Predicting teaching score using gender

Modeling with Data in the Tidyverse

Albert Y. Kim

Assistant Professor of Statistical and Data Sciences

Group means as predictions

library(ggplot2)
library(dplyr)
library(moderndive)

evals %>%
  group_by(gender) %>%
  summarize(mean_score = mean(score), sd_score = sd(score))

# A tibble: 2 x 3
  gender mean_score sd_score
  <fct>       <dbl>    <dbl>
1 female       4.09    0.564
2 male         4.23    0.522

Computing all predicted values and residuals

# Fit regression model:
model_score_3 <- lm(score ~ gender, data = evals)

# Get information on each point
get_regression_points(model_score_3)

# A tibble: 463 x 5
      ID score gender score_hat residual
   <int> <dbl> <fct>      <dbl>    <dbl>
 1     1   4.7 female      4.09    0.607
 2     2   4.1 female      4.09    0.007
 3     3   3.9 female      4.09   -0.193
 4     4   4.8 female      4.09    0.707
 5     5   4.6 male        4.23    0.366
 6     6   4.3 male        4.23    0.066

Histogram of residuals

# Fit regression model
model_score_3 <- lm(score ~ gender, data = evals)

# Get regression points
model_score_3_points <- get_regression_points(model_score_3)
model_score_3_points

# Plot residuals
ggplot(model_score_3_points, aes(x = residual)) +
  geom_histogram() +
  labs(x = "residuals",
       title = "Residuals from score ~ gender model")

Histogram of residuals

Let's practice!

Modeling with Data in the Tidyverse