A hospital uses machine learning algorithms to assist in diagnosing a certain medical

condition based on patient symptoms and test results. The algorithm classifies patients into

two categories: "Positive" for the medical condition and "Negative" for the absence of the

condition. The hospital collected data from $200$ patients, including their symptoms, test

results, and the actual diagnosis made by medical professionals.

a$)$ How a confusion matrix is useful in evaluating the performance of a classification

model?

b$)$ Given the confusion matrix for the medical diagnosis model:

Predicted Positive

Actual Positive

Actual Negative

Predicted Negative

$45$

$5$

$10$

$140$

Calculate the accuracy, precision, recall, and F$1$ score of the model.

c$)$ Based on the confusion matrix, what insights can be derived about the performance

of the medical diagnosis model, and what recommendations can be made to

improve its accuracy?