In this example we will consider data form a consumer$-$to$-$consumer $($C$2$C$)$ lending market, in which borrowers can post loan listings and lenders can invest in these loans. From the lenders perspective, it would be useful to get a sense of how likely the loan is to default, given some information on it$.$ Data is available $($you can see it in the file $$loandatamodified$.$csv$)$ on approximately $5,500$ loans and whether these loans ultimately failed $($defaulted$)$ or were current. In addition to this information, we also have data on the following $4$ features:

a$)$ The amount of the loan in $

b$)$ The age of the loan in months

c$)$ The borrower rate $($the interest rate that the borrower pays the lender$)$

d$)$ The borrower$$s credit rating $($which is either $$good$$ or $$low$).$ Since this is a categorical feature, we convert it into a dummy $($numerical$)$ feature which takes value $1$ for low and $0$ for good. $($Note: the original data has many credit rating categories that range from AA$,$ B$,$ C all the way down to High Risk. For simplicity, I clubbed these ratings into only two categories, either $$good$$ or $$low$).$

A logistic model is trained on this data, with $$fail$/$default$$ being the positive case and $$loan current$$ being the negative case. The following model is obtained:

coefficients:

Estimate

$($Intercept$)-7\mathrm{.}707$e $+00$

Amount $3\mathrm{.}171$e$-05$

Age $3\mathrm{.}624$e$-01$

Borrower.Rate $1\mathrm{.}302$e$+01$

RatingLow $7\mathrm{.}887$e$-01$

ii$)$ From the model above, what is the predicted probability that a loan will default if it is for $3000$$$,$ has age $=4$ months, a borrower rate of $0\mathrm{.}12$ and the borrower$$s credit rating is good $($Note: this means that the ratinglow feature takes a value of $0$ in the model$).$ In answering this question, it is helpful to understand the standard e$+$ and e$-$ notation that you see in the output above as follows: $3\mathrm{.}171$e$-05=0\mathrm{.}00003171,$

$3\mathrm{.}624$e$-01=0\mathrm{.}3624,1\mathrm{.}302$e$+01=13\mathrm{.}02$ and $7\mathrm{.}887$e$-01=0\mathrm{.}7887$