$(40$ points$)$ We plan to employ a linear regression model to handle credit card applications.

We use three features for each custom. We denote approval as $1,$ and denial as $0.$ Assume

last year, we had the record from $5$ customs as below. Custom $0$: $6($feature $1),20($feature

$2),3($feature $3),$ approval; Custom $1$: $7,5,7,$ denial; Custom $2$: $11,9,9,$ approval; Custom

$3$: $10,3,6,$ denial; Custom $4$: $4,4,1,$ denial.