Using dimensional analysis in building statistical response models

The method of dimensional analysis has been used for almost a century with experimental methods to obtain, among other things, prediction equations in the physical sciences and engineering. Only recently has the method been considered in the statistical sense.

A thorough literature research is presented, including history, method and theory, problems, and disadvantages of dimensional analysis.

The dimensional analysis preliminary model is transformed into a multiple linear regression model and is compared to a quadratic regression model with respect to prediction of a single variable in some practical examples. Whereas dimensions are the main consideration in the dimensional analysis model, they are ignored in the quadratic regression model. Two sets of experimental data were used, each set on both models, and the respective residual sum of squares and multiple correlation coefficients compared.

The results were similar in both cases. The correlation coefficients of the quadratic model were higher than those of the dimensional analysis model and the residual sum of squares were lower for the quadratic than for the dimensional analysis model.