I'm fitting a linear model where the response variable is a measure of physical performance-- running speed for example-- and the predictor variables are sex and drug treatment, with an interaction term.
$$Y = \beta_{0}+\beta_1X_{sex}+\beta_1X_{drug}+\beta_3X_{sex}X_{drug}$$
We suspect that body weight influences running speed, so we need to include body weight as a covariate to make sure the differences we're seeing aren't adequately explained by body weight alone.
However, body weight is affected by the drug, and of course it also correlates with sex. That makes me think that body weight should be included only as an additive term and its interactions with other terms should not be considered (because they will be spuriously significant):
$$Y = \beta_{0}+\beta_1X_{sex}+\beta_1X_{drug}+\beta_3X_{sex}X_{drug}+\beta_4X_{bw}$$
Am I correct to not include body weight interactions, and are my reasons for doing so correct? Thanks.