Enter the effect size, alpha level, power, and number of predictors into the calculator to determine the required sample size for a regression analysis. This calculator helps in planning a study by estimating the minimum number of observations needed.

Regression Sample Size Formula

The following formula is used to calculate the sample size for a regression analysis:

N = ((Z<sub>α/2</sub>² + Z<sub>β</sub>²) / f²) + k + 1

Variables:

  • N is the sample size
  • Zα/2 is the critical value of the normal distribution at α/2 (for a two-tailed test)
  • Zβ is the critical value of the normal distribution at β (power of the test)
  • f² is the effect size
  • k is the number of predictors

To calculate the sample size for regression, use the formula above where Zα/2 and Zβ are derived from the standard normal distribution for the desired alpha level and power, f² is the effect size, and k is the number of predictors in the regression model.

What is Regression Sample Size?

Regression sample size refers to the number of observations required to detect an effect of a given size with a certain degree of confidence and power in a regression analysis. It is an important aspect of study design, ensuring that the study has sufficient statistical power to detect meaningful relationships between variables.

How to Calculate Regression Sample Size?

The following steps outline how to calculate the Regression Sample Size:

  1. First, determine the desired effect size (f²) for the study.
  2. Next, determine the alpha level (α), typically 0.05 for a 95% confidence level.
  3. Then, determine the desired power (1 – β), commonly set at 0.80 or higher.
  4. Determine the number of predictors (k) in the regression model.
  5. Use the formula above to calculate the sample size (N).
  6. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem:

Use the following variables as an example problem to test your knowledge.

Effect size (f²) = 0.15

Alpha level (α) = 0.05

Power (1 – β) = 0.80

Number of predictors (k) = 3