1. i.
a. wage = -392.81 + 16.94*age + 56.37*educ + 7.4*tenure – 174.02*black + u
The variable ‘black’ captures the wage difference we are interested in.
b. All 4 coefficient estimates are, with 95% confidence, statistically different than zero, as all the P-values are lower than 0.05. All the confidence intervals lie completely to the left or right of zero, which also is an indicator of significance.
c. I used the P-value stata provides in a regression. The confidence interval of stata output looks related to the T-value, because a high T-value occurs when there is a big confidence interval.
d. The amount of money earned by someone who is 0 years old with 0 years of education and 0 years of tenure, and happens to be white. This is an unlikely scenario so the economic meaning of the intercept is not much.
e. The mean of the residuals u must be 0. In this case the residual sum of squares is much higher than the model sum of squares. R- squared is 0.16 which means 16% of the variance is explained for in the model. ii. a. You could take the square of age and regress with that in the model to see if there is non-linearity in age.
Wage = -629.09 + 31.33*age – 0.22*age^2 + 56.29*educ + 7.39*tenure – 174.03*black + u
b. No I do not think there is evidence for this non-linearity because there are very high P-Values for age and age^2 in this regression (0.750 and 0.884 respectively).
c. The P-values of age and age^2 in the regression.
2.
i. ii. Hsize will have a negative relation because bigger classes mean less focused teaching.
Hsperc will have a positive correlation because the higher the percentile the higher a student’s potential.
SAT will have a positive correlation.
Female will have a positive coefficient because females tend to spend more time in school activities.
Athlete could have a negative coefficient because student athletes might