Linear Regression Calculator

Calculate linear regression line, slope, intercept, and R-squared. Find the best-fit line for your data points.

This calculator fits a least-squares regression line through exactly three fixed data points — no more, no fewer — computing the slope and intercept that minimize the total squared vertical distance between the line and each point, plus an R-squared value describing how well that line actually fits. At the calculator's default points, (1, 2), (2, 4), and (3, 5), something specific and genuinely surprising happens: moving Y₂ up or down has zero effect on the fitted slope. That isn't a coincidence of rounding — it follows directly from how the least-squares slope formula weights each point by how far its X-coordinate sits from the mean of all three X-values, and here X₂ (2) sits exactly on that mean, since the three X-values (1, 2, 3) are evenly spaced around it. A point sitting precisely at the mean X contributes nothing to the slope calculation regardless of its Y-value, though it still fully participates in the intercept and R-squared calculations, both of which do respond to Y₂ moving. Y₃, by contrast, pulls the slope up whenever it increases, since raising the line's rightmost point tilts the whole fitted line upward. Left unaddressed here: if all three Y-values happen to be identical, the true best fit is a perfectly flat horizontal line with a technically undefined R-squared, since there is no vertical spread in the data to explain, and rather than flagging that degenerate case, the calculator simply reports an R-squared of 0.