Multiple Regression Calculator
This calculator performs multiple linear regression with support for two or more predictor variables. It calculates regression coefficients, R-squared, adjusted R-squared, F-statistic for overall model significance, and individual t-tests for each predictor.
When to Use
Multiple regression is used when you want to predict a continuous dependent variable (Y) based on two or more independent predictor variables (X₁, X₂, etc.). It's an extension of simple linear regression that allows you to model more complex relationships.
Requirements
- Continuous dependent variable (outcome)
- Two or more continuous or categorical predictor variables
- Sample size should exceed number of predictors + 1
- Linear relationship between predictors and outcome
- Residuals should be normally distributed
Output Includes
- Regression coefficients for each predictor
- Intercept value
- R-squared (coefficient of determination)
- Adjusted R-squared
- Standard error of estimate
- F-statistic and p-value for overall model fit
- t-statistics and p-values for each coefficient
- Predicted values and residuals
Regression Equation
Y = b₀ + b₁X₁ + b₂X₂ + ... + bₙXₙ
Where Y is the predicted value, b₀ is the intercept, and b₁ through bₙ are the regression coefficients for each predictor variable.
Interpreting Results
- R-squared: Proportion of variance in Y explained by all predictors (0-1)
- Adjusted R-squared: R-squared adjusted for number of predictors
- F-statistic: Tests whether the model as a whole is significant
- t-statistics: Tests significance of individual predictors
- p-values: Probability of observing results if null hypothesis is true
