Imagine you are interested in the relationship between education and self-reported marital satisfaction. Suppose the “true model” is: Marital Satisfaction = 0.08 + 0.020(Education) + 0.05(Male) +0.12(Mental Health). Where: Marital Satisfaction =1 if “satisfied”, = 0 if “unsatisfied” (Indicator variable) Education = # of Years of Schooling Male =1 if male, =0 if female (Indicator variable) Mental Health = Mental health index ranges from 0 to 1 (higher value is better) Suppose you do not have information on individuals’ mental health and run the following regression: Marital Satisfaction = β0+ β1(Education) + β2(Male) Obtaining parameter estimates: β0=0.08, β1=0.025, and β2=0.05.
a. What is the interpretation of the estimated regression parameter β2?
b. Explain in words why your parameter estimate for education (β1) is larger than it ought to be (according to the true model)