Description
Instructions: Please submit a report file that includes: a short answer, related code, printouts, etc. for each problem (where necessary). Push your answers to Github or Canvas. All programming must be in R (or R Markdown).
Problem 1
You will analyze the gradAdmit.csv dataset (the same dataset from Lab 4). This dataset contains a list of students (rows), along with whether or not they were admitted to graduate school (admit), their GRE score (gre), their GPA (gpa), and the prestige of their undergraduate university (rank). Your goal is to predict whether or not a student was admitted to graduate school based on the other data, using Support Vector Machines (SVM).
Problem 1a
Split the data into testing, training, and validation datasets for cross validation (CV). First, hold out 20% for your test dataset. On the remaining 80%, split it into 5 folds. Make sure to seed your random number generator and/or store the indices to ensure your datasets remain consistent through runs.
Problem 1b
Train a number of SVM models (using different hyperparameters) on the training set for each CV fold. For each run, report the accuracy on both the training and validation datasets, averaged over the folds. Try using various kernel functions, such as linear, polynomial, radial basis (or Gaussian), etc. Also, try to tune their respective hyperparameters (degree, gamma, and coef0), and the value for cost (or C), based on the validation accuracy. For a full list of the SVM arguments, visit https://www.rdocumentation.org/ packages/e1071/versions/1.7-2/topics/svm. Which kernel(s) perform better than others for this problem? Which hypereparameter values are optimal? Which model performed best on the validation dataset?
Problem 1c
For your best model from Problem 1b, retrain it on the full training set (the 80% that was used for training and validation) and compute the accuracy on the test dataset (the 20% that until this point was untouched).
1
