I estimate a multiple regression based on the following variables. The dependent
ID: 3314172 • Letter: I
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?
61-80Explanation / 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.
F = 101+Related Questions
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