As we can see from Eq. (1), β3 is the coefficient of the interaction term. So the existence of an interaction means that there is a significant slope difference between the two levels of the genotype because β3 = δ11 − δ01, which is also the slope difference. Note that the intercept difference between the two lines is β1 and it does not affect the interaction and can be expressed using only the G variable, as β1 = δ10 − δ00. Therefore, the slope difference is determined only by slopes δ11 and δ01, not by the intercepts δ10 and δ00. Thus, in the case of a binary-coded genetic variant (e.g., two genotypic levels, 0 and 1), the cross-product term accurately captures the interaction. Typically, however, genotypes are not binary and recoding them as binary cannot be recommended because doing so discards valuable information.
