Problem Set #5-Key Sonoma State University Dr. Cuellar Economics 317- Introduction to Econometrics

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1 Problem Set #5-Key Sonoma State University Dr. Cuellar Economics 317- Introduction to Econometrics C1.1 Use the data set Wage1.dta to answer the following questions. Estimate regression equation wage = β 0 + β 1 Education + β 2 Experience + U Source SS df MS Number of obs= 526 F( 2, 523)= Model Prob > F= Residual R-squared= Adj R-squared= Total Root MSE = wage Coef. Std. Err. t P>t [95% Conf. Interval] educ exper _cons (i) Explain each. Adjusted R 2 =.222 means that 22% of the variation in wages is explained by Sample F = is greater than the Critical F = (ii) Interpret each of the coefficients. β 1 = holding experience constant. ΔEducation β 2 = holding education constant. ΔExperience (iii) Are the coefficients statistically significant? Explain. t-statistic for β 1 = t-statistic for β 2 =6.39 both are greater than the critical t* =

2 Estimate regression equation wage = β 0 + β 1 Education + β 2 Experience + β 3 Tenure +U Source SS df MS Number of obs = 526 F( 3, 522) = Model Prob > F = Residual R-squared = Adj R-squared = Total Root MSE = wage Coef. Std. Err. t P>t [95% Conf. Interval] educ exper tenure _cons (iv) Explain each. Did your results change from the Adjusted R 2 =.3024 means that 30.24% of the variation in wages is explained by education, experience and tenure. Sample F = is greater than the Critical F = (v) β 1 = holding experience and tenure constant. ΔEducation β 2 = holding education and tenure constant. ΔExperience β 3 = holding education and experience constant. ΔTenure (vi) Provide an explanation for why you think the results changed. (vii) t-statistic for β 1 = t-statistic for β 3 =7.82 both are greater than the critical t* = t-statistic for β 2 =1.85 indicates that experience is not statistically significant.

3 Estimate regression equation ln(wage) = β 0 + β 1 Education + β 2 Experience + β 3 Tenure +U; where ln(wage) is the natural log of wage. Source SS df MS Number of obs= 526 F( 3, 522) = Model Prob > F = Residual R-squared = Adj R-squared= Total Root MSE = lwage Coef. Std. Err. t P>t [95% Conf. Interval] educ exper tenure _cons (viii) Explain each. Did your results change from the Adjusted R 2 =.3121 means that 31.21% of the variation in wages is explained by education, experience and tenure. Sample F = is greater than the Critical F = (ix) % β 1 = holding experience and tenure constant. ΔEducation % β 2 = holding education and tenure constant. ΔExperience % β 3 = holding education and experience constant. ΔTenure (x) t-statistic for β 1 = t-statistic for β 2 =2.39 t-statistic for β 3 =7.13 both are greater than the critical t* =

4 C1.3 Use the data set Meap01.dta to answer the following questions. For the regression equation Math Pass (Math4) = β 0 + β 1 Expenditures Per Pupil + U Estimate the regression equation Math Pass (Math4) = β0 + β1expenditures Per Pupil + U. Source SS df MS Number of obs= 1823 F( 1, 1821) = 1.77 Model Prob > F = Residual R-squared = Adj R-squared = Total Root MSE = math4 Coef. Std. Err. t P>t [95% Conf. Interval] exppp _cons (i) Explain each. Adjusted R 2 =.0004 means that.04% of the variation in wages is explained by Sample F = 1.77 is less than the Critical F = so we fail to reject the null hypothesis that the model has no explanatory power. (ii) Interpret each of the coefficients. ΔPass Rate β 1 =. ΔExpendituresPerPupil (iii) Are the coefficients statistically significant? Explain. Sample t = is less than the critical t* =

5 Estimate regression equation Math Pass (Math4) = β 0 + β 1 Expenditures Per Pupil + β 2 Percent of Students Eligible for Free Lunch + U Source SS df MS Number of obs= 1823 F( 2, 1820) = Model Prob > F = Residual R-squared = Adj R-squared = Total Root MSE = math4 Coef. Std. Err. t P>t [95% Conf. Interval] exppp lunch _cons (iv) Explain each. Did your results change from the Adjusted R 2 =.3677 means that 36.77% of the variation in wages is explained by Sample F = is greater than the Critical F = (v) β 1 = ΔPass Rate holding the percent of those eligible for free lunch ΔExpendituresPerPupil constant. β 2 = (vi) (vii) ΔPass Rate ΔPercentage Eligible for Free Lunch holding expenditures per pupil constant. Provide an explanation for why you think the results changed. t-statistic for β 1 = 5.95 t-statistic for β 2 =32.54 Both of which are greater than the critical t* =

6 Estimate regression equation ln(math4) = β 0 + β 1 Expenditures Per Pupil + β 2 Percent of Students Eligible for Free Lunch + U; where ln(math4) is the natural log of Math4. Source SS df MS Number of obs= 1822 F( 2, 1819) = Model Prob > F = Residual R-squared = Adj R-squared = Total Root MSE = lmath Coef. Std. Err. t P>t [95% Conf. Interval] exppp e lunch _cons (viii) Explain each. Did your results change from the Adjusted R 2 =.3193 means that 31.93% of the variation in wages is explained by Sample F = is greater than the Critical F = (ix) %ΔPass Rate β 1 = holding the percent of those eligible for free lunch ΔExpendituresPerPupil constant. β 2 = %ΔPass Rate ΔPercentage Eligible for Free Lunch holding expenditures per pupil constant. (x) t-statistic for β 1 = 4.66 t-statistic for β 2 =29.18 Both of which are greater than the critical t* =