I know that y depends linearly on x but I am not sure whethe

I know that y depends linearly on x, but I am not sure whether or not it also depends on another variable z. A friend suggests that I should regress y on x first, calculate the residuals, and then see whether they are correlated with z. What advice would you offer your friend?

This is the entire question. There is no additional information. Found in a chapter for multiple regression analysis.

Solution

To calculate a multiple regression analysis, first regress y on x, calculate the residuals and the test the correlation between Y and Z. If t is correlated then y also dependes linearly on z.