>head (college) 1 Abilene Christian University 1660 College Apps Accept Enroll Top10perc Top25perc 1232 721 23 52 2 3 Adelphi University 2186 1924 512 16 29 Adrian College 1428 1097 336 22 50 456 4 Agnes Scott College 417 349 137 60 89 5 Alaska Pacific University 193 146 55 16 44 479 158 38 Albertson College 587 62 F.Undergrad P.Undergrad Outstate Room. Board Books Personal PhD Terminal 78 123 2885 537 7440 3300 450 2200 70 2 2683 1227 12280 6450 750 1500 29 30 1036 99 11250 3750 400 1165 53 66 456 510 63 12960 5450 450 875 92 97 249 869 7560 4120 800 1500 76 72 678 41 13500 3335 500 675 67 73 23 S.F.Ratio perc. alumni Expend Grad. Rate 123 18.1 12 7041 60 2 12.2 16 10527 56 3 12.9 30 8735 54 4 7.7 37 19016 59 5 11.9 2 10922 15 9.4 11 9727 55 College Apps Accept Enroll Top10perc Top25perc Name of college Number of applications received Number of applications accepted Number of new students enrolled Percentage of new students from top 10% of H.S. class Percentage of new students from top 25% of H.S. class F. Undergrad Number of fulltime undergraduates P. Undergrad Number of parttime undergraduates Outstate Room. Board Books Personal PhD Terminal S.F.Ratio perc. alumni Out-of-state tuition Room and board costs Estimated book costs Estimated personal spending Percentage of faculty with Ph.D.s Percentage of faculty with terminal degree Student/faculty ratio Percentage of alumni who donate Expend Instructional expenditure per student Grad.rate Graduation rate Suppose that a linear regression model is to be built for predicting the number of new students enrolled (Enroll) using the other variables except the name of college (College). The original dataset was splitted into a training dataset collegetrain.csv and a test dataset collegetest.csv, with the variable College removed. (a) i. Fit a linear regression model on the training dataset and refine the model by stepwise search, using BIC as the model selection criterion. ii. Report the estimated model coefficients of the selected model. iii. Calculate the mean square prediction error of the selected model on the test dataset. (b) i. Fit a ridge regression model with ridge parameter A chosen by leave- one-out cross-validation. ii. Report the estimated model coefficients of the fitted model for the selected X. iii. Calculate the mean square prediction error of the selected model on the test dataset. (c) i. Fit a linear regression model by lasso regularization, with the regu- larization parameter A chosen by leave-one-out cross-validation. ii. Report the estimated model coefficients of the fitted model for the selected X. iii. Calculate the mean square prediction error of the selected model on the test dataset. (d) Compare and comment on the results obtained.