Regression · MLR-OM

Sample Size for Multiple Linear Regression: Omnibus Model Test

Plan a study powered to test whether a prespecified multiple linear regression model explains outcome variance.

1. Planning

How would you like to specify the model effect?

Both options describe the full model relative to an intercept-only model.

2. Information obtained from previous studies or pilot data

Use an effect estimate from a population and prespecified model that are reasonably comparable with the new study. The value should represent the expected explanatory contribution of the full model, not its observed sample R² without considering optimism.

Anticipated population R² for the full model

Use a defensible population value from comparable evidence; enter a proportion greater than 0 and less than 1.

3. Inputs decided by the researcher for the new study

These inputs define the planned model and operating requirements for the proposed study; they should be chosen for the new study rather than copied automatically from an earlier analysis.

Total number of predictor columns

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

Power (%)

Type I error, alpha (%)

Anticipated dropout/non-response (%)

4. Results

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

Formula, assumptions, limitations, and methodological note

Example clinical scenario

A researcher wants to determine whether age, body mass index, duration of diabetes, systolic blood pressure, and physical activity collectively explain variation in HbA1c among adults with type 2 diabetes. The omnibus test evaluates whether the full predictor set explains any outcome variance compared with an intercept-only model.

Formula and methodological note

The omnibus fixed-model test evaluates H₀: R² = 0. Cohen's f² is R²/(1 − R²). For N analysable participants and m predictor columns, df₁ = m, df₂ = N − m − 1, and noncentrality λ = Nf². The calculator reports the smallest whole-number N reaching the target power under the noncentral-F distribution.

The method assumes independent observations, a continuous outcome, a prespecified full-rank linear model with an intercept, correct functional form, homoscedastic normally distributed errors, and credible population R² assumptions.

Do not use this calculator to power one particular coefficient, an incremental predictor block, model selection, prediction-model development, clustered or repeated data, or generalized regression outcomes.

Method references

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.
Cohen J. Statistical Power Analysis for the Behavioral Sciences. 2nd ed. Lawrence Erlbaum Associates; 1988.

Suggested citation

Yaacob, Najib Majdi. “Sample Size for Multiple Linear Regression: Omnibus Model Test (MLR-OM).” Web calculator. NajibMY, 2026. Accessed July 31, 2026. https://najibmy.netlify.app/tools/sample-size/regression/multiple-linear-regression-omnibus/.