Calculator Inputs
Example Data Table
| Scenario | n | k | R² | SSR | SSE | F | Decision at 0.05 |
|---|---|---|---|---|---|---|---|
| Marketing mix model | 25 | 3 | 0.72 | 360.00 | 140.00 | 18.000000 | Significant |
| Demand forecast model | 40 | 4 | 0.55 | 275.00 | 225.00 | 10.694444 | Significant |
| Pricing sensitivity model | 18 | 2 | 0.21 | 84.00 | 316.00 | 1.993671 | Not significant |
Formula Used
The overall regression F test checks whether all slope coefficients are zero at once. It compares explained variation against unexplained variation.
F = MSR / MSE
MSR = SSR / k
MSE = SSE / (n - k - 1)
F = (R² / k) / ((1 - R²) / (n - k - 1))
df1 = k
df2 = n - k - 1
p value = P(F[df1, df2] ≥ observed F)
Here, n is sample size, k is the number of predictors, SSR is regression sum of squares, and SSE is error sum of squares.
How to Use This Calculator
- Select an input mode based on the values you already know.
- Enter the sample size, predictor count, and significance level.
- Provide either R squared, SSR and SSE, or MSR and MSE.
- Press Calculate F Test to place the results above the form.
- Review the F statistic, p value, critical threshold, and interpretation.
- Use the chart to compare the observed F value with the rejection region.
- Export the output with the CSV or PDF buttons if needed.
Important Notes
- This test evaluates the overall model, not each predictor separately.
- The usual assumptions include linearity, independent errors, constant variance, and approximately normal residuals.
- Very high R squared values can produce large F statistics when sample size is adequate.
- For nested models, use a partial F test rather than the overall regression F test.
FAQs
1. What does the regression F test measure?
It tests whether the regression model explains a meaningful share of variation compared with a model that contains only the intercept.
2. What is the null hypothesis?
The null hypothesis says all slope coefficients are zero, so the predictors collectively add no linear explanatory power.
3. When should I use R squared mode?
Use R squared mode when you know sample size, predictor count, and model fit, but do not have the ANOVA table available.
4. What is the difference between overall and partial F tests?
The overall F test checks the entire regression model. A partial F test compares nested models or a selected group of predictors.
5. Why are df1 and df2 important?
They define the reference F distribution. df1 reflects the predictor count, and df2 reflects remaining error degrees of freedom.
6. Can a model have high R squared but weak significance?
Yes. Small samples or too many predictors can reduce error degrees of freedom and weaken statistical evidence even when R squared looks strong.
7. Does this calculator test individual coefficients?
No. Individual coefficient significance usually requires separate t tests and standard errors for each predictor coefficient.
8. What does the critical F value show?
It is the cutoff from the F distribution at your alpha level. Values above it fall in the rejection region.