Determining Adequate Sample Sizes for Multiple Linear Regression used for Explanatory purposes - Rebernjak, Blaž (Array, 2009)
There are numerous methods for determining minimum sample sizes when using multiple linear regression, from various rules of thumb to elaborate power analysis. Different methods, however, often yield surprisingly discrepant estimations. Monte Carlo simulation was used to examine models with varying number of predictor variables (2, 3, 4, 5, 7, 9, 11, 15), average intercorrelation between predictor variables (0, 0.1, 0.3, 0.5) and standardized regression coefficient of the specific predictor variable of interest (0.1, 0.3, 0.5), resulting in 96 different situations. Samples of varying sizes (from 25 to 5000) were drawn from multivariate normal distributions with 96 specified population correlation matrices. For each situation 5000 replications were made, resulting in a total of 7680000 analyses preformed. Based on the results for each situation, interpolation was used to approximate the sample size needed for the power to reach 0.80. Results show that all of the hypothesized variables influence minimum sample size with size of the regression coefficient being the strongest determinant. Limits of the present approach are discussed, and comparisons with proposed methods for determining adequate sample size are made for three hypothetical situations.