Multiple Regression F-Test Calculator Formula
Understand the math behind the multiple regression f-test calculator. Each variable explained with a worked example.
Formulas Used
F-Statistic
f_stat = (r_squared / p) / ((1 - r_squared) / (n - p - 1))Numerator df
df1 = pDenominator df
df2 = n - p - 1Variables
| Variable | Description | Default |
|---|---|---|
r_squared | R² | 0.75 |
n | Sample Size (n) | 50 |
p | Number of Predictors (p) | 4 |
How It Works
F-Test for Overall Regression Significance
The F-test evaluates whether at least one predictor in the regression model is significantly related to the response variable.
Formula
F = (R²/p) / ((1-R²)/(n-p-1))
with df1 = p and df2 = n-p-1. If F exceeds the critical value (e.g., ~2.58 for p=4, df2=45, alpha=0.05), the model has significant predictive power.
Worked Example
A model with R² = 0.75, n = 50, p = 4 predictors.
- 01F = (0.75/4) / ((0.25)/(50-4-1))
- 02F = 0.1875 / (0.25/45)
- 03F = 0.1875 / 0.005556 = 33.75
- 04df1 = 4, df2 = 45. Highly significant.
Frequently Asked Questions
What does a significant F-test tell me?
It tells you that at least one predictor has a non-zero coefficient. It does not tell you which predictors are important. Use individual t-tests to assess each predictor separately.
Can the F-test be significant but no individual t-test is?
Yes. This happens with multicollinearity, where predictors are correlated with each other. The predictors collectively explain variance, but their individual contributions overlap and cannot be separated.
What if F is not significant?
The model has no predictive power beyond using the mean of y. None of the predictors are useful. Consider different predictors, transformations, or that there simply is no linear relationship.
Ready to run the numbers?
Open Multiple Regression F-Test Calculator