 54.00 + 15.925*expendb_0 + 7.428*expendb_1

(i)(1pt) What is the interpretation of the coefficients?

(j)(1pt) Do you think that the regression suffers from omitted variable bias due to the omission of expendB_d? Why?