Problem 1 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 = #M + {IX + 5-\". which implies that one unit change in}: will causes; unit change in E{M}. Meanwhile, a second regression model describes how Y is influenced by M. Y=py+M+a Assume 5M and e are independent errors. In other words, X does not have a direct influence on Y but can influence 1" through the intermediate variable M. which is usuallyr called a mediator. For example, in a study on X = socioeconornie status and Y = reading ability in children. you may hypothesize that M = patental 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=py+mu+aX+emi+e=yy+nM+er+weM+e). So, the total effect ofX on Y is of}. Now suppose a study collects data on the three variables X , M and Y on n randomly chosen subjects. Without thinking about the mediator mechanism. one may just fit a muttiple 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 may try to think what the expectation of this estimator is.)