Testing and accounting for interactions between variables in linear models

An interaction between variables occurs when the effect of one predictor variable on the response variable depends on the level of another predictor variable. In other words, the effect of one variable is not constant across different levels of the other variable. The interaction can occur between different drug regimes in medical trials or generally multiple experimental conditions being changed.

Linear models can model interactions by including interaction terms in the model formula. An interaction term is the product of two or more predictor variables, where each predictor variable is centered to have a mean of zero.

Suppose we have a linear regression model with two predictor variables, x1 and x2, and we want to examine their interaction. The interaction term can be included in the model as follows:

y = β 0 + β 1 x 1 + β 2 x 2 + β 3(x 1...