You have been hired as a data analytics consultant by a credit institution, and your

task is to deploy a model that can detect potentially defaulting clients among those

who apply for short$-$to$-$medium term loans. The company has provided you with

data on a sample of $2979$ customers, which include the following variables:

You fit a logistic regression model to the data, obtaining the following output.

$($a$)$ Using the $R$ output above:

$($i$)$ Explain how, according to the model, a customer's income category affects

the odds of defaulting on a loan.

$($ii$)$ Determine the percentage variation in the odds of defaulting for a subject

applying for a $7000$ euro loan compared to a subject applying for a $2500$

euro loan. $($b$)$ Two subjects having the following characteristics apply for loans:

Which of the two subjects is more likely to being given the loan? Justify your

answcr.

$($c$)$ Two classification thresbolds $T$ are taben into consideration to obtain the es$-$

timated classification yo from the estimated probabilities. Cross$-$tabulations

of predicted classification and default status are reported below for different

values of the threshold $.$

$($i$)$ In order to evaluate the predictive performance of the model, the com$-$

pany's primary concern is the classifier's ability to accurately identify

defaulting customers. In light of this information, use an appropriate ap$-$

proach to determine the optimal classification threshold. Comment on

the prodictive performance related to this optimal threshold.

$($ii$)$ Compute the prevalence of the default $-$ yes class, and explain briefly

why using the classification accuracy might not be ideal to assess the

prodictive performance of the model in this context.