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Here are outputs of Question a,b,d. Please answer c and e

Consider the model: log(wage) = Bo + Bieduc + Bzexper + B3tenure +u a) Run the regression of log(wage) on educ, exper and tenure. b) Run the regression of educ on exper and tenure. c) Save the residuals from (b) in a variable named educ_resid. Interpret this variable. Stata code: After running the regression for (b) (reg educ exper tenure) type: predict educ_resid, resid d) Run the regression of log(wage) on educ_resid. e) Compare the coefficient on educ_resid from (d) with the coefficient on educ from (a). Which theorem did you just demonstrate? regress Inwage educ exper tenure Source SS df MS 3 = Model Residual 25.6953242 139.960959 8.56510806 . 150334005 Number of obs F(3, 931) Prob > F R-squared Adj R-squared Root MSE 935 56.97 0.0000 0.1551 0.1524 38773 931 = Total 165.656283 934 . 177362188 Inwage Coef. Std. Err. t P>|t| [95% Conf. Interval] educ 11.50 0.000 0.000 4.55 exper tenure 0748638 0153285 .0133748 5.496696 0065124 0033696 .0025872 . 1105282 .062083 .0087156 .0082974 5.279782 0876446 .0219413 .0184522 5.713609 5.17 49.73 0.000 0.000 cons regress educ exper tenure Source SS df MS = 2 Model Residual 962.209217 3544.61003 481.104608 3.80322965 Number of obs F(2, 932) Prob > F R-squared Adj R-squared Root MSE 935 126.50 0.0000 0.2135 0.2118 1.9502 932 = Total 4506.81925 934 4.82528828 educ Coef. Std. Err. t P>|t| [95% Conf. Interval] 0.000 -.2089786 exper tenure -.2384953 0344348 15.97721 .0150403 .012964 . 1875178 -15.86 2.66 0.008 -.2680121 .0089928 15.60921 0598768 _cons 85.20 0.000 16.34522 regress lnwage educ_resid Source SS df MS = 935 = 127.13 Model 1 19.8660639 145.790219 19.8660639 . 156259613 Number of obs F(1, 933) Prob > F R-squared Adj R-squared Root MSE IL L LLLL Residual 933 = 0.0000 0.1199 0.1190 Total 165.656283 934 . 177362188 = 3953 Inwage Coef. Std. Err. t P>|t| [95% Conf. Interval] educ_resid 0.000 .0748638 6.779004 .0066396 0129276 11.28 524.38 .0618336 6.753633 .087894 6.804374 _cons 0.000 Consider the model: log(wage) = Bo + Bieduc + Bzexper + B3tenure +u a) Run the regression of log(wage) on educ, exper and tenure. b) Run the regression of educ on exper and tenure. c) Save the residuals from (b) in a variable named educ_resid. Interpret this variable. Stata code: After running the regression for (b) (reg educ exper tenure) type: predict educ_resid, resid d) Run the regression of log(wage) on educ_resid. e) Compare the coefficient on educ_resid from (d) with the coefficient on educ from (a). Which theorem did you just demonstrate? regress Inwage educ exper tenure Source SS df MS 3 = Model Residual 25.6953242 139.960959 8.56510806 . 150334005 Number of obs F(3, 931) Prob > F R-squared Adj R-squared Root MSE 935 56.97 0.0000 0.1551 0.1524 38773 931 = Total 165.656283 934 . 177362188 Inwage Coef. Std. Err. t P>|t| [95% Conf. Interval] educ 11.50 0.000 0.000 4.55 exper tenure 0748638 0153285 .0133748 5.496696 0065124 0033696 .0025872 . 1105282 .062083 .0087156 .0082974 5.279782 0876446 .0219413 .0184522 5.713609 5.17 49.73 0.000 0.000 cons regress educ exper tenure Source SS df MS = 2 Model Residual 962.209217 3544.61003 481.104608 3.80322965 Number of obs F(2, 932) Prob > F R-squared Adj R-squared Root MSE 935 126.50 0.0000 0.2135 0.2118 1.9502 932 = Total 4506.81925 934 4.82528828 educ Coef. Std. Err. t P>|t| [95% Conf. Interval] 0.000 -.2089786 exper tenure -.2384953 0344348 15.97721 .0150403 .012964 . 1875178 -15.86 2.66 0.008 -.2680121 .0089928 15.60921 0598768 _cons 85.20 0.000 16.34522 regress lnwage educ_resid Source SS df MS = 935 = 127.13 Model 1 19.8660639 145.790219 19.8660639 . 156259613 Number of obs F(1, 933) Prob > F R-squared Adj R-squared Root MSE IL L LLLL Residual 933 = 0.0000 0.1199 0.1190 Total 165.656283 934 . 177362188 = 3953 Inwage Coef. Std. Err. t P>|t| [95% Conf. Interval] educ_resid 0.000 .0748638 6.779004 .0066396 0129276 11.28 524.38 .0618336 6.753633 .087894 6.804374 _cons 0.000

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