$1.(4$ points$)$ This is a real dataset from a credit union $($data here Download here$),$ in which the charge$-$off information for $30,794$ customers are kept together with three variables, total monthly income, credit score, current years employed. Charge$-$off $($or bad accounts$)$ is defined as those customers who defaulted on $($failed to pay for$)$ their loan from a bank. Good accounts are those customers who are current in their payment. Apply the same intuitive approach introduced in the cancer prediction dataset on this larger dataset to answer the same questions:

How can we tell if any of these three variable can predict the risk of charge$-$off?

If so$,$ can we tell which one is most predictive?

If so$,$ how can we produce an estimate of risk of charge$-$off based on these variables?

Use the number of bins $=20(22$ bins including the overflow and underflow bins$)$ for Intuition $1,$ and make sure you choose range properly to best show the distributions. Use number of groups $=40$ for Intuition $2.$