An F-statistic calculator is used to calculate the overall significance of a regression model. It helps researchers assess whether a set of independent variables has a significant relationship with the dependent variable in a regression analysis.
F-statistic Calculation Chart
| Source | Sum of Squares (SS) | Degrees of Freedom (df) | Mean Square (MS) | F-value |
|---|---|---|---|---|
| Regression | SSR = 1000 | dfR = 2 | MSR = 500 | 25 |
| Residual | SSE = 800 | dfE = 40 | MSE = 20 | |
| Total | SST = 1800 | dfT = 42 |
F-statistic Formula
The F-statistic formula is:
F = MSR / MSEWhere:
- MSR = Mean Square Regression = SSR / dfR
- MSE = Mean Square Error = SSE / dfE
- SSR = Sum of Squares Regression
- SSE = Sum of Squares Error
- dfR = Degrees of Freedom Regression
- dfE = Degrees of Freedom Error
Using our example: F = 500 / 20 = 25This F-value of 25 suggests that the regression model explains significantly more variance than would be expected by chance alone.
How do you calculate the F-statistic?
To calculate the F-statistic, follow these steps:
- Perform regression analysis: Fit your model to the data
- Calculate SSR: Sum of squared differences between predicted and mean y values
- Calculate SSE: Sum of squared differences between observed and predicted y values
- Determine degrees of freedom: dfR = number of predictors, dfE = n – k – 1 (where n is sample size and k is number of predictors)
- Calculate MSR and MSE: MSR = SSR / dfR, MSE = SSE / dfE
- Compute F-statistic: F = MSR / MSE
Suppose you have a multiple regression model with 2 predictors and 43 observations.
After fitting the model, you find SSR = 1000 and SSE = 800
dfR = 2, dfE = 43 – 2 – 1 = 40
MSR = 1000 / 2 = 500, MSE = 800 / 40 = 20
F = 500 / 20 = 25
This F-value of 25 would then be compared to the critical F-value from an F-distribution table to determine if the regression model is statistically significant.
Related Statistics Tools