Question: Consider a multiple linear regression model with p independent variables, yi = Bo + Pixi + ... + BpXip + e;,i = 1, ..., n,

Consider a multiple linear regression model with p independent variables, yi = Bo + Pixi + ... + BpXip + e;,i = 1, ..., n, where the errors e,'s are i.i.d. with mean 0 and variance o. a. Let / be the hat matrix. Prove I - H is symmetric and idempotent. b. Prove that _ _ Var(y;) = 62(p + 1), where y; is the fitted value for the ith observation based on the OLS estimates. (Hint: The sum _: Var(y;) can be expressed as the trace of the covariance matrix for the fitted value vector (1 , ... , Vn)I

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