Linear Regression

The most-used model in all of data science. Fit a line through a cloud of points and see exactly how least squares balances the residuals — and how R² grades the fit.

Linear RegressionLive

least squares & R²

Controls

Presets

True slope

Noise level

Data points

Ordinary least squares finds the line that minimizes the sum of squared vertical residuals (the gray drop-lines). R² measures the fraction of variance the line explains — 1 is perfect, 0 is useless. Add noise or remove points to watch the fit and R² degrade.

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Data Inspector

Fitted slope0.000

Intercept0.000

R²0.000

Correlation r0.000

Governing equation

\overset{y}{^} = 0.00 + 0.00 x, β_{1} = \frac{\sum ( x - x ˉ ) ( y - y ˉ )}{\sum ( x - x ˉ ) ^{2}}, R^{2} = 0.00

Reading this result: R² = 0.00: noise (2) swamps the signal, so least squares can barely tell the slope from flat — adding data points would tighten the estimate.

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How it works

Ordinary least squares chooses the slope and intercept that minimize the sum of squared vertical residuals. R² reports the fraction of the variation the line explains, from 1 (perfect) to 0 (no better than the mean). Add noise or thin out the data to watch the estimate wobble and R² fall.

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Frequently asked questions

Is this linear regression calculator tool really free?▾

Yes. Linear Regression runs entirely in your browser using your device's own compute, so local use is free forever. You only pay Compute Tokens if you scale a job to the cloud.

Do I need to install anything?▾

No. Everything runs client-side in a modern browser — no downloads, no license, no account required to start.

Can I save or share my simulation?▾

Create a free account to save projects, and use a shareable embed or minted DOI to publish a live, interactive version anywhere.

How accurate are the results?▾

The solver uses established numerical methods, but results are for research and educational purposes and should be validated against experiment or professional review before you rely on them.