Answer the following questions: i) Obtain basic summary statistics for the COLLEGE2 dataset variables APPLICATION, SIZE, RANK, and COMMONAPP using the STATA summarize command, and then copy and paste the output into your assignment.

ii) Re-estimate the model using STATA, and then copy and paste the output into your assignment.

iii) Report your regression results in the standard format of equation (3.2) on p. 72. (Use two decimal places for the estimated coefficients, the standard errors, and the t-statistics.)

iv) Carefully explain the real-world meaning of the three estimated slope coefficients.

v) What signs would you have expected for each of the estimated slope coefficients? Carefully explain your reasoning in each case.

vi) Based on your answer to part

v), use t-tests to test these expectations about the signs of the estimated slope coefficients. Be sure to write down the null and alternative hypotheses in each case, and to explain whether you should reject or not reject the null hypothesis in each case.

vii) Test the overall significance of the regression using the step-by-step procedure outlined in the example on p.145. Be sure to write down the appropriate null and alternative hypotheses, and to explain whether you should reject or not reject the null hypothesis.

viii) Repeat part vii), but this time using the (more) general F-test formula given in equation (5.10). Be sure to write down the appropriate null and alternative hypotheses, and to explain whether you should reject or not reject the null hypothesis.

ix) Using the standard formula in equation (5.9), construct 99% 2-sided confidence intervals for each of the estimated slope coefficients. Be sure to show your working, step-by-step.

x) Using an appropriate STATA command(s), check your answers to part ix). Copy and paste the relevant STATA output into your assignment.

xi) Re-estimate the model using STATA, but this time omit the COMMONAPP variable and then copy and paste the output into your assignment. xii) Report the regression results from part xi) in the standard format of equation (3.2) on p. 72. (Use two decimal places for the estimated coefficients, the standard errors, and the t-statistics.)

xiii) Using the discussion of four important specification criteria on p. 166-167, compare the original model with a more parsimonious model which excludes COMMONAPP. Which model do you think is better? Carefully use the four specification criteria to make your decision, being sure to state which criteria support your decision and why