Q$\mathrm{.}2$: Suppose you are working on a medical dataset that contains information about patients' health metrics $($such as blood pressure, cholesterol levels, age$)$ and whether they are at risk of developing a particular disease $(1$ for at risk, $0$ for not at risk$).$ You are tasked with building a logistic regression model to predict the risk of developing the disease based on these health metrics.

Here's a sample dataset:

$\backslash$table$[[$Age $($A$),\backslash$table$[[$Blood Pressure$],[($B$)]],$Cholesterol $($C$),\backslash$table$[[$Disease Risk$],[($Output$)]]],[45,130,210,1],[60,150,220,1],[35,120,200,0],[55,140,240,1],[50,135,230,0]]$

Using the provided dataset, calculate the coefficients $($intercept and coefficients for each feature$)$ for the logistic regression model to predict the disease risk based on age, blood pressure, and cholesterol levels.

Interpret the meaning of the coefficient for blood pressure in the context of the problem.

What is the predicted probability of a $40-$year$-$old patient with blood pressure $125$ and cholesterol $190$ being at risk of developing the disease?