I estimate a multiple regression based on the following variables. The dependent

Question

I estimate a multiple regression based on the following variables. The dependent variable is student test scores. The independent variables are mother’s education and father’s education, each measured in years, and the sex of the child, coded 0 if male and 1 if female. I obtain the following regression results:

- Scores | Coef. Std. Err. -

mom_ed | 4.000 1.0000

dad_ed | 2.000 .02500

sex | -5.000 1.0000

_cons | 20.000 2.000

I estimate another regression that includes the same independent variables, as well as a measure of child age:

- Scores | Coef. Std. Err. -

mom_ed | 4.000 1.0000

dad_ed | 2.000 .02500

sex | -5.000 1.0000 age | 1.500 .03

_cons | 20.000 2.000

The R2 of the first regression is .10, while the second regression has an R2 of .30. N for both models is 1000. Calculate F to test the hypothesis that .30 is significantly higher than .10.

What’s the value of F?

How many degrees of freedom should be used in looking up F?

What’s the p value for F?

Explanation / Answer

Here we have to test the ha ypothesis that

H0 : 1 = 2

Ha : 1 < 2

Here test statistic

F = [(R22 - R12 )/ (k2 -k1 ) ] / [ (1 - R12 )/ (N - k2 -1)]

Here R22 = 0.3 , R12 = 0.1 ; N = 1000 , k1 = 3 , k2 = 4

F = [(0.3 - 0.1)/ 1] / [(1 - 0.1)/ (1000 - 4 -1)]

F = 0.2/ [0.9/995]

F = 221.111

Here we will look for degree of freedoms are

dF1 = (k2- k1) = 4 -3 =1

dF2 = N - k - 1 = 996

Here Pr(F > 221.111 ; 1; 996) = 0.00000 < 0.05

so we can say that the  .30 is significantly higher than .10.

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