Question: Consider the model Vi = B2X2 + 3333 + where for simplicity the data are centered. An alternative to OLS is stepwise regression. This estimator

Consider the model Vi = B2X2 + 3333 + where for simplicity the data are centered. An alternative to OLS is stepwise regression. This estimator first regresses y on 22 to obtain an estimate of B2, denoted B2, and residuals c = y- B282. These residuals are then regressed on 23 to obtain an estimate of B3, denoted 83 (a) Derive the expectation and variance of the stepwise estimators B2 and 33. (b) Compare the properties of the stepwise estimators (B2, B3) to those of the OLS estimators (62, 63). Which of the Gauss-Markov assumptions, if any, are violated by the stepwise regression estimators? Consider the model Vi = B2X2 + 3333 + where for simplicity the data are centered. An alternative to OLS is stepwise regression. This estimator first regresses y on 22 to obtain an estimate of B2, denoted B2, and residuals c = y- B282. These residuals are then regressed on 23 to obtain an estimate of B3, denoted 83 (a) Derive the expectation and variance of the stepwise estimators B2 and 33. (b) Compare the properties of the stepwise estimators (B2, B3) to those of the OLS estimators (62, 63). Which of the Gauss-Markov assumptions, if any, are violated by the stepwise regression estimators

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