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In the Multiple Regression Model with Two Regressors,the Formula for the Slope

Question 29

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In the multiple regression model with two regressors,the formula for the slope of the first explanatory variable is In the multiple regression model with two regressors,the formula for the slope of the first explanatory variable is (small letters refer to deviations from means as in ). An alternative way to derive the OLS estimator is given through the following three step procedure. Step 1: regress Y on a constant and ,and calculate the residual (Res1). Step 2: regress on a constant and ,and calculate the residual (Res2). Step 3: regress Res1 on a constant and Res2. Prove that the slope of the regression in Step 3 is identical to the above formula. (small letters refer to deviations from means as in In the multiple regression model with two regressors,the formula for the slope of the first explanatory variable is (small letters refer to deviations from means as in ). An alternative way to derive the OLS estimator is given through the following three step procedure. Step 1: regress Y on a constant and ,and calculate the residual (Res1). Step 2: regress on a constant and ,and calculate the residual (Res2). Step 3: regress Res1 on a constant and Res2. Prove that the slope of the regression in Step 3 is identical to the above formula. ).
An alternative way to derive the OLS estimator is given through the following three step procedure.
Step 1: regress Y on a constant and In the multiple regression model with two regressors,the formula for the slope of the first explanatory variable is (small letters refer to deviations from means as in ). An alternative way to derive the OLS estimator is given through the following three step procedure. Step 1: regress Y on a constant and ,and calculate the residual (Res1). Step 2: regress on a constant and ,and calculate the residual (Res2). Step 3: regress Res1 on a constant and Res2. Prove that the slope of the regression in Step 3 is identical to the above formula. ,and calculate the residual (Res1).
Step 2: regress In the multiple regression model with two regressors,the formula for the slope of the first explanatory variable is (small letters refer to deviations from means as in ). An alternative way to derive the OLS estimator is given through the following three step procedure. Step 1: regress Y on a constant and ,and calculate the residual (Res1). Step 2: regress on a constant and ,and calculate the residual (Res2). Step 3: regress Res1 on a constant and Res2. Prove that the slope of the regression in Step 3 is identical to the above formula. on a constant and In the multiple regression model with two regressors,the formula for the slope of the first explanatory variable is (small letters refer to deviations from means as in ). An alternative way to derive the OLS estimator is given through the following three step procedure. Step 1: regress Y on a constant and ,and calculate the residual (Res1). Step 2: regress on a constant and ,and calculate the residual (Res2). Step 3: regress Res1 on a constant and Res2. Prove that the slope of the regression in Step 3 is identical to the above formula. ,and calculate the residual (Res2).
Step 3: regress Res1 on a constant and Res2.
Prove that the slope of the regression in Step 3 is identical to the above formula.

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