F-Test Using R-Squared Calculator

Test regression strength from R-squared with accuracy. Compare F statistic, p estimate, degrees, and decisions. Export organized results for careful model reviews today online.

Calculator

Example Data Table

Case Test Type Full R-squared Reduced R-squared Sample Size Full Predictors Reduced Predictors Alpha
Marketing model Overall 0.64 0.00 90 3 0 0.05
Housing model Nested 0.78 0.69 150 6 4 0.05
Health study Overall 0.31 0.00 60 5 0 0.01

Formula Used

For an overall model test, use reduced R-squared as 0 and reduced predictors as 0.

F = ((R² full - R² reduced) / (p full - p reduced)) / ((1 - R² full) / (n - p full - 1))

df1 = p full - p reduced

df2 = n - p full - 1

Adjusted R² = 1 - ((1 - R²) × (n - 1) / (n - p - 1))

Cohen f² = (R² full - R² reduced) / (1 - R² full)

The p-value is the right-tail probability from the F distribution.

How To Use This Calculator

  1. Select the overall model test or nested model comparison.
  2. Enter the full model R-squared from your regression output.
  3. Enter the reduced model R-squared for nested comparisons.
  4. Add sample size and predictor counts.
  5. Choose alpha and decimal places.
  6. Press Calculate to see the result above the form.
  7. Use CSV or PDF to save the report.

Why This Regression Test Matters

An F-test using R-squared checks whether a regression model explains meaningful variation. It compares explained variance with unexplained variance. The result helps you decide whether the fitted predictors work better than a model with no predictors. This calculator turns R-squared, sample size, and predictor count into a complete test summary.

When To Use It

Use this method for the overall significance test in multiple regression. It is useful after you build a model and know its R-squared value. The test asks one direct question. Do the predictors, taken together, explain enough variation to be statistically useful? It is not a test for one single coefficient. For individual terms, use t tests or partial F tests.

What The Inputs Mean

R-squared shows the proportion of outcome variance explained by the model. The predictor count is the number of independent variables, not including the intercept. Sample size is the number of observations used to fit the model. The alpha level sets your decision threshold. Common choices are 0.10, 0.05, and 0.01.

How To Read The Output

A larger F statistic usually gives stronger evidence against the null model. The p-value estimates the probability of seeing such a strong model fit, assuming the predictors have no real combined effect. If the p-value is less than alpha, the model is significant. If it is higher, the result is not significant.

Practical Notes

High R-squared alone is not enough. Check residual plots, outliers, collinearity, and model assumptions. Large samples can make small effects significant. Small samples can hide useful effects. Always compare statistical significance with practical value. Also confirm that the response variable and predictors match the research question.

Reporting The Result

A clear report includes F value, numerator degrees of freedom, denominator degrees of freedom, p-value, R-squared, adjusted R-squared, and the decision rule. You can export the table as CSV or PDF. Keep the exported file with your model notes, data source, and assumption checks for later review.

Limitations

This calculator assumes an ordinary least squares setting. It also assumes the reported R-squared came from the same sample size and predictor count. Rounded inputs can slightly change the final p-value. Use original model output when possible.

FAQs

What does this F-test check?

It checks whether the selected predictors explain enough outcome variation together. For an overall test, it compares your model against an intercept-only model.

Can I use adjusted R-squared as the input?

No. Use ordinary R-squared for the F formula. Adjusted R-squared is calculated separately for reporting and model review.

What is df1?

df1 is the number of tested predictors. For nested models, it is full predictors minus reduced predictors.

What is df2?

df2 is the residual degrees of freedom. It equals sample size minus full predictors minus one.

What is a nested model comparison?

It compares a full model with a smaller model. The smaller model must use a subset of the full model predictors.

Why must R-squared be less than one?

An R-squared of one makes the residual denominator zero. That creates an infinite F statistic and no stable p-value.

What alpha should I use?

Use the alpha chosen before analysis. Many studies use 0.05, but stricter work may use 0.01.

Does significance prove a good model?

No. Check assumptions, residuals, outliers, and usefulness. A significant result can still have weak practical value.

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