Problem 3 For the sat data (available after loading the faraway package), t a model with the total SAT score as the response and expend, salary, ratio and takers as predictors. Perform the following analyses, displaying any plots that are relevant as you go. (a) State the tted linear model, and check the structure of the relation- ship between each predictor and the response using partial regression plots. (b) Perform a thorough residual analysis to check the constant variance assumption and the normality assumption. (c) Try a few transformations you learned from the lecture, and identify the most appropriate one for these data. Fit the model using the transformed data and repeat the residual analysis. (d) Use the Box-Cox method to nd the most appropriate power transfor- mation. [Hint Try the command boxcox (lmod, lambda = seq(6, 2, .1)) l