Add points or load an example to describe the trend.
Setup
Build and test a regression model
Dataset playground
Choose a classroom-ready example or click in the graph to make your own dataset.
Keyboard point entry
This provides the same point-placement function as clicking the graph.
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.
Keyboard model-line controls
Enter a slope and intercept to move or resize the line without dragging it or its endpoints.
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.
- Describe the direction of the pattern before reading the numbers.
- Interpret slope as “for each +1 in x, predicted y changes by...”
- Drag the line away from best fit and compare how the residual plot changes.
- Use the fan-shape examples to discuss non-constant variance.
Predict, then check
State the fitted slope’s direction before reading the model interpretation.
Make a prediction before checking the fitted slope.
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. Keyboard users can add points and set the line's slope and intercept in the setup controls.
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.
A line needs at least two points with different x-values.
R-squared and MSE appear once the app can fit a line.
Use the line to tell a story about how y changes as x increases.
Biblical/Ethical Stewardship and Integrity
Report association without implying causation, disclose influential points and assumption concerns, and avoid extrapolating beyond the observed range. A useful business recommendation must remain truthful about what the model cannot establish.
Static fallback: every graph has a textual readout. Print this page or use Save as PDF; your instructor can provide the same seeded dataset in an accessible worksheet.