Question

Table 1: 2012 Current Population Survey Data Dependent Variable: Av Hourly Eaming 8.31 0.2 3.85 0.2 8.34 8.32 0.22 3.81 0.22 0.51 0.04 College (X) Female (X2) Age (X3) Northeast (x) Midwest (L.) South (Xs) Intercept 3.80 0.52 04 0.18 36 1.23 31 0.43 30 2.05 17.02 1.87 Forthis question, refer to the table of estimated regressions in Table 1, computed using data from the 2012 CPS. The dataset contains information on 7,440 full-time, full-year workers. The highest educational achievement for each worker was either a high school diploma or a bachelor's degree. The working ages ranged from 25 to 34 years. The data set also contains information on region of the country where the person lived. College is a binary variable equal to 1 if a worker went to college. Female is a binary variable equal to 1 if a workeris female. Age is measured in years. 1. a. Write the population regression model that corresponds to column (1) b. Using the regression results in column (1) i. Doworkers with college degrees earn more, on average, than workers with only high school degrees? How much more? ii. Isthe college-high school earnings difference estimated from this regression statistically significant at the 5% level? Construct a 95% confidence interval of the difference i. Do men earn more than women, on average? How much more? iv. Isthe male-female earnings difference estimated from this regression significant at the 5% level? Construct a 95% confidence interval for the difference

Answer 1

there are total 10 sub-part in this question, so as HOMEWORKLIB RULES rules I am answering (a) and (b) i.e. 5 sub-parts

(a)AHE=17.02+8.31*X1-3.85*X2

(b1) yes, as the coefficient of college is significant as its t-value=8.31/0.23=36.13 is more than typical critical t(0.05/2,7437)=1.96

(b2)here (1-alpha)*100% confidence interval =coefficient ±t(alpha/2,error df)*SE(coefficient)

95% confidence interval =8.31±1.96*0.23=8.31±0.45=(7.86, 8.76)

(b3) yes, as the coefficient of Female is significant and negative

here t=-3.85/0.23=-16.74, critical t(0.05,7437)=1.96

(b4)here (1-alpha)*100% confidence interval =coefficient ±t(alpha/2,error df)*SE(coefficient)

95% confidence interval =-3.85±1.96*0.23=-3.85±0.45=(-3.40, -4.30)