Calcoid

Regression Calculator

Fit a least-squares line to your (x, y) data. Get slope, intercept, R squared, Pearson r, standard error, residuals, and a predicted y value.

Linear Regression

Separate x and y with a comma, tab, semicolon, or space. Paste spreadsheet columns directly. Needs at least 2 points with at least 2 different x values.

Optional. Leave blank to skip the point prediction.

Best-fit line

y = 1x + 1.3333

Slope (m)

1

Intercept (b)

1.3333

R squared

0.84

Pearson r

0.9165

Std. error

0.9129

Points (n)

6

Predicted value

At x = 7, y = 8.3333

Points and residuals

xyPredictedResidual
122.3333-0.3333
243.33330.6667
354.33330.6667
445.3333-1.3333
566.3333-0.3333
687.33330.6667

Regression Prediction Examples

Paired PointsBest-Fit LineInput xPredicted y
(1, 3), (2, 5), (3, 7)y = 2x + 149
(0, 10), (2, 9), (4, 8)y = -0.5x + 1067
(1, 3), (2, 6), (3, 9)y = 3x2.57.5
(0, 4), (4, 5), (8, 6)y = 0.25x + 486
(1, 5), (2, 5), (3, 5)y = 5125

Frequently Asked Questions about the Regression Calculator

What does this regression calculator do?
It fits a straight line y = mx + b through your data points using ordinary least squares. You get the slope, intercept, equation, R squared, Pearson correlation r, standard error of the estimate, and the residual for each point. Add an x value and it also predicts the matching y.
How many data points do I need?
At least 2 points with at least 2 different x values. With only 2 points you get a perfect fit by construction, so R squared equals 1 and the standard error is reported as 0. Standard error is most useful from about 5 or 6 points upward.
What does R squared mean?
R squared is the share of the variance in y that the line explains, between 0 and 1. An R squared of 0.85 means the line explains 85 percent of the variation in your y values. The rest is scatter the line cannot capture.
Why did the calculator return no result?
Two reasons. Either you entered fewer than 2 valid points, or every x value is the same. A vertical line has an undefined slope under least squares, so the calculator returns no equation rather than a misleading one.
Can I use this for curved data?
No. This tool is strictly linear regression. If your data follows a curve, transform it first (for example, take the log of y for exponential growth or use x squared for a parabola) and then fit a line to the transformed values.

Related Calculators

More calculators in "Math"

See all 202 calculators in "Math"