Brief Introduction to Regression

Quantitative Histories Workshop · Session delivered 11 August 2026 Author: Ari Kamau (TA)

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What this is

A single self-contained R Markdown lesson (Intro_to_Regression_Aug11.Rmd) that walks from "what is regression" through to a fully annotated summary(lm()) table. It is written to be run, not just read — every example uses mtcars, a dataset that ships with R, so nothing needs to be downloaded and nothing touches your own files.

Knitting the file produces a navigable HTML page with a floating table of contents, numbered sections, and foldable code chunks.

Contents

Section	Topic
1	What regression is — dependent vs. independent variables, population truth vs. sample estimates
2	Choosing a model, and why OLS — closed form, minimizing squared residuals, ubiquity in the literature
3	The data: mtcars (32 cars, Motor Trend 1974)
4	OLS with one predictor — fitting mpg ~ wt, visualizing residuals, reading every column of the output
5	Multiple predictors — mpg ~ wt + hp + am, and whether the extra variables earned their keep
6	The three numbers to check every time — p-value, $R^2$ / adjusted $R^2$, degrees of freedom
7	What can go wrong — the assumptions A1–A6, and a preview of heteroskedasticity, omitted variable bias, confounding, and collinearity
Appendix	Vocabulary glossary and a reference table of the R commands used

Along the way the lesson covers the sum-of-squares decomposition ($SS_{tot} = SS_{reg} + SS_{res}$), residual standard error, the F-statistic, and why adjusted $R^2$ is the number to compare models on.

Requirements

• R (≥ 4.0 recommended)
• RStudio — recommended, for the Knit button and per-chunk execution
• R packages:
  • rmarkdown and knitr (bundled with RStudio; otherwise install them)
  • ggplot2 — the document installs this automatically if it is missing

install.packages(c("rmarkdown", "knitr", "ggplot2"))

No other data files are needed. mtcars is built into base R.

How to run it

In RStudio

1. Open Intro_to_Regression_Aug11.Rmd.
2. Press the green play button (▶) at the top-right of any grey chunk to run just that chunk.
3. Press Knit to render the whole file to HTML.

Sources

• Yang, Q. (2017). "Regression." In L.A. Schintler & C.L. McNeely (eds.), Encyclopedia of Big Data. Springer. DOI 10.1007/978-3-319-32001-4_174-1
• Greene, W.H. (2003). Econometric Analysis, 5th ed. Prentice Hall. Ch. 2 (the classical linear regression model and its assumptions) and Ch. 3 (least squares, the sum-of-squares decomposition, and $R^2$)
• Henderson & Velleman (1981), Motor Trend 1974 — via R's mtcars