Question: Go back to the estimated equation in 6.101.d.

a. For each gender (male and female), estimate the equation to explain education (Y) from age (X2) and the number of siblings (X3). Are the effects of age and the number of siblings on education assumed the same or different for male and female? Briefly comment.

b. Now someone claims that the effect of gender may depend on age. Briefly support this conjecture. No statistical language is necessary.

c. Fit the model including this interaction (along with Female, Age, and Sibsnew). Show the estimated equation. Test whether the interaction term can be dropped from the model at the .05 level.

State the alternative, decision rule, p-value, and conclusion. Is this interaction “meaningful?” Briefly explain why or why not.

d. Suppose that we retained this interaction term. State the estimated regression equations for each gender. Explain in plain English the nature of this interaction. Are the effects of age and the number of siblings on education assumed the same or different for male and female? Briefly comment.