knitr::opts_chunk$set(eval = TRUE, message = FALSE, warning = FALSE)
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" by Hamermesh and Parker found that instructors who are viewed to be better looking receive higher instructional ratings.
Here, you will analyze the data from this study in order to learn what goes into a positive professor evaluation.
In this lab, you will explore and visualize the data using the tidyverse suite of packages. The data can be found in the companion package for OpenIntro resources, openintro.
Let's load the packages.
library(tidyverse) library(openintro) library(GGally)
This is the first time we're using the GGally
package. You will be using the ggpairs
function from this package later in the lab.
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. The result is a data frame where each row contains a different course and columns represent variables about the courses and professors. It's called evals
.
glimpse(evals)
We have observations on 21 different variables, some categorical and some numerical. The meaning of each variable can be found by bringing up the help file:
?evals
Insert your answer here
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?Insert your answer here
score
, select two other variables and describe their relationship
with each other using an appropriate visualization.Insert your answer here
The fundamental phenomenon suggested by the study is that better looking teachers are evaluated more favorably. Let's create a scatterplot to see if this appears to be the case:
ggplot(data = evals, aes(x = bty_avg, y = score)) + geom_point()
Before you draw conclusions about the trend, compare the number of observations in the data frame with the approximate number of points on the scatterplot. Is anything awry?
geom_jitter
as your layer. What
was misleading about the initial scatterplot?ggplot(data = evals, aes(x = bty_avg, y = score)) + geom_jitter()
Insert your answer here
m_bty
to predict average
professor score by average beauty rating. Write out the equation for the linear
model and interpret the slope. Is average beauty score a statistically significant
predictor? Does it appear to be a practically significant predictor?Insert your answer here
Add the line of the bet fit model to your plot using the following:
ggplot(data = evals, aes(x = bty_avg, y = score)) + geom_jitter() + geom_smooth(method = "lm")
The blue line is the model. The shaded gray area around the line tells you about the variability you might expect in your predictions. To turn that off, use se = FALSE
.
ggplot(data = evals, aes(x = bty_avg, y = score)) + geom_jitter() + geom_smooth(method = "lm", se = FALSE)
Insert your answer here
The data set contains several variables on the beauty score of the professor: individual ratings from each of the six students who were asked to score the physical appearance of the professors and the average of these six scores. Let's take a look at the relationship between one of these scores and the average beauty score.
ggplot(data = evals, aes(x = bty_f1lower, y = bty_avg)) + geom_point() evals %>% summarise(cor(bty_avg, bty_f1lower))
As expected, the relationship is quite strong---after all, the average score is calculated using the individual scores. You can actually look at the relationships between all beauty variables (columns 13 through 19) using the following command:
evals %>% select(contains("bty")) %>% ggpairs()
These variables are collinear (correlated), and adding more than one of these variables to the model would not add much value to the model. In this application and with these highly-correlated predictors, it is reasonable to use the average beauty score as the single representative of these variables.
In order to see if beauty is still a significant predictor of professor score after you've accounted for the professor's gender, you can add the gender term into the model.
m_bty_gen <- lm(score ~ bty_avg + gender, data = evals) summary(m_bty_gen)
Insert your answer here
bty_avg
still a significant predictor of score
? Has the addition
of gender
to the model changed the parameter estimate for bty_avg
?Insert your answer here
Note that the estimate for gender
is now called gendermale
. You'll see this name change whenever you introduce a categorical variable. The reason is that R recodes gender
from having the values of male
and female
to being an indicator variable called gendermale
that takes a value of $0$ for female professors and a value of $1$ for male professors. (Such variables are often referred to as "dummy" variables.)
As a result, for female professors, the parameter estimate is multiplied by zero, leaving the intercept and slope form familiar from simple regression.
[ \begin{aligned} \widehat{score} &= \hat{\beta}_0 + \hat{\beta}_1 \times bty_avg + \hat{\beta}_2 \times (0) \ &= \hat{\beta}_0 + \hat{\beta}_1 \times bty_avg\end{aligned} ]
ggplot(data = evals, aes(x = bty_avg, y = score, color = pic_color)) + geom_smooth(method = "lm", formula = y ~ x, se = FALSE)
Insert your answer here
The decision to call the indicator variable gendermale
instead of genderfemale
has no deeper meaning. R simply codes the category that comes first alphabetically as a $0$. (You can change the reference level of a categorical variable, which is the level that is coded as a 0, using therelevel()
function. Use ?relevel
to learn more.)
m_bty_rank
with gender
removed and rank
added in. How does R appear to handle categorical variables that have more
than two levels? Note that the rank variable has three levels: teaching
,
tenure track
, tenured
.Insert your answer here
The interpretation of the coefficients in multiple regression is slightly different from that of simple regression. The estimate for bty_avg
reflects how much higher a group of professors is expected to score if they have a beauty rating that is one point higher while holding all other variables constant. In this case, that translates into considering only professors of the same rank with bty_avg
scores that are one point apart.
We will start with a full model that predicts professor score based on rank, gender, ethnicity, language of the university where they got their degree, age, proportion of students that filled out evaluations, class size, course level, number of professors, number of credits, average beauty rating, outfit, and picture color.
Insert your answer here
Let's run the model...
m_full <- lm(score ~ rank + gender + ethnicity + language + age + cls_perc_eval + cls_students + cls_level + cls_profs + cls_credits + bty_avg + pic_outfit + pic_color, data = evals) summary(m_full)
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