 # Question 3 The following table shows estimation results using the ...

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Question 3 The following table shows estimation results using the ordinary least squares method: Dependent Variable: LWAGE Method: Least Squares (Gauss-Newton / Marquardt steps) Date: 10/10/17 Time: 14:01 Sample: 1 50 Included observations: 50 LWAGE = c(1) + C(2)*EDUC + C(3)*MARRIED + C(4)'URBAN Coefficient Std. Error t-Statistic Prob. C(1) 5.804356 0.393738 14.74166 0.0000 C(2) 0.047844 0.021277 2.248627 0.0294 C(3) 0.297224 0.179578 1.655130 0.1047 C(4) 0.198999 0.156047 1.275245 0.2086 R-squared 0.165986 Mean dependent var 6.948572 Adjusted R-squared 0.111594 S.D. dependent var 0.361979 S.E. of regression 0.341185 Akaike info criterion 0.763833 Sum squared resid 5.354721 Schwarz criterion 0.916795 Log likelihood -15.09582 Hannan-Quinn criter. 0.822081 F-statistic 3.051644 Durbin-Watson stat 2.107641 Prob(F-statistic) 0.037780 where Iwage is monthly income measured in pounds (in logarithmic form), educ is years of formal education, married is 1 if the person is married, urban is 1 if the person lives in urban area. a) Report the results and interpret the estimates. [20 marks] b) Explain the difference between R2 and R². [10 marks] Dependent Variable: LWAGE Method: Least Squares (Gauss-Newton /Marquardt steps) Date: 10/10/17 Time: 14:02 Sample: 1 50 Included observations: 50 LWAGE = C(1) + C(2) *EDUC Coefficient Std. Error t-Statistic Prob. C(1) 6.346068 0.309441 20.50815 0.0000 C(2) 0.041438 0.021005 1.972725 0.0543 R-squared 0.074996 Mean dependent var 6.948572 Adjusted R-squared 0.055725 S.D. dependent var 0.361979 S.E. of regression 0.351749 Akaike info criterion 0.787381 Sum squared resid 5.938916 Schwarz criterion 0.863862 Log likelihood -17.68452 Hannan-Quinn criter. 0.816505 F-statistic 3.891645 Durbin-Watson stat 2.167601 Prob(F-statistic) 0.054302 c) Together with estimation results from part (a), evaluate the statement that 'both gender and location should be excluded from the model'. [20 marks] [50 marks total] Question 4 The following table shows estimation results using the ordinary least squares method: Dependent Variable: LWAGE Method: Least Squares (Gauss-Newton / Marquardt steps) Date: 10/10/17 Time: 14:10 Sample: 1 50 Included observations: 50 LWAGE = C(1) + C(2)*EDUC + C(3)*EDUC^2 + C(4) *EXPER + C(5) *MARRIED Coefficient Std. Error t-Statistic Prob. C(1) -0.240916 2.093658 -0.115070 0.9089 C(2) 0.897313 0.281610 3.186364 0.0026 C(3) -0.028876 0.009495 -3.041280 0.0039 C(4) 0.022303 0.016498 1.351835 0.1832 C(5) 0.168860 0.181068 0.932576 0.3560 R-squared 0.284714 Mean dependent var 6.948572 Adjusted R-squared 0.221133 S.D. dependent var 0.361979 S.E. of regression 0.319459 Akaike info criterion 0.650265 Sum squared resid 4.592439 Schwarz criterion 0.841468 Log likelihood -11.25663 Hannan-Quinn criter. 0.723076 F-statistic 4.477966 Durbin-Watson stat 2.114982 Prob(F-statistic) 0.003939 where Iwage is monthly income measured in pounds (in logarithmic form), educ is years of formal education, exper is years of workforce experience. a) Report the results and interpret the estimates. [20 marks] b) Calculate the precise impact of married on wage. [10 marks] c) Evaluate the statement that 'one more year of education always has a positive impact on wage. [20 marks] [50 marks total] Question 5 a) Explain the five assumptions for the simple linear model, and show the theorem associated with the mean and variance of estimate B1. [30 marks] b) Use the expression for the variance of B1 from (a), derive the standard error of B1. [20 marks] [50 marks total]

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