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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) = σe2. 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) = σe2inc, 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.
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