A researcher conducted a study in which children with problems learning mathematics were offered the opportunity to purchase time with special tutors. The number of weeks that children met with their tutors varied from 1 to 20. He found that the number of weeks of tutoring predicted these children’s mathematics performance and recommended that parents of such children send them for tutoring. 

a. List one problem with that interpretation. Explain your answer. 

b. If you were to develop a study that uses a multiple regression equation instead of a simple linear regression equation, what additional variables might be good independent variables? List at least one variable that can be manipulated (e.g., weeks of tutoring) and at least one variable that cannot be manipulated (e.g., parents’ years of education).