Consider the following regression model relating health y to age a and whetherthe individual has a degree, d = 1, or otherwise, d = 0.

y=0 +1a+2(a/10)2 +0d+1da+2d(a/10)2 +u.

u is an error term that satisfies the usual exogeneity assumptions.

(a) (2 points) Derive expressions for E(y|a, d = 1) and E(y|a, d = 0).

(b) (4 points) A plausible quadratic relationship between average health and age is one where E(y) declines from birth and the decline is faster and faster as one gets older. What parameter restriction(s) on the model ensures that this is true for graduates?

(c) (4 points) Write down a null hypothesis on parameter values in the above regression model that ensures that average health of 50-year-old graduates is equal to average health of 50-year-old non-graduates.