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Dimensional analysis (DA) is a widely used methodology in engineering and physical sciences. The importance of DA in statistics has been recognized only recently. One of fundamental rules in DA is to maintain dimensional homogeneity in model building. The Buckingham pi theorem is the key theorem in DA which provides a method of computing the dimensionless variables. However, the choice of the basis quantities is not unique.
This paper proposes a guideline based on data to obtain an optimal choice of basis quantities. From statistics point of view, this optimal choice can guarantee less confounding pattern among dimensionless variables. One of data-driven criteria is based on the coefficient of variation. It is shown that considering a variable with smaller coefficient of variation as a basis quantity results smaller correlations among dimensionless variables. Theoretical result is provided and a real-life case study is used to illustrate the benefit of using the optimal choice.
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