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# Hw4 - Greg Smith Dr Cuellar Econ 317 Problem Set 4 1 Use...

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Greg Smith 10/18/2009 Dr. Cuellar – Econ 317 Problem Set 4 1. Use the data set Wage1.dta to answer the following questions. Estimate regression equation wage = β0 + β1Education + U i. . reg wage educ Source | SS df MS Number of obs = 526 -------------+------------------------------ F( 1, 524) = 103.36 Model | 1179.73204 1 1179.73204 Prob > F = 0.0000 Residual | 5980.68225 524 11.4135158 R-squared = 0.1648 -------------+------------------------------ Adj R-squared = 0.1632 Total | 7160.41429 525 13.6388844 Root MSE = 3.3784 ------------------------------------------------------------------------------ wage | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- educ | .5413593 .053248 10.17 0.000 .4367534 .6459651 _cons | -.9048516 .6849678 -1.32 0.187 -2.250472 .4407687 ii. Use the R2 and F-test to test for overall significance of the estimate regression. Explain each. a. Adj R-squared = 0.1632 which means that only 16 % of the variation in wage is explained by Education. b. . display invFtail(1, 523, .05) 3.8593004 F( 1, 524) = 103.36 which is larger than our critical F. iii. Interpret each of the coefficients. a. β1 is the change in wage divided by the change in education. iv. Are the coefficients statistically significant? Explain. a. . . display invttail(524, .05/2) 1.9645015 = Crit T Sample T = 10.17 so we reject the null hypothesis and hold education coefficient as statistically significant. Estimate regression equation wage = β0 + β1Education + β2Experience + U . reg wage educ exper Source | SS df MS Number of obs = 526 -------------+------------------------------ F( 2, 523) = 75.99 Model | 1612.2545 2 806.127251 Prob > F = 0.0000

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Residual | 5548.15979 523 10.6083361 R-squared = 0.2252 -------------+------------------------------ Adj R-squared = 0.2222 Total | 7160.41429 525 13.6388844 Root MSE = 3.257 ------------------------------------------------------------------------------ wage | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- educ | .6442721 .0538061 11.97 0.000 .5385695 .7499747 exper | .0700954 .0109776 6.39 0.000 .0485297 .0916611 _cons | -3.390539 .7665661 -4.42 0.000 -4.896466 -1.884613 ------------------------------------------------------------------------------ v. Use the R2 and F-test to test for overall significance of the estimate regression. Explain each. a. Adj R-squared = 0.2222 which means that 22 % of the variation in wage is explained by experience and education. b. . display invFtail(2, 523, .05) 3.0129575 sample F is F( 2, 523) = 75.99 which is bigger than our critical F value of 3.0129575. vi. Interpret each of the coefficients. a. β1 is the change in wage divided by the change in education without experience applied. b. β2 is the change in wage divided by the change in Experience without education applied. vii. Are the coefficients statistically significant? Explain. a. . display invttail(523, .05/2) 1.9645102 = Crit T statistic β1 sample t = 11.97 β2 sample t = 6.39 Both are greater than Crit T meaning they are statistically significant and grounds for a rejection of the null hypothesis. Estimate regression equation wage = β0 + β1Education + β2Experience + β3Tenure +U viii. Use the R2 and F-test to test for overall significance of the estimate regression. Explain each. Did your results change from the previous model?
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