For the sat data, fit a model with the total SAT score (from faraway package) as the response and expend, salary, ratio and takers as predictors. Perform regression diagnostics on this model to answer the following questions. Display any plots that are relevant as you go. Note: do not provide any plots about which you have nothing to say. Suggest possible improvements or corrections to the model where appropriate. (a) State the fitted linear model. (b) Check for large leverage points and display graphically on a halfnormal plot. (c) Check for outliers using jackknife residuals, and use the Bonferroni correction to decide if the largest outlier is significant at the 5% level. (d) Check for influential points using Cook's D statistic and display graphically on a half-normal plot. Comment on whether anything is notable. (e) Calculate the VIF for each predictor. Comment on whether anything is notable. For the sat data, fit a model with the total SAT score (from faraway package) as the response and expend, salary, ratio and takers as predictors. Perform regression diagnostics on this model to answer the following questions. Display any plots that are relevant as you go. Note: do not provide any plots about which you have nothing to say. Suggest possible improvements or corrections to the model where appropriate. (a) State the fitted linear model. (b) Check for large leverage points and display graphically on a halfnormal plot. (c) Check for outliers using jackknife residuals, and use the Bonferroni correction to decide if the largest outlier is significant at the 5% level. (d) Check for influential points using Cook's D statistic and display graphically on a half-normal plot. Comment on whether anything is notable. (e) Calculate the VIF for each predictor. Comment on whether anything is notable