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Create and include the density plot for the outcome. Does the distribution foreshadow problems for the normality assumption?

INSTRUCTIONS TO CANDIDATES
ANSWER ALL QUESTIONS

Background of the Data Set

Research. Teaching. Service. The trifecta upon which that almost every university instructor is evaluated, and, ultimately compensated. One way which academic administrators judge teaching quality is through teachers’ course evaluations. While we know evaluation scores are not perfectly measures of teaching quality, nonetheless, they do play a role in the tenure and promotion process. Unfortunately, many other non-teaching related factors are also associated with evaluation scores (e.g., professor’s ethnicity, professor’s sex).

For this part  of  the  assignment,  you  will  examine  whether  instructor  attractiveness  explains  differences in course evaluation scores—and thus on earnings differences. To do so, you will use the data in the evaluations.csv file to fit a regression model that uses professors’ beauty ratings to predict the variation in course evaluation ratings.

The data in evaluations.csv come from Hamermesh & Parker (2005) and were made available by Gelman & Hill (2007). This data were collected from student evaluations of instructors’ beauty and teaching quality for several courses at the University of Texas. The teaching evaluations were conducted at the end of the semester, and the beauty judgments were made later, by six students who had not attended the classes and were not aware of the course evaluations. The variables are:

prof_id: Professor ID number

avg_eval: Average course rating

num_courses: Number of courses for which the professor has evaluations

num_students: Number of students enrolled in the professor’s courses

perc_evaluating: Average percentage of enrolled students who completed an evaluation

beauty: Measure of the professor’s beauty composed of the average score on six standardized beauty ratings

tenured: Is the professor tenured? (0 = non-tenured; 1 = tenured)

native_english: Is the professor a native English speaker? (0 = non-native English speaker; 1 = native English speaker)

age: Professor’s age (in years)

female: Is the professor female? (0 = not female; 1 = female)

 

Part I: Evaluating Assumptions for the Simple Regression Model

Fit the regression model to predict the variation in course evaluation ratings using professors’ beauty ratings. You will use the output from the fitted model to answer the questions in Part I.

 

Preliminary Examination of Model Assumptions

1. Create and include the density plot for the outcome. Does the distribution foreshadow problems for the normality assumption? Explain.

2. Create and include the scatterplot of the outcome vs. the predictor. Does this relationship foreshadow problems for the linearity assumption? Explain.

 

Examination of the Standardized Residuals from the Simple Regression Model

3. Create and include the density plot of the marginal distribution of the standardized residuals from the fitted model. Add the confidence envelope for the normal distribution. Does this plot suggest problems about meeting the normality assumption? Explain.

4. Create and include the scatterplot of the standardized residuals versus the fitted values from the fitted model.  In the plot identify observation with extreme residuals (        3 or      3) by indicating the row number of that observation in the plot.

5. Does this plot suggest problems about meeting the linearity assumption? Explain.

6. Does this plot suggest problems about meeting the homogeneity of variance assumption? Explain.

7. Is the independence assumption tenable?  Explain.

 

Part II: Evaluating Assumptions for the Multiple Regression Model

Human overpopulation is a growing concern and has been associated with depletion of Earth’s natural resources (water is a big one that ) and degradation of the environment. This, in turn, has social and economic consequences such as global tension over resources such as water and food, higher cost of living and higher unemployment rates.  For this part of the assignment, you will use the file fertility.csv to fit a model in order to explore the effects of contraceptive use on fertility rates.

For the background of the data set, please refer to Homework 5.

Fit the regression model to predict the variation in fertility rates using contraception use, female education, and infant mortality rate (three predictors). You will use the output from the fitted model to answer the questions in Part II.

 

Preliminary Examination of Model Assumptions

8. Create and include the density plot for the outcome. Does the distribution foreshadow problems for the normality assumption? Explain.

9. Create and include the scatterplot of the outcome vs. each predictor (three total). Do any of these relationships foreshadow problems for the linearity assumption? Explain.

 

Examination of the Standardized Residuals from the Multiple Regression Model

10. Create and include the density plot of the marginal distribution of the standardized residuals from the fitted model. Add the confidence envelope for the normal distribution. Does this plot suggest problems about meeting the normality assumption? Explain.

11. Create and include the scatterplot of the standardized residuals versus the fitted values from the fitted model. In the plot identify observation with extreme residuals (    3 or     3) by indicating the country associated with that observation in the plot.

12. Does this plot suggest problems about meeting the linearity assumption? Explain.

13. Does this plot suggest problems about meeting the homogeneity of variance assumption? Explain.

14. Is the independence assumption tenable?  Explain.

 

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