Forthemodel E(Yi) = 0 + 1xi, considertheexpressionfor 1 in equation(6.1). (a) Specifythesamplingdistributionof 1 and showthat E( 1)

Forthemodel E(Yi) = β0 + β1xi, considertheexpressionfor ˆβ1 in equation(6.1).

(a) Specifythesamplingdistributionof ˆβ1 and showthat E( ˆβ1) = β1 and var( ˆβ1) =

σ2~[Σi(xi − x)2].

(b) Fromthevariance formula,explainwhymorepreciseestimationof β1 is possiblewhenthe data have(i)morevariationin x; (ii)lessvariationin y given x; (iii)moreobservations.