Download the data file Rateprof . csv from Canvas. The variables we will use are quality, easiness, and raterInterst. All three variables are ratings made by students on the scale of 1 to 5, with 1 being the worst (least), and 5 the best (most). quality and easiness are students' ratings of a professor or their course. raterInterest measures how interested the students are in the subject matter. (a) Fit the model quality ~ raterInterest and the model quality ~ easiness. In each model, what proportion of the variation in quality is explained by the predictor variable? (b) Fit the model quality ~ raterInterest + easiness. Write down the equation of the fitted model. (c) For the model in Part (b), interpret the coefficient of easiness in the context. (d) What is the R of the model quality ~ raterInterest + easiness? Compare the value to the sum of the R" values of the two models in Part (a). Explain why the R values in Part (a) should or should not add up the R of the model quality ~ raterInterest + easiness