The following equation represents a regression model for the number of children in a family:
Children = β0 + β1motherseduc + β2fatherseduc + β3 familyincome + u,
Where children is the number of children, motherseduc and fatherseduc are the years of education of the mother and father respectively and familyincome is the income of the family. We expect β1 < 0, β2 < 0 and β3 < 0.
a. What is the effect of omitting family income from the regression model on β1 andβ2 if each parent's education is positively correlated with family income?
b. Write the null hypothesis, restricted regression, test statistic and degrees of freedom for a test of the hypothesis that the effect of mother's education equals the effect of father's education.