Read carefully the new york times article titled "revisiting the value of elite colleges", describing an application of multiple regression and omitted variable bias. тake the following three variables: a. a dummy variable equal to one if the individual attended an elite universityb. an individual’s earningsc. ambition/self-confidencebased on the text, match the above variables to: a. dependent variable: b. main explanatory variable of interest: c. missing variable: b. write down the simple regression model (with one explanatory right hand side variable): c. what sign do the authors find for the slope coefficient of the simple regression model? is it what you expected? d. what is the problem of interpreting this slope estimate as a causal effect? e. what happens to this slope when the authors include in the above model sat scores, high school grades an a proxy for the missing variable? what is the proxy they use? explain the change in the coefficient using the model of omitted variable bias.1f. what is the main conclusion of the study?