Calculators/Multiple Regression Calculator

Regression & Correlation

Multiple Regression Calculator

Fit a linear regression with several predictors at once, and see every coefficient, its significance, and how well the whole model fits.

Your data

First row: comma-separated headers, outcome first (e.g. y,x1,x2). Each row after that: one observation. Up to 6 predictors work well here; for more, use dedicated statistics software.

ŷ = -16.836 + 3.3062·x1 + 3.9153·x2

Term	Coef.	SE	t	p-value
Intercept	-16.8361	7.9971	-2.105	0.0733
x1	3.3062	0.62	5.333	0.0011
x2	3.9153	0.615	6.366	0.0004

R²

0.9784

Adjusted R²

0.9722

F statistic

158.567

F p-value

< 0.0001

The model explains 97.8% of the variation in y (adjusted for the number of predictors: 97.2%). The overall F-test (158.57 on 2 and 7 degrees of freedom, p < 0.0001) tests whether the predictors jointly explain more than chance. Each coefficient's own p-value tests that predictor while holding the others constant, following the logic in multiple regression.

How to use this tool

Paste your data as comma-separated values, with the outcome in the first column and each predictor in its own column.
The first row must be headers, for example y,x1,x2.
Read the fitted equation, the coefficient table, and R-squared.
Check the overall F-test to see whether the predictors jointly explain more than chance, and each coefficient's own p-value.

Formula Reference

Fitted model

y-hat = b0 + b1*x1 + b2*x2 + ...

Normal equations

b = (X'X)^-1 X'y

R-squared

1 - SSres / SStot

Adjusted R-squared

1 - (1 - R2)(n - 1) / (n - p - 1)

ArticleMultiple Linear Regression ArticleSimple Linear Regression ArticleThe F-Test for Regression ArticleInteraction Effects in Regression CalcLinear Regression Calculator GlossaryGlossary: Multiple Linear Regression

Frequently Asked Questions

How is this different from the simple Linear Regression Calculator?+

That calculator fits a line through one predictor and one outcome. This one fits a plane, or higher-dimensional surface, through several predictors at once, and each coefficient shows the effect of its predictor while holding the others constant.

What does a coefficient's p-value tell me?+

It tests whether that predictor adds explanatory power beyond what the other predictors already provide. A predictor can look important alone (in simple regression) but lose significance once a correlated predictor is added.

Why might the calculator say the predictors are too closely related?+

When two predictors carry almost the same information, called multicollinearity, the coefficients cannot be estimated uniquely. Remove one of the redundant predictors or combine them.

How many predictors can I use?+

The maths handles any number up to the sample size, but this browser-based tool is meant for small, exploratory models, typically up to about 6 predictors. For larger models use dedicated statistics software.

Term

Coef.

p-value

Intercept

-16.8361

7.9971

-2.105

0.0733

3.3062

0.62

5.333

0.0011

3.9153

0.615

6.366

0.0004

How to use this tool

Paste your data as comma-separated values, with the outcome in the first column and each predictor in its own column.

The first row must be headers, for example y,x1,x2.

Read the fitted equation, the coefficient table, and R-squared.

Check the overall F-test to see whether the predictors jointly explain more than chance, and each coefficient's own p-value.