Grading the professor

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.

Getting Started

Load packages

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

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)
## Rows: 463
## Columns: 23
## $ course_id     <int> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 1…
## $ prof_id       <int> 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5,…
## $ score         <dbl> 4.7, 4.1, 3.9, 4.8, 4.6, 4.3, 2.8, 4.1, 3.4, 4.5, 3.8, 4…
## $ rank          <fct> tenure track, tenure track, tenure track, tenure track, …
## $ ethnicity     <fct> minority, minority, minority, minority, not minority, no…
## $ gender        <fct> female, female, female, female, male, male, male, male, …
## $ language      <fct> english, english, english, english, english, english, en…
## $ age           <int> 36, 36, 36, 36, 59, 59, 59, 51, 51, 40, 40, 40, 40, 40, …
## $ cls_perc_eval <dbl> 55.81395, 68.80000, 60.80000, 62.60163, 85.00000, 87.500…
## $ cls_did_eval  <int> 24, 86, 76, 77, 17, 35, 39, 55, 111, 40, 24, 24, 17, 14,…
## $ cls_students  <int> 43, 125, 125, 123, 20, 40, 44, 55, 195, 46, 27, 25, 20, …
## $ cls_level     <fct> upper, upper, upper, upper, upper, upper, upper, upper, …
## $ cls_profs     <fct> single, single, single, single, multiple, multiple, mult…
## $ cls_credits   <fct> multi credit, multi credit, multi credit, multi credit, …
## $ bty_f1lower   <int> 5, 5, 5, 5, 4, 4, 4, 5, 5, 2, 2, 2, 2, 2, 2, 2, 2, 7, 7,…
## $ bty_f1upper   <int> 7, 7, 7, 7, 4, 4, 4, 2, 2, 5, 5, 5, 5, 5, 5, 5, 5, 9, 9,…
## $ bty_f2upper   <int> 6, 6, 6, 6, 2, 2, 2, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 9, 9,…
## $ bty_m1lower   <int> 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 7, 7,…
## $ bty_m1upper   <int> 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 6,…
## $ bty_m2upper   <int> 6, 6, 6, 6, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 6, 6,…
## $ bty_avg       <dbl> 5.000, 5.000, 5.000, 5.000, 3.000, 3.000, 3.000, 3.333, …
## $ pic_outfit    <fct> not formal, not formal, not formal, not formal, not form…
## $ pic_color     <fct> color, color, color, color, color, color, color, color, …

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

Exploring the data

  1. Is this an observational study or an experiment? The original research question posed in the paper is whether beauty leads directly to the differences in course evaluations. Given the study design, is it possible to answer this question as it is phrased? If not, rephrase the question.

Insert your answer here This is an observational study, not an experiment. The data was collected without manipulating any variables, such as the professor’s physical appearance or teaching methods.

The original research question, “Does beauty lead directly to differences in course evaluations?” cannot be answered as it is phrased because causation cannot be established in observational studies. Instead, the question should be rephrased to something like:

“Is there an association between professors’ physical appearance and their course evaluation scores?”

This framing acknowledges that only correlation, not causation, can be assessed.

  1. Describe 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?

Insert your answer here The distribution of score is slightly right-skewed, meaning that most scores cluster at the higher end of the scale (e.g., 4.0 to 5.0), with fewer lower scores.

This indicates that students tend to rate courses positively overall, suggesting leniency or satisfaction in evaluations. This is not unexpected because students often hesitate to give extremely low scores unless the course experience is particularly poor. Positive skewness aligns with prior findings in educational research, where student evaluations are generally favorable.

To visualize the distribution:

ggplot(evals, aes(x = score)) +
  geom_histogram(binwidth = 0.2, fill = "blue", alpha = 0.7) +
  labs(title = "Distribution of Evaluation Scores", x = "Score", y = "Count") +
  theme_minimal()

  1. Excluding score, select two other variables and describe their relationship with each other using an appropriate visualization.

Insert your answer here Excluding score, let’s examine the relationship between bty_avg (beauty rating) and age. A scatterplot with a trend line is appropriate

ggplot(evals, aes(x = age, y = bty_avg)) +
  geom_point(alpha = 0.6, color = "blue") +
  geom_smooth(method = "lm", se = FALSE, color = "red") +
  labs(title = "Relationship Between Age and Beauty Rating", 
       x = "Age", y = "Average Beauty Rating") +
  theme_minimal()

Simple linear regression

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?

  1. Replot the scatterplot, but this time use 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 The initial scatterplot appears misleading because it doesn’t account for overlapping data points. Observations with the same or very similar bty_avg and score values stack directly on top of each other, making it difficult to assess the true distribution of the points.

Using geom_jitter, which adds a small amount of random noise to the points, resolves this issue:

ggplot(data = evals, aes(x = bty_avg, y = score)) +
  geom_jitter(width = 0.2, height = 0.2) +
  labs(title = "Scatterplot of Score vs. Beauty (Jittered)", x = "Beauty Rating (Average)", y = "Score")

This reveals clusters of overlapping points and better illustrates the density of the data at various regions.

  1. Let’s see if the apparent trend in the plot is something more than natural variation. Fit a linear model called 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

m_bty <- lm(score ~ bty_avg, data = evals)
summary(m_bty)
## 
## Call:
## lm(formula = score ~ bty_avg, data = evals)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.9246 -0.3690  0.1420  0.3977  0.9309 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  3.88034    0.07614   50.96  < 2e-16 ***
## bty_avg      0.06664    0.01629    4.09 5.08e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5348 on 461 degrees of freedom
## Multiple R-squared:  0.03502,    Adjusted R-squared:  0.03293 
## F-statistic: 16.73 on 1 and 461 DF,  p-value: 5.083e-05

The linear model equation \(\text{score} = \beta_0 + \beta_1 \times \text{bty_avg}\) describes how evaluation scores are predicted based on beauty ratings. The intercept (\(\beta_0\)) and slope (\(\beta_1\)) are provided by the model. The slope (\(\beta_1\)) indicates how much the score increases for each one-unit increase in the beauty rating. For example, if \(\beta_1 = 0.05\), a one-point increase in beauty rating results in a 0.05-point increase in the score. Statistical significance of the slope is determined by its p-value, with a value below 0.05 indicating significance. However, practical significance depends on the magnitude of the slope—small slopes may have minimal real-world impact despite statistical significance. 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)

ggplot(data = evals, aes(x = bty_avg, y = score)) +
  geom_jitter(width = 0.2, height = 0.2) +
  geom_smooth(method = "lm", se = FALSE) +
  labs(title = "Regression Line: Score vs. Beauty", x = "Beauty Rating (Average)", y = "Score")

6. Use residual plots to evaluate whether the conditions of least squares regression are reasonable. Provide plots and comments for each one (see the Simple Regression Lab for a reminder of how to make these).

Insert your answer here

#Linearity: Plot residuals vs. fitted values to check for patterns. A random scatter suggests linearity is satisfied:
plot(m_bty, which = 1)

#Normality: Use a Q-Q plot to assess if residuals follow a normal distribution:
plot(m_bty, which = 2)

#Homoscedasticity: Residuals vs. fitted values plot should show no clear pattern or funnel shape, indicating constant variance:
plot(m_bty, which = 3)

## Multiple linear regression

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))
## # A tibble: 1 × 1
##   `cor(bty_avg, bty_f1lower)`
##                         <dbl>
## 1                       0.844

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)
## 
## Call:
## lm(formula = score ~ bty_avg + gender, data = evals)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.8305 -0.3625  0.1055  0.4213  0.9314 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  3.74734    0.08466  44.266  < 2e-16 ***
## bty_avg      0.07416    0.01625   4.563 6.48e-06 ***
## gendermale   0.17239    0.05022   3.433 0.000652 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5287 on 460 degrees of freedom
## Multiple R-squared:  0.05912,    Adjusted R-squared:  0.05503 
## F-statistic: 14.45 on 2 and 460 DF,  p-value: 8.177e-07
  1. P-values and parameter estimates should only be trusted if the conditions for the regression are reasonable. Verify that the conditions for this model are reasonable using diagnostic plots.

Insert your answer here

par(mfrow = c(2, 2))
plot(m_bty_gen)

The four diagnostic plots indicate:

Residuals vs Fitted: The residuals appear randomly scattered around zero, suggesting linearity and equal variance are reasonably satisfied.

Q-Q Plot: The residuals mostly follow the diagonal line, indicating that normality of residuals is approximately satisfied, though there might be slight deviations at the tails.

Scale-Location Plot: The spread of residuals is relatively consistent, supporting the assumption of homoscedasticity.

Residuals vs Leverage: There are no high-leverage points with extreme residuals, suggesting there are no significant outliers or influential points.

Conclusion: The assumptions of least squares regression are reasonably met for this model.

  1. Is 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 Significance of bty_avg after Adding gender The regression summary likely shows that bty_avg remains a statistically significant predictor of score (with a p-value < 0.05). However, the addition of gender to the model slightly changes the parameter estimate for bty_avg, as accounting for gender explains some variability in score. This suggests that both bty_avg and gender independently influence course evaluations.

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)

  1. What is the equation of the line corresponding to those with color pictures? (Hint: For those with color pictures, the parameter estimate is multiplied by 1.) For two professors who received the same beauty rating, which color picture tends to have the higher course evaluation score?

Insert your answer here Equation of the Line for Color Pictures From the plot with two lines, the equation for color pictures (based on pic_color) can be written as:

# = _0 + _1 + _2 (1) Where:

#β 0 is the intercept.

#β1 is the slope for bty_avg.

#β2 is the adjustment for pic_color = color. Since the red line (black-and-white) has a higher slope and intercept than the blue line (color), professors with black-and-white pictures tend to have higher course evaluation scores for the same beauty rating.

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.)

  1. Create a new model called 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

m_bty_rank <- lm(score ~ bty_avg + rank, data = evals)
summary(m_bty_rank)
## 
## Call:
## lm(formula = score ~ bty_avg + rank, data = evals)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.8713 -0.3642  0.1489  0.4103  0.9525 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       3.98155    0.09078  43.860  < 2e-16 ***
## bty_avg           0.06783    0.01655   4.098 4.92e-05 ***
## ranktenure track -0.16070    0.07395  -2.173   0.0303 *  
## ranktenured      -0.12623    0.06266  -2.014   0.0445 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5328 on 459 degrees of freedom
## Multiple R-squared:  0.04652,    Adjusted R-squared:  0.04029 
## F-statistic: 7.465 on 3 and 459 DF,  p-value: 6.88e-05

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.

The search for the best model

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.

  1. Which variable would you expect to have the highest p-value in this model? Why? Hint: Think about which variable would you expect to not have any association with the professor score.

Insert your answer here The variable with the highest p-value is likely to be cls_profs (number of professors) because it may not have a meaningful association with the professor’s score. In general, the number of professors teaching a course may not directly influence students’ evaluations, which tend to focus more on individual traits and perceptions.

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)
## 
## Call:
## lm(formula = 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)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.77397 -0.32432  0.09067  0.35183  0.95036 
## 
## Coefficients:
##                         Estimate Std. Error t value Pr(>|t|)    
## (Intercept)            4.0952141  0.2905277  14.096  < 2e-16 ***
## ranktenure track      -0.1475932  0.0820671  -1.798  0.07278 .  
## ranktenured           -0.0973378  0.0663296  -1.467  0.14295    
## gendermale             0.2109481  0.0518230   4.071 5.54e-05 ***
## ethnicitynot minority  0.1234929  0.0786273   1.571  0.11698    
## languagenon-english   -0.2298112  0.1113754  -2.063  0.03965 *  
## age                   -0.0090072  0.0031359  -2.872  0.00427 ** 
## cls_perc_eval          0.0053272  0.0015393   3.461  0.00059 ***
## cls_students           0.0004546  0.0003774   1.205  0.22896    
## cls_levelupper         0.0605140  0.0575617   1.051  0.29369    
## cls_profssingle       -0.0146619  0.0519885  -0.282  0.77806    
## cls_creditsone credit  0.5020432  0.1159388   4.330 1.84e-05 ***
## bty_avg                0.0400333  0.0175064   2.287  0.02267 *  
## pic_outfitnot formal  -0.1126817  0.0738800  -1.525  0.12792    
## pic_colorcolor        -0.2172630  0.0715021  -3.039  0.00252 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.498 on 448 degrees of freedom
## Multiple R-squared:  0.1871, Adjusted R-squared:  0.1617 
## F-statistic: 7.366 on 14 and 448 DF,  p-value: 6.552e-14
  1. Check your suspicions from the previous exercise. Include the model output in your response.

Insert your answer here Based on the model output:

The p-value for cls_profs is 0.77806, the highest among all variables. This aligns with our earlier suspicion. Since its p-value is much higher than 0.05, it is not statistically significant in predicting professor scores.

  1. Interpret the coefficient associated with the ethnicity variable.

Insert your answer here The coefficient for ethnicitynot minority is 0.12349, with a p-value of 0.117. This suggests:

Professors identified as “not a minority” tend to receive scores that are, on average, 0.12349 higher than those identified as “minority,” holding all other variables constant. However, since the p-value is greater than 0.05, this difference is not statistically significant at the 5% level.

  1. Drop the variable with the highest p-value and re-fit the model. Did the coefficients and significance of the other explanatory variables change? (One of the things that makes multiple regression interesting is that coefficient estimates depend on the other variables that are included in the model.) If not, what does this say about whether or not the dropped variable was collinear with the other explanatory variables?

Insert your answer here After removing cls_profs, the model should be re-fitted. The coefficients and significance of other variables might remain unchanged if cls_profs was not collinear with the other variables. If the results for other variables change, it would suggest some level of multicollinearity.

lm(formula = score ~ rank + gender + ethnicity + language + age + 
    cls_perc_eval + cls_students + cls_level + cls_credits + 
    bty_avg + pic_outfit + pic_color, data = evals)
## 
## Call:
## lm(formula = score ~ rank + gender + ethnicity + language + age + 
##     cls_perc_eval + cls_students + cls_level + cls_credits + 
##     bty_avg + pic_outfit + pic_color, data = evals)
## 
## Coefficients:
##           (Intercept)       ranktenure track            ranktenured  
##             4.0872523             -0.1476746             -0.0973829  
##            gendermale  ethnicitynot minority    languagenon-english  
##             0.2101231              0.1274458             -0.2282894  
##                   age          cls_perc_eval           cls_students  
##            -0.0089992              0.0052888              0.0004687  
##        cls_levelupper  cls_creditsone credit                bty_avg  
##             0.0606374              0.5061196              0.0398629  
##  pic_outfitnot formal         pic_colorcolor  
##            -0.1083227             -0.2190527
  1. Using backward-selection and p-value 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.

Insert your answer here

lm(formula = score ~ gender + cls_perc_eval + cls_credits + bty_avg + 
    pic_color, data = evals)
## 
## Call:
## lm(formula = score ~ gender + cls_perc_eval + cls_credits + bty_avg + 
##     pic_color, data = evals)
## 
## Coefficients:
##           (Intercept)             gendermale          cls_perc_eval  
##              3.586646               0.189381               0.004401  
## cls_creditsone credit                bty_avg         pic_colorcolor  
##              0.463685               0.061047              -0.175367
  1. Verify that the conditions for this model are reasonable using diagnostic plots.

Insert your answer here

# Fit the final model
final_model <- lm(formula = score ~ gender + cls_perc_eval + cls_credits + bty_avg + pic_color, data = evals)

# Generate diagnostic plots
par(mfrow = c(2, 2))  # Arrange the plots in a 2x2 grid
plot(final_model)

These plots include: Residuals vs. Fitted to assess the linearity assumption and detect patterns in residuals; the Normal Q-Q Plot to verify if residuals follow a normal distribution; the Scale-Location Plot to check for homoscedasticity (constant variance of residuals); and the Residuals vs. Leverage Plot to identify influential observations. These diagnostics help ensure the robustness and validity of the linear regression model.

  1. The original paper describes how these data were gathered by taking a sample of professors from the University of Texas at Austin and including all courses that they have taught. Considering that each row represents a course, could this new information have an impact on any of the conditions of linear regression?

Insert your answer here Since the data represent courses taught by professors, there could be dependency within the data (e.g., multiple rows for the same professor). This violates the independence assumption of linear regression. If a professor teaches several courses, the evaluation scores for these courses might be correlated, introducing clustering effects. To account for this, it may be necessary to use hierarchical modeling or include random effects to handle professor-level variation.

  1. 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.

Insert your answer here Based on the final model, several factors contribute to higher evaluation scores for professors. Male professors are predicted to score higher, as are those teaching courses with high student participation in evaluations. One-credit courses tend to have higher evaluation scores compared to multi-credit courses. Professors with higher beauty ratings and those using black-and-white pictures also receive higher scores. Therefore, to achieve a high evaluation score, a professor would likely be male, teach a one-credit course with high participation, have a high beauty rating, and use a black-and-white picture.

  1. Would you be comfortable generalizing your conclusions to apply to professors generally (at any university)? Why or why not?

Insert your answer here No, it would not be appropriate to generalize these findings to professors at other universities. The data were collected exclusively from the University of Texas at Austin, and the evaluation scores might be influenced by university-specific factors such as the culture, demographics, or expectations of students. Additionally, beauty rating, picture color, and gender bias might vary significantly across institutions. A more diverse dataset including professors from various universities would be needed to make generalized conclusions.