Data-Centric Statistical Inference Using R and Tidyverse/

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Regression Refresher

Regression Refresher

Learn about evaluation analysis and sampling scenarios in inference for regression.

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Needed packages

Let’s load all the packages needed for this chapter. Loading the tidyverse package by running library(tidyverse) loads the following commonly used data science packages all at once:

  • ggplot2: This is for data visualization.

  • dplyr: This is for data wrangling.

  • tidyr: This is for converting data to the tidy format.

  • readr: This is for importing spreadsheet data into R.

  • purrr, tibble, stringr, and forcats: These are the more advanced packages.

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library(tidyverse) 
library(moderndive) 
library(infer)

Before jumping into inference for regression, let’s remind ourselves of the University of Texas Austin teaching evaluations analysis.

Teaching evaluations analysis

Using simple linear regression, we modeled the relationship between:

  • A numerical outcome variable y (the instructor’s teaching score)

  • A single numerical explanatory variable x (the instructor’s beauty score)

We first created an evals_ch5 data frame that selected a subset of variables from the evals data frame included in the moderndive package. This evals_ch5 data frame contains only the variables of interest for our analysis, in particular the instructor’s teaching score and the beauty rating bty_avg:

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evals_ch5 <- evals %>%
select(ID, score, bty_avg, age)
glimpse(evals_ch5)

We performed an exploratory data analysis of the relationship between the two variables score and bty_avg. We saw there that a weakly positive correlation of 0.187 existed between the two variables.

This is evidenced in the figure below of the scatterplot along with the best-fitting regression line that summarizes the linear relationship between the two variables score and bty_avg. We defined a best-fitting line as the line that minimizes the sum of the squared residuals.

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ggplot(evals_ch5,
aes(x = bty_avg, y = score)) +
geom_point() +
labs(x = "Beauty Score",
       y = "Teaching Score",
title = "Relationship between teaching and beauty scores") + geom_smooth(method = "lm", se = FALSE)

Looking at this plot again, the following questions might be asked: Does that line really have all that positive of a slope? It does increase from left to right as the bty_avg variable increases, but by how much?

To get to this information, recall that we followed a two-step procedure:

  1. We first fit the linear regression model using the lm() function with the formula score ~ bty_avg and save this model in score_model.

  2. We get the regression table by applying the get_regression_table() function from the moderndive package to score_model.

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# Fit regression model:
score_model <- lm(score ~ bty_avg, data = evals_ch5) 
# Get regression table:
get_regression_table(score_model)

Using the values in the estimate column of the resulting regression table, we can then obtain the equation of the best-fitting regression line in the figure above:

Here, 𝑏0𝑏_0 is the fitted intercept and 𝑏1𝑏_1 ...