Four classification methods are denoted by M1, M2, M3 and M4. These are tested using a validation dataset YT RUE. The table below lists the output from the validation exercise for the first two methods.

(a) Calculate the confusion matrix for each of methods M1 and M2.

(b) Calculate the false positive rate (FPR) and true positive rate (TPR) for M1 and M2.

(c) For methods M3 and M4, the results are summarized as follows.

Draw an ROC plot (by hand) using the data for all four methods, clearly labelling the quantities that are plotted on each axis.

(d) Based on the ROC plot, which method is the best classifier? Comment on the performance of method M4.

YTRUE0100111101M10101111100M21000001101 Method FPR TPR M3M40.50.50.8330.333