Regression · MLR-R2I

Sample Size for Multiple Linear Regression: R² Increase

Plan a nested-model test of whether a prespecified predictor block increases explained outcome variance.

1. Planning

How would you like to specify the incremental effect?

The reduced model excludes the tested block; the full model contains both the reduced-model columns and the tested block.

2. Information obtained from previous studies or pilot data

Use a conservative population effect from comparable evidence. Observed sample R² values can be optimistic, especially in small or data-driven models.

Anticipated full-model R²

Anticipated reduced-model R²

3. Inputs decided by the researcher for the new study

Number of tested predictor columns

Count the columns added to the reduced model. A categorical predictor can require several dummy-variable columns.

Total predictor columns in the full model

Exclude the intercept. Count dummy variables, interactions, spline bases, and polynomial terms as fitted columns.

Power (%)

Type I error, alpha (%)

Anticipated dropout/non-response (%)

4. Results

Enter the nested-model effect and design assumptions, then select Calculate sample size.

Formula, assumptions, limitations, and methodological note

Example clinical scenario

A researcher is modelling HbA1c using age, sex, diabetes duration, and body mass index, then asks whether adding diet-quality and physical-activity scores provides meaningful additional explanatory value. The calculator powers the increase in R² attributable to that prespecified two-predictor block.

Formula and methodological note

The test compares nested reduced and full fixed-predictor models. Cohen's f² = (R²full − R²reduced)/(1 − R²full). With N analysable participants, q tested columns, and m total full-model predictor columns, df₁ = q, df₂ = N − m − 1, and λ = Nf². The smallest whole-number N reaching the target noncentral-F power is reported.

Assumptions include independent observations, a continuous outcome, an intercept, a prespecified full-rank nested model, correct functional form, homoscedastic normally distributed errors, and a credible population effect. The tested block must be identical to the block intended for the primary hypothesis.

This calculator is not for an omnibus full-model test, one particular coefficient, prediction-model development, automated model selection, clustered or repeated data, or generalized regression outcomes. It supports research planning and does not replace statistical consultation.

Method references

Cohen J. Statistical Power Analysis for the Behavioral Sciences. 2nd ed. Lawrence Erlbaum Associates; 1988. Chapter 9.
Faul F, Erdfelder E, Buchner A, Lang AG. Statistical power analyses using G*Power 3.1: tests for correlation and regression analyses. Behavior Research Methods. 2009;41:1149–1160.
Faul F, Erdfelder E, Lang AG, Buchner A. G*Power 3: a flexible statistical power analysis program. Behavior Research Methods. 2007;39:175–191.

Suggested citation

Yaacob, Najib Majdi. “Sample Size for Multiple Linear Regression: R² Increase (MLR-R2I).” Web calculator. NajibMY, 2026. Accessed July 31, 2026. https://najibmy.netlify.app/tools/sample-size/regression/multiple-linear-regression-r-squared-increase/.