Dependent variable functionally related to independent variable My question pertains to the case where a dependent variable is functionally related to an independent variable in a multiple linear regression. Here is a fictional scenario suppose that $Sales_A,Sales_B,Sales_C,Sales_D,Sales_E$ represent the sales  resulting from products A,B,C,D,E
and Total Sales = $Sales_A +Sales_B +Sales_C + Sales_D + Sales_E$.   Consider the following model:
$$Sales_D = Sales_I + Total Sales + \text{other control variables}$$
Assuming the assumptions for linear regression are met and there is no multicollinearity between the independent variables. If the goal is to determine how increases in $Sales_I$  effect changes in $Sales_D$ would the above model work or does the fact that the dependent variable is "part" of one of the independent variables cause problems?

I don't see an issue as formulated it looks like the model would look at how additional sales from product I are cannibalizing or complementing sales from product D assuming observations are stores  or something similar. Others more well informed in statistics may be able to pinpoint where the model is incorrect.
