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Linear Regression Slope from Sums Calculator

b = (n·Σxy − Σx·Σy) / (n·Σx² − (Σx)²).

Compute the OLS slope coefficient of a simple linear regression y = a + b·x directly from the five paired-sample summary statistics (n, Σx, Σy, Σxy, Σx²) without raw data: b = (n·Σxy − Σx·Σy) / (n·Σx² − (Σx)²). Pair with the intercept calculator to get the full line.

Daniel Oh By Daniel Oh
Published Last reviewed 1 min read

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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

b = (n·Σxy − Σx·Σy) / (n·Σx² − (Σx)²).

In depth

Compute the OLS slope coefficient of a simple linear regression y = a + b·x directly from the five paired-sample summary statistics (n, Σx, Σy, Σxy, Σx²) without raw data: b = (n·Σxy − Σx·Σy) / (n·Σx² − (Σx)²). Pair with the intercept calculator to get the full line.