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# describe a suitable measure of the model’s fit to the data comment on the fit indicated by your measur

INSTRUCTIONS TO CANDIDATES

### Question 1. [20 Marks]

Run a regression of course_eval on beauty. Answer parts a)-d).

a)     Derive the normal equations corresponding to this estimation and explain your understanding of them. [7]

b)    Obtain the expression for the sample mean of course_eval in terms of the estimated model parameters. Comment on this. [5]

c)     Construct and implement a two-tailed t-test to determine whether the estimated coefficient on beauty is significant at the 5% level. Comment on your finding. [5]

d)    Calculate the p-value from a one-tailed t-test to determine whether the estimated coefficient on beauty is statistically greater than zero at the 1% level. [3]

Question 2. [35 Marks]

Run a regression of course_eval on beauty and include all available control variables. Answer parts a)-e).

a)     Describe a suitable measure of the model’s fit to the data. Comment on the fit indicated by your measure. [5]

b)    What is the nature of the relationship between an instructor’s age and course_eval? Construct a test for the joint significance of age and age2 on course_eval. Implement the test and comment on your finding. [7]

c)     Professor Jones is a 40 year old black female with average beauty. She teaches a one-credit upper-division course. Use the estimation output to predict Professor Jones’s course evaluation. [5]

d)    Professor Jones has a makeover and her beauty increases by one standard deviation. What is the expected increase in her evaluation arising from the makeover? Construct the 90% confidence interval for this increase. [8]

e)     Explain how you could test whether beauty’s effect on course evaluation differs for men and women. Conduct the test and comment on your findings. [10]

Question 3. [35 Marks]

In no more than 750 words critically evaluate estimations when a regression of course_eval on beauty is conducted (Question 1) and when all the available control variables are included (Question 2).

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