MULTIPLE PREDICTORS
Multiple Linear Regression Calculator
Fit y = β₀ + β₁x₁ + … + βₚxₚ by ordinary least squares with an intercept, using a Householder QR solve on centered and scaled predictors. Review coefficients as conditional associations, inspect conditioning warnings, and export row-level predictions and residuals.
YOUR DATA
Enter observations and choose columns
Paste or upload numeric columns. Select one outcome (Y) and one or more predictor columns. Use a period as the decimal mark. Up to 5,000 rows, 128 columns and 32 predictors are accepted.
The file is read locally by your browser; it is not sent to this website.
Rows with missing or non-numeric values are reported, not silently dropped.
YOUR RESULTS
Multiple linear fit
Fitted plane for two predictors
The fitted model is a plane. Observed rows are shown as points; rotate the view to inspect how they sit around it. Available when exactly two predictors are selected.
Fixed 3D view. Choose Interactive 3D to rotate and zoom.
Coefficients
Each slope describes the conditional association with Y when the other predictors are held constant.
| Term | Coefficient | Predictor mean | Predictor scale |
|---|
Predictions and residuals by observation
Residual = observed Y − predicted Y.
| Row | Observed Y | Predicted Y | Residual |
|---|
How to use this calculator
- Paste a table with numeric columns, or load the worked example.
- Select the outcome column (Y) and the predictor columns (X). The intercept is always included.
- Click Fit model to see coefficients, R², RMSE and residuals.
- Review any conditioning or scaling warnings before interpreting the coefficients.
- Download the full result summary as JSON for your own notes.
Formula and calculation method
The model is ŷ = β₀ + β₁x₁ + … + βₚxₚ. To avoid forming and inverting XᵀX, the calculator centres each predictor to its mean and scales it by its root-mean-square distance from the mean, builds the design matrix [1, z₁, …, zₚ], and solves the least-squares problem with a Householder QR transformation. Coefficients are then transformed back to the original predictor scale.
R² = 1 − SSE/SST and RMSE = √(SSE/n). The reported reciprocal condition ratio is an estimate of the scaled design matrix’s conditioning; a very small value suggests near-collinearity or predictors on extremely different scales.
Assumptions and limitations
- At least p + 1 complete observations are needed for p predictors plus an intercept.
- Predictor columns must vary; constant predictors are rejected with an explicit message.
- R² measures fit on these input observations. It does not test significance, causation, or performance on new data.
- Coefficients are conditional associations given the other predictors in the model. Adding, removing or rescaling predictors can change every coefficient.
- The calculator does not check regression assumptions such as independence, linearity, or homoscedasticity.
- The current input limit is 5,000 observations, 128 columns and 32 predictors; files are limited to 5 MB.
Related calculators
Linear regression · Polynomial regression · Pearson correlation