Assumptions for simple linear regression model:

Consider the savings function sav = β₀ + β₁inc + u, u = √inc. e, where e is a random variable with E(e) = 0 and Var(e) = σ_e². Assume that e is independent of inc.

(i) Show that E (u|inc) = 0, so that the key zero conditional mean assumption (Assumption SLR.4) is satisfied. [Hint: If e is independent of inc, then E (e|inc) = E (e).]

(ii) Show that Var (u|inc) = σ_e²inc, so that the homoskedasticity Assumption SLR.5 is violated. In particular, the variance of sav increases with inc. [Hint: Var (e|inc) = Var (e), if e and inc are independent.]

(iii) Provide a discussion that supports the assumption that the variance of savings increases with family income.