Problem 1. For the sat data, fit a model with the total SAT score as the response and expend, salary, ratio and takers as predictors (same as the last homework). 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. Note: you may repeat what you obtained for Problem 3(a) on the last homework. (b) Check for large leverage points and display graphically on a half-normal 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. (f) Use the select() function to find the best for the ridge regression. Use this to preform the ridge regression, and report the ridge estimators of the coefficients. [Hint. Remember to use the coef() function to extract the coefficients.) (g) Perform the lasso method and use cross validation to choose the (fractional) value of t. Report the lasso coefficients at the chosen t. Which predictors are selected? Problem 1. For the sat data, fit a model with the total SAT score as the response and expend, salary, ratio and takers as predictors (same as the last homework). 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. Note: you may repeat what you obtained for Problem 3(a) on the last homework. (b) Check for large leverage points and display graphically on a half-normal 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. (f) Use the select() function to find the best for the ridge regression. Use this to preform the ridge regression, and report the ridge estimators of the coefficients. [Hint. Remember to use the coef() function to extract the coefficients.) (g) Perform the lasso method and use cross validation to choose the (fractional) value of t. Report the lasso coefficients at the chosen t. Which predictors are selected
