For the regression with only a constant Yi ui with ui IID(0, 2), show that the least squares estimate of is OLS Y , var(OLS) 2 n, and the residual sums of squares is n i 1 y2 i n i 1(Yi Y )2

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Question: For the regression with only a constant Yi = + ui with ui IID(0, 2), show that the least squares estimate of

For the regression with only a constant Yi = α + ui with ui ∼ IID(0, σ2), show that the least squares estimate of α is αOLS = ¯Y , var(αOLS) = σ2/n, and the residual sums of squares is n i=1 y2 i =

n i=1(Yi − ¯ Y )2.

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