** Programming language R ** Please use program RStudio for this question **

Predicting wine quality by using support vector machine classication algorithm.

(a) Download the full wine quality training and testing datasets, and use the training dataset to nd out the optimal value of hyperparameter C for a linear kernel-based svm.

(b) Train a svm classier by using the linear kernel and the corresponding optimal value of hyperparameter C, then make predictions on the testing dataset, report the classication accuracy. (c) Use the training dataset to nd out the optimal values of hyperparameters C and for an RBF kernel-based svm.

(d) Train a svm classier by using the RBF kernel and the corresponding optimal values of hyperparameters C and , then make predictions on the testing dataset, report the classication accuracy.

(e) Train a logistic regression model. Then use the testing dataset to conduct an ROC curve analysis to compare the predictive performance of the trained logistic regression model and those two svm classiers trained by using linear and RBF kernels respectively.

Hint: Dene set.seed(1). Given a pre-dened hyperparameter space - C: [0.01, 0.1, 1, 10, 100], and : [0.01, 0.1, 1, 10, 100].

Full Wine Quality Training Dataset

fixed acidity,volatile acidity,citric acid,residual sugar,chlorides,free sulfur dioxide,total sulfur dioxide,density,pH,sulphates,alcohol,quality 9.1,0.27,0.45,10.6,0.035,28,124,0.997,3.2,0.46,10.4,Good 6.6,0.36,0.29,1.6,0.021,24,85,0.98965,3.41,0.61,12.4,Good 7.4,0.24,0.36,2,0.031,27,139,0.99055,3.28,0.48,12.5,Good 7.1,0.26,0.49,2.2,0.032,31,113,0.9903,3.37,0.42,12.9,Good 6.2,0.66,0.48,1.2,0.029,29,75,0.9892,3.33,0.39,12.8,Good 6.2,0.66,0.48,1.2,0.029,29,75,0.9892,3.33,0.39,12.8,Good 6.8,0.26,0.42,1.7,0.049,41,122,0.993,3.47,0.48,10.5,Good 6.7,0.23,0.31,2.1,0.046,30,96,0.9926,3.33,0.64,10.7,Good 5.2,0.44,0.04,1.4,0.036,43,119,0.9894,3.36,0.33,12.1,Good 5.2,0.44,0.04,1.4,0.036,43,119,0.9894,3.36,0.33,12.1,Good 6.8,0.53,0.35,3.8,0.034,26,109,0.9906,3.26,0.57,12.7,Good 7,0.24,0.36,2.8,0.034,22,112,0.99,3.19,0.38,12.6,Good 6.1,0.31,0.58,5,0.039,36,114,0.9909,3.3,0.6,12.3,Good 5,0.55,0.14,8.3,0.032,35,164,0.9918,3.53,0.51,12.5,Good 6,0.25,0.28,2.2,0.026,54,126,0.9898,3.43,0.65,12.9,Good

Full Wine Quality Testing Dataset

fixed acidity,volatile acidity,citric acid,residual sugar,chlorides,free sulfur dioxide,total sulfur dioxide,density,pH,sulphates,alcohol,quality 6.6,0.26,0.31,4.8,0.138,41,168,0.9951,3.2,0.38,9.3,Bad 7.6,0.36,0.49,11.3,0.046,87,221,0.9984,3.01,0.43,9.2,Bad 6.7,0.41,0.24,5.4,0.035,33,115,0.9901,3.12,0.44,12.8933333333,Good 7.3,0.19,0.27,13.9,0.057,45,155,0.99807,2.94,0.41,8.8,Good 5.7,0.29,0.16,7.9,0.044,48,197,0.99512,3.21,0.36,9.4,Bad 6.3,0.37,0.28,6.3,0.034,45,152,0.9921,3.29,0.46,11.6,Good 9,0.55,0.3,8.1,0.026,14,71,0.993,2.94,0.36,11.8,Bad 6.5,0.32,0.12,11.5,0.033,35,165,0.9974,3.22,0.32,9,Bad 6.2,0.25,0.47,11.6,0.048,62,210,0.9968,3.19,0.5,9.5,Bad 7.1,0.28,0.44,1.8,0.032,32,107,0.9907,3.25,0.48,12.2,Good 6.9,0.54,0.26,12.7,0.049,59,195,0.99596,3.26,0.54,10.5,Good 7.1,0.32,0.4,1.5,0.034,13,84,0.9944,3.42,0.6,10.4,Bad 7,0.26,0.26,10.8,0.039,37,184,0.99787,3.47,0.58,10.3,Good 5.8,0.13,0.22,12.7,0.058,24,183,0.9956,3.32,0.42,11.7,Good 7,0.39,0.31,5.3,0.169,32,162,0.9965,3.2,0.48,9.4,Bad