Formula Used
The calculator uses Cohen f squared for multiple regression planning.
f² = R² / (1 - R²)
For a block test, use partial R squared in the same formula.
df1 = tested predictors
df2 = N - total predictors - 1
lambda = f² × N
The required sample size is the smallest N where noncentral F power reaches the target power.
Power = 1 - Fnoncentral(Fcritical; df1, df2, lambda)
Attrition adjustment is calculated as complete N divided by one minus attrition rate.
How To Use This Calculator
Choose the analysis type first. Use overall model when all predictors are tested together. Use block test when new variables are added after controls. Use single predictor when one coefficient is central.
Enter the total number of predictors in the final model. Enter tested predictors for block or single tests. Choose R squared, partial R squared, or f squared. Add alpha, target power, attrition, and maximum search N. Press calculate. Review the result above the form.
Why Regression Sample Size Matters
Multiple variable regression can look precise with too few cases. That is risky. A small study may miss a true effect. It can also give unstable coefficients. Sample size planning gives the model enough information. It links design choices to power before data collection starts.
What This Calculator Estimates
This calculator estimates the minimum number of observations for a regression model. It can test the whole model. It can also test a block of predictors. You may enter total predictors, tested predictors, alpha, desired power, and an expected effect size. The tool converts R squared or partial R squared into Cohen f squared. It then searches for the smallest sample size that reaches the target power.
Choosing Inputs Carefully
The most sensitive input is the expected effect. Use pilot data when available. You can also use published studies from a similar field. Avoid choosing a large effect only to reduce the sample size. That makes the design weak. A smaller effect is safer when evidence is uncertain.
Understanding Predictors
Total predictors are all variables inside the final model. These include controls, dummy variables, interaction terms, and main predictors. Tested predictors are the variables being tested in the F test. For an overall model test, this number usually equals the total predictors. For a block test, it equals the number of variables added in that block.
Power And Alpha
Power is the chance of detecting the expected effect. Many studies use 0.80 or 0.90. Alpha is the false positive threshold. A common value is 0.05. Lower alpha values need larger samples. Higher power also needs larger samples.
Interpreting Results
The required sample size is the minimum complete observation count. If missing data is expected, use the adjusted target. The attrition value inflates the sample before recruitment. Also review observations per predictor. Very low values can produce fragile estimates, even when the power test is met.
Good Practice
Treat the output as a planning guide. Check assumptions later. Regression needs linearity, independent errors, stable variance, and sensible variable coding. Report the effect size, predictor count, alpha, power, and method in your study protocol. A sensitivity check with smaller effects strengthens the final justification too.
FAQs
What is multiple variable regression?
It is a regression model with more than one predictor. The predictors explain variation in one outcome. The method estimates each predictor while holding the others in the model constant.
What sample size does this tool estimate?
It estimates the minimum complete observations needed to reach the selected power for an F test in a multiple regression model.
What is Cohen f squared?
Cohen f squared is a regression effect size. It equals R squared divided by one minus R squared. For block tests, use partial R squared.
Should I use R squared or partial R squared?
Use R squared for the full model test. Use partial R squared when testing a block or one predictor after other variables are already included.
Why do more predictors require more cases?
Each predictor consumes model degrees of freedom. More predictors leave fewer residual degrees of freedom. That reduces precision and often raises the needed sample size.
What power value should I choose?
Many studies use 0.80. Higher values, such as 0.90, give stronger assurance. They also require more observations.
How is attrition handled?
The calculator inflates the complete sample size. It divides complete N by one minus the expected attrition rate. This gives a recruitment target.
Can this replace statistical review?
No. It supports planning. A statistician should review complex designs, clustered data, nonlinear models, missing data patterns, and unusual measurement structures.