What does multiple linear regression do?

Multiple linear regression estimates the relationship between one outcome (dependent variable) and two or more predictors by fitting a line Y = b0 + b1X1 + b2X2 + ... + bkXk using least squares.

What outputs should I report?

Report coefficients, standard errors, t-statistics, p-values, R-squared, adjusted R-squared and the ANOVA table if available.

Does this tool support predictions?

Yes. After estimating the regression, you can enter new predictor values and get the predicted Y.

Multiple Linear Regression Calculator – OLS, ANOVA, Predictions

Multiple Linear Regression Calculator

Fit a multiple linear regression model of the form: Y = β₀ + β₁X₁ + β₂X₂ + ... + βₖXₖ. Paste your data, hit “Run Regression”, and get coefficients, standard errors, t and p-values, R², adjusted R² and the ANOVA table. Then use the predictor panel to get a forecast for new X values.

Number of predictors (k)

up to 8 predictors

Number of rows (n)

min 3 obs

You can also paste CSV values directly into the table cells.

Observations (n)

—

R-squared

—

Adj. R-squared

—

Std. error

—

Coefficients

Variable	Coefficient	Std. Error	t	p-value
No results yet

ANOVA

Source	SS	df	MS	F	p-value
Regression	—	—	—	—	—
Residual	—	—	—	—	—
Total	—	—	—	—	—

Formula used

OLS solution: \( \boldsymbol{\beta} = (X'X)^{-1} X' y \)

where X is n×(k+1) including the intercept column of 1s, and y is n×1.

Residuals: \( e = y - X\beta \)

SSE: \( \text{SSE} = e'e \) (residual sum of squares)

SST: \( \text{SST} = \sum (y_i - \bar{y})^2 \)

SSR: \( \text{SSR} = \text{SST} - \text{SSE} \)

Assumptions

Linearity between each X and Y
Independence of errors
Homoscedasticity (constant variance)
Normality of residuals for small samples

Tips

Keep n reasonably larger than k+1 to avoid overfitting and unstable estimates. Check p-values for individual coefficients and the overall F-test to ensure the model is meaningful.