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.)

In this lab we 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 aslightly 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.

`load("more/evals.RData")`

variable | description |
---|---|

`score` |
average professor evaluation score: (1) very unsatisfactory - (5) excellent. |

`rank` |
rank of professor: teaching, tenure track, tenured. |

`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 second 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 second upper level male: (1) lowest - (10) highest. |

`bty_avg` |
average beauty rating of professor. |

`pic_outfit` |
outfit of professor in picture: not formal, formal. |

`pic_color` |
color of professor’s picture: color, black & white. |

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.

This is an observational study. The current question cannot be answered with an observational study, only with an experiment that controls for confounding variables. A more accurate question is whether there is a relationship between beauty and course evations.

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?The distribution of score is centered at 4.3, and is strongly skewed to the left. This tells me that most students rated professors between a 4 and 5, and lower ratings were less common. I expected to see ratings centered at 3 and distributed more symmetrically. This distribution shows that students included in this study view their teachers rather favorably.

`hist(evals$score)`

`summary(evals$score)`

`## Min. 1st Qu. Median Mean 3rd Qu. Max. ## 2.300 3.800 4.300 4.175 4.600 5.000`

Excluding

`score`

, select two other variables and describe their relationship using an appropriate visualization (scatterplot, side-by-side boxplots, or mosaic plot).I decided to visualize the relationship between age and average beauty rating of a teacher. It seems like age and beauty of teachers has a weak, linear, and negative relationship.

`plot(evals$bty_avg ~ evals$age)`

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:

`plot(evals$score ~ evals$bty_avg)`

Before we 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?

It seems like there may be overlap in the points on the scatter plot.

Replot the scatterplot, but this time use the function

`jitter()`

on the \(y\)- or the \(x\)-coordinate. (Use`?jitter`

to learn more.) What was misleading about the initial scatterplot?The initial scatterplot was misleading because it did not show duplicate values with the same beauty rating and evalation score.

`r plot(evals$score ~ jitter(evals$bty_avg))`

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 and add the line to your plot using`abline(m_bty)`

. 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?The equation is \(y=3.88034 + 0.06664x\). The slope means that for every point the beauty evaluation score increases, the teaching evaluation score increases by 0.06664. The Pr(>|t|) is almost 0, which means it is highly unlikely to observe a relationship between bty_avg and score by chance. Although the p-value shows that bty_avg is a statistically significant predictor, it does not seem to be a practically significant predictor. The scatter plot shows a very weak relationship between bty_avg and score with a very low R-squared value of 0.03502.

```
plot(evals$score ~ jitter(evals$bty_avg))
m_bty <- lm(score ~ bty_avg, data = evals)
abline(m_bty)
summary(m_bty)
```

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).

*Linearity*: The scatter plot of bty_avg and score residuals appear to be close to the normal line.

```
qqnorm(m_bty$residuals)
qqline(m_bty$residuals)
```

`*Nearly normal residuals*: The distribution of residuals is skewed to the left and is centered close to zero.`

```
m_bty <- lm(score ~ bty_avg, data = evals)
hist(m_bty$residuals)
```

`*Constant variability*: The scatter plot of residuals (above) shows constant variability for all values of bty_avg.`

```
plot(m_bty$residuals ~ evals$bty_avg)
abline(h = 0, lty = 3)
```