HW 07 - Modeling course evaluations

Team assignment

Due: Oct 30 at 10:05am

Many college courses conclude by giving students the opportunity to evaluate the course and the instructor anonymously. However, the use of these student evaluations as an indicator of course quality and teaching effectiveness is often criticized because these measures may reflect the influence of non-teaching related characteristics, such as the physical appearance of the instructor. The article titled, “Beauty in the classroom: instructors’ pulchritude and putative pedagogical productivity” (Hamermesh and Parker, 2005) found that instructors who are viewed to be better looking receive higher instructional ratings. (Daniel S. Hamermesh, Amy Parker, Beauty in the classroom: instructors pulchritude and putative pedagogical productivity, Economics of Education Review, Volume 24, Issue 4, August 2005, Pages 369-376, ISSN 0272-7757, 10.1016/j.econedurev.2004.07.013. http://www.sciencedirect.com/science/article/pii/S0272775704001165.)

For this assignment you will analyze the data from this study in order to learn what goes into a positive professor evaluation.

The data were gathered from end of semester student evaluations for a large sample of professors from the University of Texas at Austin. In addition, six students rated the professors’ physical appearance. (This is a slightly modified version of the original data set that was released as part of the replication data for Data Analysis Using Regression and Multilevel/Hierarchical Models (Gelman and Hill, 2007).) The result is a data frame where each row contains a different course and columns represent variables about the courses and professors.

Packages

In this lab we will work with the tidyverse and broom packages. We can install and load them with the following:

library(tidyverse)
library(broom)

The data

In this lab you will first download the data, then upload it to the data/ folder in your RStudio Cloud project.

Then, you can load the data as usual using the following.

Codebook

Variable name Description
score Average professor evaluation score: (1) very unsatisfactory - (5) excellent
rank Rank of professor: teaching, tenure track, tenure
ethnicity Ethnicity of professor: not minority, minority
gender Gender of professor: female, male
language Language of school where professor received education: english or non-english
age Age of professor
cls_perc_eval Percent of students in class who completed evaluation
cls_did_eval Number of students in class who completed evaluation
cls_students Total number of students in class
cls_level Class level: lower, upper
cls_profs Number of professors teaching sections in course in sample: single, multiple
cls_credits Number of credits of class: one credit (lab, PE, etc.), multi credit
bty_f1lower Beauty rating of professor from lower level female: (1) lowest - (10) highest
bty_f1upper Beauty rating of professor from upper level female: (1) lowest - (10) highest
bty_f2upper Beauty rating of professor from upper level female: (1) lowest - (10) highest
bty_m1lower Beauty rating of professor from lower level male: (1) lowest - (10) highest
bty_m1upper Beauty rating of professor from upper level male: (1) lowest - (10) highest
bty_m2upper Beauty rating of professor from upper level male: (1) lowest - (10) highest

Exercises

Part 1: Data Manipulation

  1. Create a new variable called bty_avg that is the average attractiveness score of the six students for each professor (bty_f1lower through bty_m2upper). Add this new variable to the evals data frame. Incomplete code is given below to guide you in the right direction, however you will need to fill in the blanks. Hint: What text string do the variables that need to be all averaged start with?

Part 2: Exploratory Data Analysis

  1. Visualize the distribution of score. Is the distribution skewed? What does that tell you about how students rate courses? Is this what you expected to see? Why, or why not? Include any summary statistics and visualizations you use in your response.

  2. Visualize the relationship between score and the new variable you created, bty_avg. Then, replot the scatterplot from Exercise 3, but this time use geom_jitter()? What does “jitter” mean? What was misleading about the initial scatterplot?

Part 3: Evaluation scores vs. beauty scores

Let’s see if the apparent trend in the plot is something more than natural variation.

  1. Fit a linear model called m_bty to predict average professor evaluation score by average beauty rating (bty_avg).
    (a) Based on the regression output, write the linear model.
    (b) Replot your visualization from Exercise 3, and add the regression line to this plot. Turn off the shading for the uncertainty of the line.
    (c) Interpret the slope of the linear model in context of the data.
    (d) Interpret the intercept of the linear model in context of the data. Comment on whether the intercept makes sense in this context.

  2. Determine the \(R^2\) of the model and interpret it in context of the data.

Part 4: Evaluation scores vs. beauty scores and gender

Next, we consider beauty scores and gender together.

  1. Fit a linear model,m_bty_gen, predicting average professor evaluation score based on average beauty rating (bty_avg) and gender. Write the linear model, and note the \(R^2\) and the adjusted \(R^2\).

  2. (a) What is the equation of the line corresponding to male professors?
    (b) What is it for female professors?
    (c) For two professors who received the same beauty rating, which gender tends to have the higher course evaluation score?
    (d) How does the relationship between beauty and evaluation score vary between male and female professors?

  3. Compare the slopes of bty_avg under the two models (m_bty and m_bty_gen). Has the addition of gender to the model changed the parameter estimate (slope) for bty_avg?

  4. How do the adjusted \(R^2\) values of m_bty_gen and m_bty compare? What does this tell us about how useful gender is in explaining the variability in evaluation scores when we already have information on the beaty score of the professor.

Part 5: Evaluation scores vs. beauty scores and rank

Now we turn our attention to beauty scores and rank.

  1. Fit a new linear model called m_bty_rank to predict average professor evaluation score average beauty rating (bty_avg) and rank. Based on the regression output, write the linear model and interpret the slopes and the intercept in context of the data.

  2. Create a new variable called rank_relevel where "tenure track" is the baseline level.

  3. Fit a new linear model called m_bty_rank_relevel to predict average professor evaluation score based on rank_relevel of the professor. This is the new (releveled) variable you created in Exercise 13. How is the regression output for this model similar to / different from the regression output for m_bty_rank? How do the \(R^2\)s of these models compare? Is this expected? Explain your reasoning.

Part 6: The search for the best model

Going forward, only consider the following variables as potential predictors: rank, ethnicity, gender, language, age, cls_perc_eval, cls_did_eval, cls_students, cls_level, cls_profs, cls_credits, bty_avg.

  1. Which variable, on its own, would you expect to be the worst predictor of evaluation scores? Why? Hint: Think about which variable would you expect to not have any association with the professor’s score.

  2. Check your suspicions from the previous exercise. Include the model output for that variable in your response.

  3. Suppose you wanted to fit a full model with the variables listed above. If you are already going to include cls_perc_eval and cls_students, which variable should you not include as an additional predictor? Why?

  4. Fit a full model with all predictors listed above (except for the one you decided to exclude) in the previous question. Then, using backward-selection with adjusted R-squared as the selection criterion, determine the best model. You do not need to show all steps in your answer, just the output for the final model. Also, write out the linear model for predicting score based on the final model you settle on.

  5. Based on your final model, describe the characteristics of a professor and course at University of Texas at Austin that would be associated with a high evaluation score.