The number of subjects per variable required in linear regression analyses

Abstract

ObjectivesTo determine the number of independent variables that can be included in a linear regression model. Study Design and SettingWe used a series of Monte Carlo simulations to examine the impact of the number of subjects per variable (SPV) on the accuracy of estimated regression coefficients and standard errors, on the empirical coverage of estimated confidence intervals, and on the accuracy of the estimated R2 of the fitted model. ResultsA minimum of approximately two SPV tended to result in estimation of regression coefficients with relative bias of less than 10%. Furthermore, with this minimum number of SPV, the standard errors of the regression coefficients were accurately estimated and estimated confidence intervals had approximately the advertised coverage rates. A much higher number of SPV were necessary to minimize bias in estimating the model R2, although adjusted R2 estimates behaved well. The bias in estimating the model R2 statistic was inversely proportional to the magnitude of the proportion of variation explained by the population regression model. ConclusionLinear regression models require only two SPV for adequate estimation of regression coefficients, standard errors, and confidence intervals.