Consider a mechanism that involves three variables. X . M and F. It is Known that there is a causal relationship between X and Mdescribed by the simple linear regression M = PM + [xx + 9M . which implies that one unit change in}; will causea unit change in Elrf}. Meanwhile, a second regression model describes how Y is inuenced by M. Y=py+M+a Assume 5M and a are independent errors. In other words, X does not have a direct inuence on Y but can influence 1' through the intermediate variable M. which is usually called a mediator. For example, in a study on X = socioeconomic status and Y = leading ability in children. you may hypothesize that M = parental education level is a mediator. This means that socioeconomic status affects reading ability mainly through its influence on parental education levels. By combining the two models together. we have Y=Fr+LUM+GX+M)+ =Fr+m+x+ta +5)- So, the total effect oiX on Y is [113. Now suppose a study collects data on the three variables X , M and 1' on n randomly.r chosen subjects. Without thinking about the mediator mechanism. one may iust fit a multiple linear regression by regressing Y on X and M. Then should the slope coefficient estimate for X be interpreted as the effect of X on 1'? Explain. (Hint: You mayr try to think what the expectation of this estimator is.)