StatReason

Regression Model Comparison Calculator

Test whether adding predictors to a regression model genuinely improves fit, beyond what the smaller model without them already explains, using a formal partial F-test rather than just comparing R-squared values by eye.

What this answers

This calculator answers "does adding these extra predictors improve the model meaningfully, or could the improvement in fit plausibly be explained by chance alone?" a sharper question than comparing two R-squared values informally, since R-squared always increases (or stays flat) whenever more predictors are added, useful or not.

How it is calculated

Both models are fit on the exact same rows. The partial F statistic compares how much the residual sum of squares drops when moving from the smaller (reduced) model to the larger (full) model, relative to the number of additional parameters used, against the full model's own remaining residual variability. This is only a valid test when the reduced model's predictors are a genuine subset of the full model's predictors, the "nested" requirement in the name.

Worked example

For a reduced model with one predictor and a full model adding a second, genuinely useful predictor, R-squared rises from the reduced to the full model, and the partial F-test confirms that rise is large relative to what residual noise alone would produce, evidence the added predictor earns its place in the model.

Assumption audit

Calculated from your data: both models' R-squared values, the difference between them, and the partial F statistic and p-value testing that difference.
Evidence to review: whether the full model's coefficient table (from the Multiple Linear Regression Calculator) shows the newly added predictors as individually significant, consistent with what this omnibus comparison found.
You must verify: that the reduced model's predictor set is genuinely a subset of the full model's, fit on the exact same complete-case rows; comparing non-nested models, or models fit on different rows due to different missing-data patterns, invalidates this test.

What this result does not mean

A significant partial F-test means the added predictors improve fit beyond chance, not that each individual added predictor is itself significant, and not that the added predictors have a causal effect on the outcome.

Limitations

This calculator does not verify that your reduced-model predictors are truly a subset of your full-model predictors; entering genuinely non-nested models will produce a numeric result that does not mean what a nested-model comparison is supposed to mean.