$(27$ points$)$ Model Evaluation in Machine Learning: In a medical context, we need to develop a model

to diagnose a rare disease. We use a binary classifier $($logistic regression$)$ to predict whether a patient

has the disease or not. Assume the disease is rare, affecting only $3\%$ of the tested population. Our

trained model has classified $10,000$ patients, whereby $300$ have been classified as sick, and $9,700$ as

healthy. The model has made the following predictions: True Positives $($TP$)$: $50$; False Positives $($FP$)$:

$70$; True Negatives $($TN$)$: $9,630$; False Negatives $($FN$)$: $250.$

a$)(4$ points$)$ Create the confusion matrix based on the above predictions.

b$)(2$ points$)$ Calculate the accuracy of the model.

c$)(3$ points$)$ Explain why accuracy is not a suitable metric for evaluating the model in this case.

d$)(8$ points$)$ Calculate the True Positive Rate $($TPR$)$ and the False Positive Rate $($FPR$)$ of the model.

Interpret the TPR and FPR values obtained. Explain what these values indicate about the model's

performance.

e$)(5$ points$)$ Explain why in our case TPR and FPR$,$ along with the ROC $($Receiver Operating

Characteristic$)$ curve, are more informative metrics than accuracy. Note: You do not need to plot

the ROC curve.

f$)(5$ points$)$ Describe how the ROC curve is generated. What does the area under the curve $($AUC$)$

signify in our case?