describe a suitable measure of the model’s fit to the data comment on the fit indicated by your measur
INSTRUCTIONS TO CANDIDATES
ANSWER ALL QUESTIONS
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. 
b)Obtain the expression for the sample mean of course_eval in terms of the estimated model parameters. Comment on this. 
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. 
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. 
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. 
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. 
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. 
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. 
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. 
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).