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Least-Squares Regression Line from Running Sums Calculator

slope = (n·Σxy − Σx·Σy) / (n·Σx² − (Σx)²); intercept = (Σy − slope·Σx) / n.

Fit an ordinary least-squares regression line y = m·x + b directly from the standard running sums Σx, Σy, Σxy, Σx², and the sample size n: slope = (n·Σxy − Σx·Σy) / (n·Σx² − (Σx)²); intercept = (Σy − slope·Σx) / n. Useful when raw observations have already been streamed/aggregated.

Daniel Oh By Daniel Oh
Published Last reviewed 1 min read

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Results

Enter values and click Calculate to see results.
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How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

slope = (n·Σxy − Σx·Σy) / (n·Σx² − (Σx)²); intercept = (Σy − slope·Σx) / n.

In depth

Fit an ordinary least-squares regression line y = m·x + b directly from the standard running sums Σx, Σy, Σxy, Σx², and the sample size n: slope = (n·Σxy − Σx·Σy) / (n·Σx² − (Σx)²); intercept = (Σy − slope·Σx) / n. Useful when raw observations have already been streamed/aggregated.