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.
r_squared = 0.75n = 50p = 4
- 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.
Ready to run the numbers?
Open Multiple Regression F-Test Calculator