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Data-Centric Statistical Inference Using R and Tidyverse

Regression Refresher

Explore the fundamentals of simple linear regression with R and Tidyverse. Learn to fit regression models, interpret slope and intercept values, and understand sampling variability through a teaching evaluations dataset. This lesson builds your ability to analyze and infer relationships between variables in a data-centric context.

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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.

R
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:

R
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 ...