$($a$)$ Two machine learning algorithms $($methods A and B$)$ were trained to identify different types of cancer using $8$ predictor variables $($measured through a blood test$)$ and an outcome variable called Tumor $($categorised as malignant or benign$).$ When the tumour is considered to be malignant, the patient must undergo medical intervention as quickly as possible. When the tumour is benign, other types of less invasive procedures are available, and intervention is less urgent. The dataset was split into training $(140$ patients$)$ and test $(35$ patients$)$ sets. See below for the confusion tables generated using the test set, for each method:

$35$

i$.$ What is the overall accuracy of method A$?$ What are the true positive rates $($assuming malignant is the positive class$)$ and true negative rates for detecting malignant tumours for method A$?$

$[6$ marks$]$

ii$.$ What is the overall accuracy of method B$?$ What are the true positive rates $($assuming malignant is the positive class$)$ and true negative rates for detecting malignant tumours for method B$?$

$[6$ marks$]$

iii. Which method do you believe is most appropriate for the problem at hand? Why?