Assignment -
Overview - In the first problem set, you investigated the relationship between professors' attractiveness and their average course evaluations. In this problem set, you will use the same data set to investigate a related set of questions-the relationship between professors' age and their course evaluations. Is age related to course evaluations that professors receive? How and why?
Data - The data we will use for this study describes a sample of 463 courses from the University of Texas, that 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).
The variable eval is the average of student responses to the question "Overall, this course was (1) very unsatisfactory; (2) unsatisfactory; (3) satisfactory; (4) very good; (5) excellent."
The variable age is the professors' age (ranging from 29 to 73).
The variable beauty is the average rating of the physical attractiveness of the instructor (based on the instructor's photo on the web), as rated by 6 undergraduates (3 men and 3 women who were not in the class) on a scale of 1 (least attractive) to 10 (most attractive). The distribution of beauty has been shifted so that the mean value of beauty in the sample is 0.
The variable female is an indicator variable for the professor's sex, taking on the value 0 for men and 1 for women.
The variable one credit is an indicator variable, taking on the value of 1 for classes that are one-credit elective courses, and 0 for classes that are full credit. One-credit courses are typically elective courses taken for fun (e.g., yoga, surfing, advanced numismatology).
Other variables in the data set will not be used for this assignment.
Assignment -
In this assignment, you will propose and test a set of hypotheses regarding the relationships among a set of characteristics of professors and classes and the evaluations of the professors.
Note: When asked to interpret and explain the results of models you fit, make sure you are thorough. 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.
Note: Don't forget to make a regression table (Question #7 below).
1. First, describe what (univariate) relationship you expect to observe between professors' ages and average course evaluations, and explain why you might expect that.
State a null hypothesis that will provide a test of your idea.
Fit a (univariate) regression model that tests your null hypothesis, and interpret and explain your results; in particular, explain what the results imply regarding your null hypothesis test.
2. Next, describe what (univariate) relationship you expect to observe between professor's gender and his or her average course evaluation, and explain why you might expect that. State a null hypothesis that will provide a test of your idea.
Fit a (univariate) regression model that tests your null hypothesis, and interpret and explain your results; in particular, explain what the results imply regarding your null hypothesis test.
3. In this question, we would like to find out how the relationship between professors' age and course evaluations would change once we control for gender, considering the fact that the average female teacher is younger than the average male teacher, and the relationship between gender and course evaluation observed in (2) above.
Note: The average female teacher is roughly 45 years old and the average male teacher is roughly 50 years old.
First, given this fact and the results of parts (1) and (2) above, explain what you think you might find regarding the age-evaluation relationship when you regress course evaluations on both age and gender. Specifically, what do you expect the association between age and course evaluations will be once you control for gender as compared to the univariate association between age and course evaluation? (Note: there is no single right answer here; just give an explanation for what you think you might find, and why).
Second, fit a regression model that tests your prediction(s), and interpret and explain your results. (don't forget to discuss whether the results support your prediction(s). In particular, explain why the coefficient on age from this model differs from the coefficient on age from the univariate model you fit in (1) above.
4. Using the results from the multiple regression model you fit in (3) above, construct a scatterplot of course evaluations against professor's age. Specifically;
On this scatterplot, draw three lines: a) the fitted line from the model from (1) above (the fitted univariate association between evaluations and age); and the fitted lines for b) male and c) female teachers from (3) above. (You can draw the lines by hand or using Stata)
Regardless of how you draw the lines, demonstrate how you would construct them if you were to do it by hand (you need to write the equations you use to make these lines).
Make sure the graph is clearly labeled with a title, and make sure the 3 lines are clearly marked.
5. A colleague points out that course evaluations for one-credit courses are much higher (.55 points higher, on average) than evaluations for full-credits courses. She argues that this may explain the association between age and course evaluations observed in (3) above (after controlling for gender). Your task is to test this hypothesis.
Specifically, discuss how you would test her hypothesis and what you expect to find if her hypothesis is supported.
State the null hypothesis regarding the age-evaluation relationship if her hypothesis is supported.
Conduct an analysis and discuss/explain whether your result supports your colleague's hypothesis.
6. Your task here is to understand the role of beauty in the association between age and course evaluations.
First, examine the data to determine what, if any is the relationship between age and rated beauty (a simple look at the correlation is all you need here).
Given this association, explain what you think you might find when you add beauty to the regression model from (5) (Note: there is no single right answer here; just give an explanation for what you think you might find, and why). In particular, what do you think will be the relationship between age and course evaluations once you control for beauty? State the null hypothesis for this analysis.
Fit a model that includes age, gender, course credit, and beauty to predict course evaluations, and test your hypothesis stated above.
Explain what each of the coefficients means, and interpret the results.
In particular, compare the estimates from this model to the previous models and explain what they tell you. Discuss whether your result supports your hypothesis.
7. Please create a single regression table (like I illustrated in class) that contains the coefficient estimates, standard errors, and R2 for each model you fit to answer the questions above.
Make sure the table has a title, clear labels, and is easily readable.
8. In a few thoughtful paragraphs, summarize your findings from the series of analyses you conducted above regarding the relationship between professors' ages and their course evaluations. When summarize your findings,
Construct a graph (clearly labeled) that illustrates your main findings.
Your graph should describe the relationship among course evaluations, age, and at least one other variable.
Attachment:- Assignment Files.rar