(a) (11 points) Run a regression of the score obtained in an exam (response variable) on whether the grader observes a Brahmin caste, the age observed by the grader, and the sex observed by the grader (explanatory variables). Show the Stata command and its output. Interpret all the coefficients. Are any of the coefficients statistically significant? How do you interpret this result - is there grading discrimination? (b) (6 points) Re-estimate the model by adding as a variable the underlying quality of exams. Show the Stata command and its output. Is there any grading discrimination based on this regression? (c) (4 points) Which of the two regressions estimated above better fits the data? How do you know? (d) (6 points) Obtain the residuals of the previous model you estimated. Use the residuals to check whether the assumptions of OLS are satisfied. Show the Stata commands and their output. What can you conclude