Getting started

library(usethis)
use_git_config(user.name = "Your Name", 
               user.email = "your.email@address.com")

evals <- read_csv("data/evals-mod.csv")

library(tidyverse)
library(broom)

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. Do this in one pipe, using the rowMeans() function within a mutate().

evals <- evals %>% 
  mutate(bty_avg = rowMeans(select(., bty_f1lower:bty_m2upper)))

Let’s pause for a second to see what is happening in this piece of code. We are mutating the evals data frame by adding a new variable, bty_avg, that is calculated as the mean of the columns titled bty_f1lower through bty_m2upper in the evals data frame (denoted with a . here).

Part 2: Exploratory Data Analysis

2. 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.

3. Visualize and describe the relationship between score and the new variable you created, bty_avg.

⊕Hint: See the help page for the function at http://ggplot2.tidyverse.org/reference/index.html.

4. 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: Linear regression with a numerical predictor

⊕Linear model is in the form \(\hat{y} = b_0 + b_1 x\).

5. 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 evaluation score by average beauty rating (bty_avg). Based on the regression output, which you can obtain with tidy(m_bty), write the linear model.

6. Replot your visualization from Exercise 3, and add the regression line to this plot in orange color. Turn off the shading for the uncertainty of the line.

7. Interpret the slope of the linear model in context of the data.

8. Interpret the intercept of the linear model in context of the data. Comment on whether or not the intercept makes sense in this context.

⊕Refer back to this week’s reading if you don’t remember what \(R^2\) means.

9. Determine the \(R^2\) of the model and interpret it in context of the data. You can obtain this value with glance(m_bty).

Part 4: Linear regression with a categorical predictor

10. Fit a new linear model called m_gen to predict average professor evaluation score based on gender of the professor. Based on the regression output, write the linear model and interpret the slope and intercept in context of the data.

11. What is the equation of the line corresponding to male professors? What is it for female professors?

12. Fit a new linear model called m_rank to predict average professor evaluation score based on rank of the professor. Based on the regression output, write the linear model and interpret the slopes and intercept in context of the data.

⊕Refer to the forcats package for changing the order of levels.

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

14. Fit a new linear model called m_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. Based on the regression output, write the linear model and interpret the slopes and intercept in context of the data. Also determine and interpret the \(R^2\) of the model.