Regression Studio

Place the data. Read the line. Explain the relationship.

Students can build or load datasets, inspect a best-fit line, and compare the formal regression fit to custom lines they drag by hand.

Return to Stats & Operations Analysis

Setup

Build and test a regression model

Dataset playground

Choose a classroom-ready example or click in the graph to make your own dataset.

Prediction lab

Enter an x-value, make a prediction, and compare it to the current line.

Predicted y-hat —

Add at least two points to unlock predictions.

Graph layers

Turn on visual supports that help students see what least squares is doing.

Learning flow

Use this talk track to keep the tool instructional instead of just interactive.

Start with a strong trend, then drag the line away from the cloud and compare the residual plot.

  1. Describe the direction of the pattern before reading the numbers.
  2. Interpret slope as “for each +1 in x, predicted y changes by...”
  3. Drag the line away from best fit and compare how the residual plot changes.
  4. Use the fan-shape examples to discuss non-constant variance.

Visualization

Data cloud, model line, and residuals

Click without dragging to add points. Drag the graph to pan, use the wheel or zoom buttons to scale, and drag the line or endpoints to test non-optimal fits.

Zoom
Legend Data Model line Residual
Residuals show vertical prediction error. The highlighted mean point sits on the least-squares line. Drag the line to see how R-squared and residual structure react.

ANOVA table

This table updates for the current draggable line. When the line is not at least squares, treat it as a teaching comparison rather than a formal inference table.

Source SS df MS F p-value

Add at least three points with different x-values to compute the regression ANOVA table.

Residual plot

A well-matched linear model tends to leave residuals scattered around zero. Curves or fan shapes suggest trouble.

Variance test Waiting

A Breusch-Pagan-style signal check will appear here once the app can evaluate residual spread.

Live readout

The app translates the regression into language students can explain.

Data pattern Waiting

Add points or load an example to describe the trend.

Model equation Not ready

A line needs at least two points with different x-values.

Model quality Waiting

R-squared and MSE appear once the app can fit a line.

Slope interpretation Explainable

Use the line to tell a story about how y changes as x increases.