Spurious Correlation in Dimensional Analysis

Dimensional analysis often leads to the appearance of common or highly correlated variables in the independent and dependent parameters. A new quantitative measure of spurious correlation, ρ_s, is introduced. Its variation is studied from equations derived for jointly normally distributed variables and for nonparametric distributions with coefficients of variation η<1. For the general case of nonparametric distribution with η>1, ρ_s is studied by digital simulation and is found to be less than that predicted by the method of differentials developed for η<1. Guidelines for reducing ρ_s and its effect on predictive inferences are presented. It is recommended that the repeating variables should have smaller η than the variables of interest and should not be highly correlated with each other. Where the statistical distributions for the variables involved are unavailable, it is recommended that confidence intervals around the predictive relations be determined from the calculated standard error of prediction.