When should a variable be included in the regression? Suppose you are doing a study to asses the effect of a state tax levied on large sodas, on the rates of diabetes across states. You hypothesize that higher taxes on large sodas will cause people to consume less sugar, thereby resulting in fewer instances of diabetes and propose the following model:
B0+B1 tax +B2 percmale +B3 perc18 +u diabetes
where
diabetes rate of diabetes in the population
tax level of taxes on large sodas
percmale percentage of the population that is male
u error term
Suppose males are genetically more predisposed to develop diabetes than females, and that the passage of tax laws is independent of the gender breakdown of the state.
True or False: Including a variable to control for the percentage of males in the population would reduce the error variance while not inducing mutlicollinearity
A. True
B. False