Question

1. Consider the following equation where we report estimates along with their standard errors in brackets: =3683.25-0.148to twrk-11.13educ+ 2.20age (0.017) = 706, R2 = .113 sleep (5.88) (1.45) (112.28) n

Answer 1

Ho: B2 = 0; B3 = 0

Ha: Atleast one of them is significant

Let's calculate the F-statistic from the following formula:

(R-Rq F (1-RiR)(n-k-1)

R²_UR = R-square value in the unrestricted model = 0.113

R²_R = R-square value in the restricted model = 0.103

q = 2 (Number of restrictions)

n - k - 1 = 706 - 3 - 1 = 702

Hence, inputting the values into the formula:

F = 3.957

F-critical value at df = 2 and 702 is: 3.009

As the F-statistic = 3.957 > 3.009, we will reject the null hypothesis.

We conclude that at 5% level of significance, educ and age are jointly significant.