5. A researcher estimated two regression models to examine the determinants of 'wage' (hourly wage in...

 

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5. A researcher estimated two regression models to examine the determinants of 'wage' (hourly wage in Malaysia Ringgit) using a sample of 84 individuals. The independent variable 'educ' represents the years of schooling; 'age' represents how old an individual is; 'exper' and 'expersq' represent the years of experience and the square of the years of experience, respectively. The results are presented in the table below. Dependent variable: wage Independent variables exper expersq R² 0.3476 RSS 85142.3 const educ Model A age -12.6897 2.1628 0.6792 (0.0684) (0.0023) (0.2339) -23.8851 0.0452 Model B 1.6784 1.2768 -0.0168 0.4163 (0.5229) (0.0008) (0.5568) (0.0466) (0.0186) Note: Estimated coefficients of each model are given in the table. Numbers in parentheses are corresponding P-values. RSS represents the Residual (Error) Sum of Squares. (a) Interpret the estimated coefficient of 'exper' in Model B. 78014.6 (b) Explain why the researcher included the square of experience in Model B. [5 marks] [3 marks] (c) Using the results of Model B, test the hypothesis that older people earn higher wages at the 10% significance level. State the null and alternative hypotheses clearly. [5 marks] (d) Conduct a F-test for the joint significance of 'exper' and 'expersq'. State the null and alternative hypotheses clearly. [8 marks] (e) Based on your conclusion of the test in (d), explain the consequences of omitting 'exper' and 'expersq' in Model A. [7 marks] (f) Based on the regression results of Model B and the test conducted in part (d), explain the nature of the relationship between wage and experience. Find the years of experience at which the hourly wage of an individual is the highest, holding other variables constant. [7 marks] 5. A researcher estimated two regression models to examine the determinants of 'wage' (hourly wage in Malaysia Ringgit) using a sample of 84 individuals. The independent variable 'educ' represents the years of schooling; 'age' represents how old an individual is; 'exper' and 'expersq' represent the years of experience and the square of the years of experience, respectively. The results are presented in the table below. Dependent variable: wage Independent variables exper expersq R² 0.3476 RSS 85142.3 const educ Model A age -12.6897 2.1628 0.6792 (0.0684) (0.0023) (0.2339) -23.8851 0.0452 Model B 1.6784 1.2768 -0.0168 0.4163 (0.5229) (0.0008) (0.5568) (0.0466) (0.0186) Note: Estimated coefficients of each model are given in the table. Numbers in parentheses are corresponding P-values. RSS represents the Residual (Error) Sum of Squares. (a) Interpret the estimated coefficient of 'exper' in Model B. 78014.6 (b) Explain why the researcher included the square of experience in Model B. [5 marks] [3 marks] (c) Using the results of Model B, test the hypothesis that older people earn higher wages at the 10% significance level. State the null and alternative hypotheses clearly. [5 marks] (d) Conduct a F-test for the joint significance of 'exper' and 'expersq'. State the null and alternative hypotheses clearly. [8 marks] (e) Based on your conclusion of the test in (d), explain the consequences of omitting 'exper' and 'expersq' in Model A. [7 marks] (f) Based on the regression results of Model B and the test conducted in part (d), explain the nature of the relationship between wage and experience. Find the years of experience at which the hourly wage of an individual is the highest, holding other variables constant. [7 marks]