statistics-202 — Simple Linear Regression

A Shiny app for performing simple linear regression both by hand and in R.

Live app: https://antoinesoetewey.shinyapps.io/statistics-202/

Blog post: https://statsandr.com/blog/a-shiny-app-for-simple-linear-regression-by-hand-and-in-r/

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Purpose and overview

This app is designed to help students understand and perform simple linear regression. Given a set of paired observations for two numeric variables ($x$ and $y$), the app estimates the regression line, displays step-by-step formulas for computing the coefficients by hand, and provides full R output alongside an interactive plot. It is intended as both a learning tool and a computation aid for introductory statistics courses.

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Key features

• Data input — Enter $x$ and $y$ values directly as comma-separated lists. Summary statistics (means and sample size) are displayed automatically.
• By-hand computation — Shows the OLS formulas for the slope ($\hat{\beta}_1$) and intercept ($\hat{\beta}_0$) with the computed values filled in, so students can follow each calculation step.
• R output — Displays the full lm() summary, including coefficient estimates, standard errors, t-statistics, p-values, $R^2$, and the F-statistic.
• Interactive regression plot — Renders a scatter plot with the fitted regression line via ggplot2 and plotly. An optional confidence interval band can be toggled on or off.
• Automatic interpretation — Provides a plain-language interpretation of the estimated coefficients based on their statistical significance ($\alpha = 0.05$), including appropriate caveats.
• Assumption checks — A collapsible section displays the standard linear regression diagnostic plots (linearity, homoscedasticity, normality of residuals, influential observations) generated by the performance package.
• Downloadable report — Exports a self-contained HTML report (via R Markdown) that reproduces the analysis, with an option to include or hide the underlying R code.

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Running the app locally

Prerequisites: R ($\ge 4.0$) and the following packages:

install.packages(c(
  "shiny",
  "shinythemes",
  "ggplot2",
  "plotly",
  "DT",
  "rmarkdown",
  "knitr",
  "pander",
  "performance",
  "see"
))

Launch the app:

shiny::runGitHub("statistics-202", "AntoineSoetewey")

Or clone the repository and run locally:

# In the project directory
shiny::runApp()

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Dependencies

Package	Role
shiny	Web application framework
shinythemes	UI theme (Flatly)
ggplot2	Regression plot
plotly	Interactive plot rendering
DT	Interactive data table with export buttons
rmarkdown / knitr	Report generation
pander	Report formatting
performance / see	Regression assumption diagnostic plots

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Part of a set of complementary Shiny apps

This app is part of a set of three complementary Shiny apps developed for students while the author was a teaching assistant at UCLouvain. All three apps are still actively used when teaching introductory statistics and probability courses.

• statistics-101 — compute probabilities for the main probability distributions: https://github.com/AntoineSoetewey/statistics-101
• statistics-201 — perform statistical inference on mean(s), proportion(s), and variance(s): https://github.com/AntoineSoetewey/statistics-201
• statistics-202 — simple linear regression by hand: https://github.com/AntoineSoetewey/statistics-202 (this app)

License

This project is licensed under the terms of the MIT License.