Spreadsheet paste
Paste Y in the first column and X predictors in the remaining columns from Excel, Google Sheets, CSV, or text.
Free statistics calculator
Multiple Regression Calculator
Paste raw data columns with Y first and X predictors after it. Calculate multiple linear regression coefficients, regression ANOVA, R-squared, adjusted R-squared, p-values, confidence intervals, prediction intervals, and residuals in an Excel/PHStat-style layout.
- Spreadsheet paste Paste Y in the first column and X predictors in the remaining columns from Excel, Google Sheets, CSV, or text.
- PHStat-style output Review regression ANOVA, coefficients, standard errors, t statistics, p-values, and confidence intervals.
- Model fit Calculate R-squared, adjusted R-squared, residual standard error, F statistic, and significance F.
- Prediction intervals Enter new X values and calculate y-hat, mean-response confidence interval, and individual prediction interval.
Calculate a Multiple Regression Model
Paste a table where the first column is the response variable Y and each remaining column is an X predictor. Use the first-row checkbox when the first line contains variable names.
Excel tabs work best. Commas, semicolons, or spaces also work. Column 1 is Y; columns 2 and onward are X predictors.
Results
Multiple linear regression
Regression Equation
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Observations
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Predictors
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R-Squared
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Adjusted R-Squared
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Residual Std. Error
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Overall F
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Significance F
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Prediction
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Confidence Interval for Mean Response
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Prediction Interval for Individual Response
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Multiple regression assumes a linear relationship, independent errors, no severe multicollinearity, and roughly constant residual variance. Use software and assignment instructions for final reporting.
Regression ANOVA Table
| Source | SS | df | MS | F | Significance F |
|---|---|---|---|---|---|
| Calculate a model to view regression ANOVA output. | |||||
Coefficient Table
| Term | Coefficient | Standard Error | t Stat | P-value | Lower | Upper |
|---|---|---|---|---|---|---|
| Calculate a model to view coefficient output. | ||||||
Residuals
| Row | Observed Y | Predicted Y | Residual |
|---|---|---|---|
| Calculate a model to view residuals. | |||
What This Calculator Includes
This calculator fits an ordinary least squares multiple regression model with an intercept. It is designed for coursework checks, Excel/PHStat comparisons, and interpretation practice.
PHStat-style output
Review regression ANOVA, coefficients, standard errors, t statistics, p-values, and confidence intervals.
Model fit
Calculate R-squared, adjusted R-squared, residual standard error, F statistic, and significance F.
Prediction intervals
Enter new X values and calculate y-hat, mean-response confidence interval, and individual prediction interval.
Multiple Regression Output Guide
| Output | Meaning |
|---|---|
| Coefficient | Estimated change in Y for a one-unit increase in that X predictor, holding other predictors constant. |
| Regression ANOVA | Tests whether the model explains a significant amount of variation in Y compared with residual variation. |
| Adjusted R-squared | R-squared adjusted for sample size and predictor count, useful when comparing models. |
| Prediction interval | Range for one new individual Y value at the entered X values; usually wider than the mean-response confidence interval. |
Calculator Methodology and Validation
The calculator builds the design matrix with an intercept and computes ordinary least squares using the normal equation beta = (X'X)^-1 X'Y. It then calculates residual sums of squares, regression ANOVA, coefficient standard errors, t tests, confidence intervals, and optional prediction intervals from the inverse X'X matrix.
The default example is included in the local regression test suite so coefficient, ANOVA, p-value, confidence interval, and prediction interval calculations can be checked after edits.
Common Multiple Regression Mistakes
- Putting predictor columns before the response column when this calculator expects Y first.
- Using duplicate or perfectly related predictor columns, which makes the regression matrix singular.
- Interpreting a coefficient without holding the other predictors constant.
- Making predictions outside the range of the original predictor data without noting extrapolation risk.
Multiple Regression Calculator FAQs
How should I paste data into the multiple regression calculator?
Put the response variable Y in the first column and each predictor X variable in the columns to the right. Tab-separated data copied from Excel or Google Sheets keeps the columns aligned.
What is multiple regression?
Multiple regression estimates a linear equation that predicts one response variable from two or more predictor variables.
What does a multiple regression coefficient mean?
A coefficient estimates the expected change in Y for a one-unit increase in that predictor, holding the other predictors in the model constant.
What is adjusted R-squared?
Adjusted R-squared modifies R-squared for the number of predictors and sample size, making it more useful when comparing models with different predictor counts.
Why did the calculator say the regression matrix is singular?
A singular matrix usually means one predictor is a duplicate, a constant, or an exact linear combination of other predictors. Remove or revise the redundant column.
Is this different from the linear regression calculator?
Yes. The linear regression calculator uses one X predictor. This multiple regression calculator supports two or more X predictors.
Need Help Interpreting Multiple Regression?
Regression assignments often require coefficient interpretation, assumption checks, ANOVA tables, confidence intervals, prediction intervals, and a written conclusion in context.
Related Statistics Help
Use Calculators Responsibly
Use this calculator to check computations, understand regression output, and prepare tutoring questions. For graded work, follow your course rules and show the required method.