3. Consider the following estimated regressions: In(bught) 4.75486-0.00500cigs+

Question

3. Consider the following estimated regressions: In(bught) 4.75486-0.00500cigs+ 0.00 050faminc = 03591) (0.00113) (0.00037) +0.00576fatheduc?0.00560mothed?c (0.00296) (0.00322) 0.0293n 1011 In(bught) 4igs000famine 01275 (0.00111) (0.00033) R20.0250 1011, where bwght is the birth weight of a newborn, cigs is the number of cigarrettes the mother smoked per day while pregnant, faminc is the newborn's family income, fatheduc is the years of education of the newborn's father, and motheduc is the years of education of the newborn's mother. Use the information above to test, at the 10 percent significance level, the joint hypothesis that the educational attainment of the father and mother does not affect the weight of a newborn child

Explanation / Answer

We will use the partial F-test to test the joint hypothesis. The formula used will be:

F = [(R^2_Full - R^2_Reduced) / (4 - 2) ] / [ (1-R^2_Full) / ( N - 4 - 1) ]

Here R^2_Full is the R-square value for the model with all variables

F = [(0.0293 - 0.0250)/2 ] / [ (1 - 0.0250)/1006

F = (0.0022)*1006/0.9750 = 2.27

For 10% significance level and df (num) = 2, df (den) = 1006, F critical value = 2.31

Therefore, as Fc > F , we fail to reject the null hypothesis. It means that there is no significant variation in R-squared value. Hence, we can say that educational attainment of the father and mother does not affect the weight of a newborn child.

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