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Regression · MLR-1B

Sample Size for Multiple Linear Regression: One Adjusted Coefficient

Plan an adjusted analysis of one prespecified predictor in a multiple linear regression model with a continuous outcome.

1. Planning

Regression coefficient is the recommended default for clinically interpretable planning. All four options are converted to Cohen's f².

2. Information obtained from previous studies or pilot data

Use estimates from a population and model that are reasonably comparable with the new study. These values describe variability and relationships expected in the target population.

Help calculate predictor SD for a binary predictor

Use this helper only when the predictor of interest is binary and coded 0/1. Enter the anticipated population proportion coded X=1. The regression coefficient is then the adjusted mean outcome difference between X=1 and X=0.

Enter a proportion greater than 0 and less than 1. Continue to specify the predictor R² with the other predictors separately.

Help estimate residual SD from reported study information

Enter a proportion from 0 to less than 1.

Uses SD(residual) = SD(outcome) × √(1 − R²). Use values from a comparable population, outcome scale, and full-model specification. The anticipated R² should represent the population model effect rather than an optimistic unadjusted sample R².

Enter 0 only when assuming no correlation with the other predictors. VIF = 1/(1 − R²).

3. Inputs decided by the researcher for the new study

These inputs define the effect worth detecting and the design requirements for the proposed study; they should not simply reproduce every choice made in an earlier study.

Specify the smallest adjusted change in the outcome per one-unit increase in the predictor that the new study should be able to detect.

Usually 0 when testing whether the adjusted association differs from no association.

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

4. Results

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

Formula, assumptions, limitations, and methodological note

Example clinical scenario

A researcher wants to test whether daily sodium intake is associated with systolic blood pressure after adjusting for age, sex, body mass index, antihypertensive treatment, and physical activity. The target is the adjusted regression coefficient for sodium intake rather than the significance of the full model.

Formula and methodological note

All input modes are converted to Cohen's local effect size f². For total analysable sample size N and m predictor columns, the test uses df = N − m − 1 and noncentrality magnitude δ = √(Nf²). The smallest integer N reaching the requested power is reported.

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 effect assumptions.

Do not use this calculator for omnibus model significance, joint testing of multi-column factors, variable selection, prediction-model development, clustered or repeated data, or non-linear outcome models.

Method references

  1. 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.
  2. 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: One Adjusted Coefficient (MLR-1B).” Web calculator. NajibMY, 2026. Accessed July 29, 2026. https://najibmy.netlify.app/tools/sample-size/regression/multiple-linear-regression-one-coefficient/.