Suppose you are interested in how exercising impacts a person's mental health. You have access to a dataset of 100,000 observations which includes the following variables: 1 mentalhealth: mental health score from [1-10] of person i determined by a rigorous psychiatric evaluation where 10 is the healthiest exercise: the number of hours per week that person i spends exercising work: the number of hours per week that person i spends working in their job (a) Write down a Core Model using Bivariate OLS that measures the effect of exercising on mental health. (b) Do you think exercise, and work, are correlated? If yes, why and in what direction? (c) Do you think mentalhealth, and work, are correlated? If yes, why and in what direction? (d) Suppose work, is indeed the omitted variable in this model. What is the sign of the omitted variable bias? Is the coefficient on exercise, from part (a) over-estimated or under- estimated? (e) Update your model in part (a) to include the effects of both exercising and work hours on mental health. In other words, rewrite the Core Model using Multivariate OLS.