Assignment Overview -
In the second problem set, you investigated the relationships among four factors-professors' age, attractiveness, gender, and course credits-and their average course evaluations. In this problem set, you will use the same data set to investigate a more nuanced set of questions. In particular you will investigate the complexities of the relationship between professors' attractiveness and their course evaluations.
Data - The data we will use for this study describe a sample of 463 courses from the University of Texas, Austin taught in 2000-2002 (these data are from Hamermesh, D.S, & Parker, A. (2005). Beauty in the classroom: Instructors' pulchritude and putative pedagogic productivity. Economics of Education Review 24(4): 369-376). The data are available on blackboard (data file beautiful_professors.dta). See problem set 2 for a description of the variables used in this assignment.
Assignment -
Note: Be careful to thoroughly address the exact question asked. In particular:
- When asked to fit a model and/or report the results of a model, include the fitted regression equation.
- When asked to "explain" or "interpret" a model, the reader should know what the coefficient estimate(s) are, how much uncertainty there is in them, and what statistics you looked at to test your null hypotheses.
- When asked to "explain," "interpret" or "discuss" a coefficient, be sure to fully interpret the coefficient estimate(s) of interest; e.g., "Female professors on average score β points lower than male professors, controlling for X...," including how much uncertainty is in it.
- Graphs and tables of regression results should have titles and clear and thorough labels so a reader knows exactly what models you are displaying.
Problem 1. In problem set 1, you found that the relationship between professors' average course evaluations and their rated attractiveness was positive-professors rated as more attractive had, on average, higher course evaluations than those rated as less attractive.
a. Test whether a polynomial model better describes the relationship between evaluations and attractiveness. In particular, fit three models where you specify the relationship between evaluations and beauty as linear, quadratic, and cubic (for simplicity, leave out any other variables here).
b. Report the results of the three models in a single table.
c. Determine which of these models fits the data best, and explain how you determined this (be thorough by providing multiple pieces of evidence to support your claim).
d. Using the model you determined as best, compute the predicted course evaluations for 4 professors, with beauty ratings of -1, 0, +1, and +2.
d. Plot a scatterplot of evaluations against beauty and draw (by hand or computer), including the fitted line/curve from your preferred model (the one you chose in c above).
e. Describe how you would interpret the results from this preferred model. Give at least one plausible theoretical explanation for the results you observe.
Note: for part 2 below, begin with the final model you fit in problem set 2-the model in which you regressed average course evaluations on four variables: professors' age, attractiveness, gender, and the course credit indicator variable (i.e., no need to use the polynomial model). Any models you fit in part 2 below should include these four variables in addition to any you add to answer the specific questions addressed below.
Problem 2. In problem set 2, you observed a positive association between professors' attractiveness and their course evaluations, controlling for their age, gender, and course credits.
a. Do you think that the association between professorial appearance and evaluations will be the same or different for male and female professors? Give two theoretical reasons-one explaining why and how you might expect it to be different, and the other explaining why you might expect it to be the same.
b. Using a single regression model, investigate whether the association between attractiveness and course evaluations is the same for men and women. Explain exactly how you built and chose this model (this might include creating new variables, testing hypotheses, etc.). Report and interpret your regression results.
c. What is your estimate of the slope on beauty for male professors? Explain how you got this estimate. Can you reject the null hypothesis that the true association between attractiveness and evaluations for male professors is zero?
d. What is your estimate of the slope on beauty for female professors? Explain how you got this estimate. Can you reject the null hypothesis that the true association between attractiveness and evaluations for female professors is zero? (explain how you test this and conduct the test)
e. Explain how you can test whether the slopes on beauty are equal for male and female professors, then conduct the test.
f. Draw a graph illustrating the estimated relationships between professor's attractiveness and course evaluations for both male and female professors. For this figure, the lines should represent professors of average age and who teach full-credit courses. Write the equations used to create the two fitted lines (one for male and one for female).
g. Summarize your findings on the question: Is the association between professorial appearance and evaluations the same or different for male and female professors. If different, discuss in what way they differ and give an explanation for why you might observe the patterns you do. Also, discuss whether your hypothesis is supported by your findings.
Problem 3. In the third part of this assignment, consider the regression results below from the beautiful_professors.dta data. The variable agebeaut is the product of the variables age and beauty (i.e., the interaction between age and beauty).
a. Explain what the coefficient on agebeaut (.0100574) means. Your discussions should include substantive discussions (i.e., explain what this coefficient means using non-statistical language.)
b. The results show that a test of the null hypothesis that the true coefficient on agebeaut is 0 has a p-value of 0.001. State the null hypothesis in English (i.e., non-statistical language stating what it would mean about the relationships of professors' age and beauty to their course evaluations if the null were true?). State what it means to reject the null hypothesis in English (what does it mean about the relationships of professors' age and beauty to their course evaluations?).
c. Using the results from the model below, compute the estimated slopes on beauty for professors who are 30 years old, 45 years old, and 60 years old. Describe what these results mean.
d. Using the results from the model (attached), compute the estimated slopes on age for professors who have beauty ratings of -1, 0, and 1. Describe what these results mean.
Attachment:- Assignment Files.rar