Linear regression worksheet

Fit a line to paired data and inspect fitted values, correlation, residuals and a labelled estimate.

Your input

Outputs are cleared when the input changes.

Result

Enter your data or use the example, then run the tool.

Worked example

(1,3), (2,5), (3,7) fit y = 1 + 2x, with R² = 1 and zero residuals.

x = 4 gives an estimated y = 9, labelled extrapolation outside the observed range 1–3.

Method

Ordinary least squares with an intercept uses slope Sxy/Sxx and intercept mean(y) − slope × mean(x). Centered calculation reduces cancellation.

Each residual is observed y minus fitted y. The two charts show observations with the fitted line and residuals against x.

Limits

All x equal is rejected. Constant y makes correlation and R² undefined. Extreme scales or insufficient floating-point variation may be rejected.

No causal conclusions, automatic confidence intervals, professional forecasts or outlier removal. Extrapolation is only a model estimate.

Sources

NIST: least-squares estimation

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