Suppose a data set of 350 observations (N 350) was analyzed using OLS to examine the factors that influence the salaries of professional baseball players. The regression results are as follows, with standard errors in parentheses:

log(salary) = 10.1+ 0.05 years+0.03 gamesyr+0.0008 bavg+0.03 hrunsyr +0.02 rbisyr
(0.01) (0.029) (0.005) (0.003) (0.03) (0.02)
where,
salary = total salary in 2003
years = years in the league
bavg = career batting average
gamesyr = average games played per year
hrunsyr = home runs per year
rbisyr = runs batted in per year

R² = 0.562
SSR = 228.79

Suppose you would like to test the null hypothesis that career batting average, home runs per year, and runs batted in per year have no effect on the salaries of baseball players, once the effects of years of experience and games played per year have been controlled for.
This null hypothesis includes which of the following exclusion restrictions? Check all that apply.

a) β5=0
b) β3=0
c) β1=0
d) β4=0
e) β2=0
f) βo=0

To test the null hypothesis, you estimate the following restricted model:

log(salary) = 10.2 + 0.06 years + 0.037 gamesyr
(0.23) (0.03) (0.003)
where
SSR (restricted) = 232.11
R² (restricted) = 0.556
Since the unrestricted model has degrees of freedom, while the restricted model has degrees of freedom, you know that the number of exclusion restrictions must be q = .

Suppose you would like to test your original null hypothesis using an F-test at the 99% level.
Note: The critical value for the F statistic with this number of exclusion restrictions, with greater than 120 observations, at the 99% level, is 3.78. null hypothesis.
After calculating the F-statistic and comparing it to the critical value, you the null hypothesis.

a) reject
b) fail to reject