Deeply digging the interaction effect in multiple linear regressions using a fractional-power interaction term.

We have provided a new R package, interactionFPIR, to estimate the values of M and N , and suggest using FPIR whenever the interaction term is likely to be significant. • Introduced fractional-power interaction regression (FPIR) as Y ~ β 0 + β 1 X 1 + β 2 X 2 + β 3 X 1 M X 2 N + ɛ to replace the current regression model Y ~ β 0 + β 1 X 1 + β 2 X 2 + β 3 X 1 X 2 + ɛ; • Clarified the rationale of FPIR, and compared it with regular regression model, polynomial regression, generalized additive model, and random forest using regression models for 4692 species; • Provided an R package, interactionFPIR, to calculate the values of M and N , and other model parameters.

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