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.
up to 8 predictors
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.
Formula (LaTeX) + variables + units
','\
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: \( \text{SSR} = \text{SST} - \text{SSE} \)
- PMI = private mortgage insurance (monthly) (currency)
- NIST — Weights and measures — nist.gov · Accessed 2026-01-19
https://www.nist.gov/pml/weights-and-measures - FTC — Consumer advice — consumer.ftc.gov · Accessed 2026-01-19
https://consumer.ftc.gov/
Last code update: 2026-01-19
- Initial audit spec draft generated from HTML extraction (review required).
- Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
- Confirm sources are authoritative and relevant to the calculator methodology.