The number of subjects per variable required in linear regression analyses

Area of Science:

• Statistics
• Statistical Modeling
• Regression Analysis

Background:

• Linear regression is a widely used statistical method.
• Determining the optimal number of independent variables relative to sample size is crucial for model reliability.
• Previous guidelines for sample size in regression have varied.

Purpose of the Study:

• To ascertain the minimum number of subjects per variable (SPV) required for robust linear regression models.
• To evaluate the impact of SPV on the accuracy of regression coefficients, standard errors, and confidence intervals.
• To assess SPV's influence on the estimation of R-squared.

Main Methods:

• Monte Carlo simulations were employed to systematically vary the number of SPV.
• The simulations assessed the bias in regression coefficients and R-squared.
• Accuracy of standard errors and empirical coverage of confidence intervals were evaluated.

Main Results:

• Approximately two SPV were sufficient for accurate estimation of regression coefficients (bias < 10%), standard errors, and confidence intervals.
• Adjusted R-squared estimates demonstrated good performance across simulations.
• Minimizing bias in the overall model R-squared required a higher SPV, with bias inversely related to explained variance.

Conclusions:

• Linear regression models achieve adequate estimation of key parameters with as few as two SPV.
• The findings provide a practical guideline for sample size determination in regression analysis.
• Adjusted R-squared is a more reliable measure than R-squared for model fit assessment with limited SPV.