F Test Multiple Regression Calculator

Check whether predictors improve regression model significantly. Use R squared or sums squares for testing. Review decisions, exports, formulas, FAQs, and interactive charts easily.

Calculator

Choose an input mode, enter regression summary values, and submit to test overall model significance.

Input mode

Sample size (n)

Predictors (k)

Significance level (alpha)

Decimal places

R squared

Total SST

SSR

SSE

SST (optional)

Example Data Table

This example uses a model with 30 observations and 3 predictors.

n	k	Alpha	R squared	SST	SSR	SSE	F statistic	P value	Decision
30	3	0.0500	0.6200	100.0000	62.0000	38.0000	14.1404	1.1594e-5	Reject H0: the regression is significant overall.

Formula Used

The overall F test checks whether the regression model explains enough variation compared with unexplained error.

R squared: R² = SSR / SST

Mean square regression: MSR = SSR / k

Mean square error: MSE = SSE / (n - k - 1)

F statistic: F = MSR / MSE

Equivalent F form: F = (R² / k) / ((1 - R²) / (n - k - 1))

Adjusted R squared: 1 - ((1 - R²)(n - 1) / (n - k - 1))

Decision rule: Reject H0 when F is greater than the critical F, or when the p value is less than alpha.

How to Use This Calculator

Select whether you want to work from R squared or from sums of squares.
Enter the sample size, number of predictors, significance level, and preferred decimal places.
Provide either R squared with SST, or SSR and SSE with optional SST.
Click the calculate button to display the result block above the form.
Review the F statistic, p value, critical F, variance measures, and final significance decision.
Use the CSV and PDF buttons to download the computed output.

FAQs

1. What does the overall F test check?

It tests whether the regression model explains a meaningful share of variation. In practice, it checks whether at least one predictor has a nonzero slope in the full model.

2. When should I use R squared mode?

Use R squared mode when your regression output already reports R², sample size, and predictor count. Entering SST also lets the calculator recover SSR and SSE values for reporting.

3. When should I use sums of squares mode?

Use sums of squares mode when software gives you SSR and SSE directly. It is common in ANOVA tables, model comparison summaries, and regression diagnostics reports.

4. What are df1 and df2?

df1 is the numerator degrees of freedom and equals k. df2 is the denominator degrees of freedom and equals n minus k minus 1.

5. Why can R squared look high but significance stay weak?

A model can fit the sample reasonably well yet still lack strong evidence overall. Small sample sizes, many predictors, or unstable data patterns can reduce the F test strength.

6. What does the p value mean here?

It is the probability of observing an F statistic at least this large if the null hypothesis were true. Smaller values provide stronger evidence against the null.

7. Does this replace coefficient t tests?

No. The F test checks overall model significance. Individual t tests examine each predictor separately, so both views are useful in regression analysis.

8. What assumptions matter for this test?

Typical assumptions include linearity, independent errors, constant error variance, and approximately normal residuals. Serious violations can distort p values and weaken interpretation.