Linear Regression Playground
Ordinary least squares fits the line minimising the sum of squared vertical distances to the data, and here you build the data yourself: click empty space to add a point, drag one to move it, click one to delete it — the fitted line, slope, intercept, R² and mean squared error update instantly. Toggle the residual segments to see exactly what is being minimised, and load presets showing a clean linear trend, the pull a single outlier exerts on the fit, and a curved dataset a straight line underfits. A second canvas draws the loss surface over (slope, intercept) as contours with the closed-form solution marked — press Play and gradient descent walks the surface toward the same point the formula reaches in one step.
Runs 100% in your browser — models are trained and computed locally on your device.
Read the full guide to this tool
Notes
- Closed form: slope = Σ(x−x̄)(y−ȳ) / Σ(x−x̄)² and intercept = ȳ − slope·x̄, the unique minimum of the MSE, which is a convex paraboloid in the two parameters.
- Squared error grows quadratically with distance, so a single far-off outlier can drag the whole line — the reason robust alternatives such as least absolute deviations exist.
- R² compares the model’s squared error with that of a horizontal line at ȳ: 1 is a perfect fit, 0 means no better than predicting the mean for everything.
- With uncentred x values the loss surface is a stretched valley: gradient descent zigzags quickly down the steep slope direction but crawls along the flat intercept direction.
- Runs 100% in your browser — models are trained and computed locally on your device.
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