Suppose we fi t the model y X12 when the true model is actually given by y X12 X22 For both models, assume E ( ) 0 and Var( ) 2 I Find the expected value and variance of the ordinary least squares estimate, b1 Under what conditions is this estimate unbiased

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Question: Suppose we fi t the model y = X12 + when the true model is actually given by y = X12 + X22 +

Suppose we fi t the model y = X1β2 + ε when the true model is actually given by y = X1β2 + X2β2 + ε . For both models, assume E ( ε ) = 0 and Var( ε ) = σ2 I .

Find the expected value and variance of the ordinary least - squares estimate,

b1. Under what conditions is this estimate unbiased?

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