title: Simple and multiple linear regression: sample size considerations.
abstract: The suggested "two subjects per variable" (2SPV) rule of thumb in the Austin and Steyerberg article is a chance to bring out some long-established and quite intuitive sample size considerations for both simple and multiple linear regression.
  
  
  
  This article distinguishes two of the major uses of regression models that imply very different sample size considerations, neither served well by the 2SPV rule. The first is etiological research, which contrasts mean Y levels at differing "exposure" (X) values and thus tends to focus on a single regression coefficient, possibly adjusted for confounders. The second research genre guides clinical practice. It addresses Y levels for individuals with different covariate patterns or "profiles." It focuses on the profile-specific (mean) Y levels themselves, estimating them via linear compounds of regression coefficients and covariates.
  
  
  
  By drawing on long-established closed-form variance formulae that lie beneath the standard errors in multiple regression, and by rearranging them for heuristic purposes, one arrives at quite intuitive sample size considerations for both research genres.
authors.affiliation: Department of Epidemiology, Biostatistics and Occupational Health, McGill University, 1020 Pine Avenue West, Montreal, Quebec H3A 1A2, Canada. Electronic address: james.hanley@mcgill.ca.
authors.forename: James A
authors.initials: JA
authors.lastname: Hanley
mesh_terms: D015340:Epidemiologic Research Design; D006801:Humans; D016014:Linear Models; D015999:Multivariate Analysis; D018401:Sample Size
keywords: Confounding; Degrees of freedom; Power; Precision; Prediction