Assume the linear regression model yi = β0 + β1xi + εi where the usual assumptions for the stochastic term εi are satisf

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Assume the linear regression model yi = β0 + β1xi + εi where theusual assumptions for the stochastic term εi are satisfied, thatis:E[εi|xi] = 0 ; Var(εi|xi) = σ2 ; Cov(εi,εj) = 0 if idifferent from j
Show why the following statements are true or false.
a) The line fitted by the model passes through the point (̄x, ̄y); that is, the average values of X andof Y .b) The average of the estimated yi is equal to theaverage value of the yi' s.c) The sum of the cross products between the explanatory variable Xand the residuals ei is zero.d ) The sum of the cross products between the estimated yi and thexi values is zero.