Work with this confusion matrix
HOMEWORK #41. Work with this confusion matrix, representing the results of a model used to differentiatebetween fraudulent and legitimate transactions (where p = actually fraudulent, n = actuallylegitimate, T = labelled fraudulent, F = labelled legitimate):Raw Counts(Model 1) True Classp n PredictedClass T 30 58 F 32 920 a. (4 points) Convert this matrix to one of expected rates (i.e., probabilities) and determinethe class priors. (Please round to 3 digits for all the calculations in this assignment.)Raw Counts(Model 1)PredictedClass True Classp n TF Prob (p) =Prob (n) = b. (4 points) Calculate the following rates:TP Rate = FP Rate = FN Rate = TN Rate = c. (4 points) Develop a cost-benefit matrix, where any transaction classified as fraudulentcosts a standard unit (i.e., -1) to handle, but a fraudulent transaction misclassified aslegitimate costs 100 times that amount. Correctly identifying a legitimate transaction hasneither a cost nor a benefit. Raw Counts(Model 1)PredictedClass TF True Classp n Calculate the expected cost of this model.Expected cost =d. (3 points) Calculate the following metrics for this model:Accuracy =Sensitivity =Specificity = e. (5 points) Now consider a second model that has managed to cut in half the falsenegatives from the original model, but at the same time has also cut in half the truenegatives. (Remember that there are 1040 instances in total.)Perform the same calculations as above.Raw Counts(Model 2)PredictedClass p n TF Raw Counts(Model 2)PredictedClass True Class True Classp n TF Prob (p) =Prob (n) =TP Rate = FP Rate = FN Rate = TN Rate = Expected cost (using the same costs/benefits) = f. Plot the two classifier models in ROC space. Label the axes and draw the “guessing” line. 0.0 0.2 0.4 0.6 0.8 1.0 g. Which model would you recommend to management, and why?
