Linear Regression Calculator

Fits the straight line that best describes how Y changes with X.

Line of best fit

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Share sends a link that reopens these numbers. Copy details pastes the full breakdown as a list.

Values read in each list —

Slope —

Intercept —

R² —

Predicted Y —

Standard error of the slope —

p-value for the slope —

Residual standard deviation —

Reading this —

The formula

slope = Σ(x − x̄)(y − ȳ) ÷ Σ(x − x̄)² intercept = ȳ − slope × x̄

This is ordinary least squares, which minimises the sum of squared vertical distances from the line.

The slope is the change in Y for a one-unit rise in X. Swapping X and Y gives a different line, because the fit minimises vertical distances only.

What is a worked example?

For X = 1, 2, 3, 4, 5 and Y = 2, 4, 5, 4, 5, the line is y = 0.6x + 2.2, with R² = 0.6.

Does a good fit prove X causes Y?

No. A third factor or a coincidence can produce a good fit.