Bonus Problem (10 points) Use the Sacremento data from the caret library by running data(Sacremento) after loading caret. This data is about housing prices in Sacramento, California. Remove the zip and city variables. a. Explore the variables to see if they have reasonable distributions and show your work. We will be predicting the type variable does that mean we have a class imbalance? b. There are lots of options for working on the data to try to improve the performance of SVM, including (1) removing other variables that you know should not be part of the prediction, (2) dealing with extreme variations in some variables with smoothing, normalization or a log transform, (3) applying PCA, and (4) to removing outliers. Pick one now and continue. c. Use SVM to predict type and use grid search to get the best accuracy you can. The accuracy may be good, but look at the confusion matrix as well. Report what you find. Note that the kappa value provided with your SVM results can also help you see this. It is a measure of how well the classifier performed that takes into account the frequency of the classes. d. Return to (b) and try at least one other way to try to improve the data before running SVM again, as in (c). e. In the end, some data are just so imbalanced that a classifier is never going to predict the minority class. Dealing with this is a huge topic. One simple possibility is to conclude that we do not have enough data to support predicting the very infrequent class(es) and remove them. If they are not actually important to the reason we are making the prediction, that could be fine. Another approach is to force the data to be more even by sampling. Create a copy of the data that includes all the data from the two smaller classes, plus a small random sample of the large class (you can do this by separating those data with a filter, sampling, then attaching them back on). Check the distributions of the variables in this new data sample to make sure they are reasonably close to the originals using visualization and/or summary statistics. We want to make sure we did not get a strange sample where everything was cheap or there were only studio apartments, for example. You can rerun the sampling a few times if you are getting strange results. If it keeps happening, check your process. Use SVM to predict type one this new, more balanced dataset and report its performance with a confusion matrix and with grid search to get the best accuracy.