2. [30 marks] Your parents would like to find out more about the effects of education on wage rates (in case they want to reclaim costs of raising you). They have data on wages ($/hour), education and years of experience, so they decided to estimate the following model: Wage, = Bo + B, Educ, + B, Exper, + B, Exper, + E; where Wage= earnings per hour, Educ = years of education and Exper = years of experience and Exper is the squared years of experience. Following is EXCEL output of a correlation matrix involving all of these variables and regression output CORRELATION MATRIX Wage Educ Exper Exper Wage 1 Educ 0.418 1 Exper 0.089 -0.128 1 Exper2 0.033 -0.139 0.965 1 SUMMARY OUTPUT Regression Statistics Multiple R 0.476 R Square 0.226 Adjusted R Square 0.224 Standard Error 11.307 Observations 1000 ANOVA df SS MS F Significance F Regression 3 37232.64 12410.88 97.08 0.00 Residual 996 127332.79 127.84 Total 999 164565.43 Standard Upper Coefficients Error t Stat P-value Lower 95% 95% Intercept 17.941 2.318 -7.741 0.000 22.489 -13.393 Educ 2.018 0.133 15.143 0.000 1.757 2.280 Exper 0.787 0.106 7.420 0.000 0.579 0.996 Exper2 -0.012 0.002 6.280 0.000 0.015 0.008 (a) What is the correlation between wage and education? Interpret this result [2 marks] (b) Interpret the estimated regression coefficient of Educ. Is the sign of the coefficient what you would expect from economic theory? [3 marks]