Forthemodel E(Yi) 0 1xi, considertheexpressionfor 1 in equation(6 1) (a) Specifythesamplingdistributionof 1 and showthat E( 1) 1 and var( 1) 2 i(xi x)2 (b) Fromthevariance formula,explainwhymorepreciseestimationof 1 is possiblewhenthe data have(i)morevariationin x (ii)lessvariationin y given x (iii)moreobservations

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Question: Forthemodel E(Yi) = 0 + 1xi, considertheexpressionfor 1 in equation(6.1). (a) Specifythesamplingdistributionof 1 and showthat E( 1) = 1 and var( 1) = 2~[i(xi

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.

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