Problem Set #3-Key. wage Coef. Std. Err. t P> t [95% Conf. Interval]

Transcription

1 Problem Set #3-Key Sonoma State University Economics 317- Introduction to Econometrics Dr. Cuellar 1. Use the data set Wage1.dta to answer the following questions. a. For the regression model Wage i = β + β 1 Education i + u i, describe the expected effects of education on wages (i.e., what is the expected sign of β 1 ). b. Run the above regression. Are your results consistent with your expected effects in (a)? Source SS df MS Number of obs = 526 F(1, 524) = Model Prob > F =. Residual R-squared =.1648 Adj R-squared =.1632 Total Root MSE = wage Coef. Std. Err. t P> t [95% Conf. Interval] educ _cons c. Show graphically the regression equation. Describe you results. 5 Average Hourly Wage Years of Education Actual Predicted d. Use the R 2 and F-test to test for overall significance of the estimate regression. Explain each. R 2 =.1648 F-test H : β 1 = H 1 : β 1 Critical F df1,df 2,α=F 1,525,.5 = < Sample F = so you reject H

2 Use the three methods covered in class to test the coefficient on education for statistical significance. Be sure to formally state you hypothesis, use a 5% level of significance. Provide an explanation for each. Using a one-sided hypothesis test. Why? H : β 1 H 1 : β 1 > β 1 * = H + t df,α S β (.53248) = Sample β 1 > Critical β 1 so reject H Using the t-test, sample t = 1.17 > the critical t* = , so reject H. Using the p-value, p=. <.5, so reject H. α = Rejection region β 1 t df,α e. Construct a 95% confidence interval around the estimated coefficient β 1. Explain. Confidence Interval =β 1 ± t df,α S β ± (.53248) to

3 2. Use the data set Bwght.dta to answer the following questions. a. For the regression model Birth Weight i = β + β 1 Cigarettes i + u i, describe the expected effects of cigarettes on birth weight (i.e., what is the expected sign of β 1 ). b. Run the above regression. Are your results consistent with your expected effects in (a)? Source SS df MS Number of obs = 1,388 F(1, 1386) = Model Prob > F =. Residual , R-squared =.227 Adj R-squared =.22 Total , Root MSE = bwght Coef. Std. Err. t P> t [95% Conf. Interval] cigs _cons c. Show graphically the regression equation. Describe you results. Birth Weight Cigarretes Smoked Per Day Actual Predicted d. Use the R 2 and F-test to test for overall significance of the estimate regression. Explain each. R 2 =.227 F-test H : β 1 = H 1 : β 1 Critical F df1,df 2,α=F 1,525,.5 = < Sample F = so you reject H e. Use the three methods covered in class to test the coefficient on cigarettes for statistical

4 significance. Be sure to formally state you hypothesis, use a 5% level of significance. Provide an explanation for each. H : β 1 H 1 : β 1 < β 1 * = H t df,α S β (.9499) = Sample β 1 < Critical β 1 so reject H Using the t-test, sample t = < the critical t* = , so reject H. Using the p-value, p=. <.5, so reject H. β 1 t df,α f. Construct a 95% confidence interval around the estimated coefficientβ 1. Explain. Confidence Interval =β 1 ± t df,α S β ± (.9499) to Use the data set Meap1.dta to answer the following questions. a. For the regression model Math Pass i = β + β 1 Expenditures Per Pupil i + u i

5 describe the expected effects of per pupil expenditures on the percentage of people who score satisfactorily on the mathematics test (i.e., what is the expected sign of β 1 ). b. Run the above regression. Are your results consistent with your expected effects in (a)? Source SS df MS Number of obs = 1,823 F(1, 1821) = 1.77 Model Prob > F =.1831 Residual , R-squared =.1 Adj R-squared =.4 Total , Root MSE = math4 Coef. Std. Err. t P> t [95% Conf. Interval] exppp _cons c. Show graphically the regression equation. Describe you results Expenditures Per Pupil Actual Predicted d. Use the R 2 and F-test to test for overall significance of the estimate regression. Explain each. R 2 =.1 F-test H : β 1 = H 1 : β 1 Critical F df1,df 2,α=F 1,525,.5 = < Sample F = 1.77 so you fail to reject H e. Use the three methods covered in class to test the coefficient on expenditures per pupil

6 H : β 1 H 1 : β 1 < for statistical significance. Be sure to formally state you hypothesis, use a 5% level of significance. Provide an explanation for each. β 1 * = H t df,α S β (.428) = Sample β 1 > Critical β 1 so fail to reject H Using the t-test, sample t = > the critical t* = , so fail to reject H. Using the p-value, p = >.5, so fail to reject H. β 1 t df,α f. Construct a 95% confidence interval around the estimated coefficient β 1. Explain. Confidence Interval =β 1 ± t df,α S β -.57 ± (.428) to.13436