4.5 Conditional Conditional Means (not a typo) AKA using controls

If we really want to know if ice cream-eating affects shorts-wearing, we would want to know how much of a relationship is there between ice cream and shorts that isn’t explained by temperature? So we would get the mean of ice cream conditional on temperature, and then take the residual, getting only the variation in ice cream that has nothing to do with temperature. Then we would take the mean of shorts-wearing conditional on temperature, and take the residual, getting only the variation in shorts-wearing that has nothing to do with temperature. Finally, we get the mean of the shorts-wearing residual conditional on the ice cream residual. If the shorts mean doesn’t change much conditional on different values of ice cream eating, then the entire relationship was just explained by heat! If there’s still a strong relationship there, maybe we do have something.