Dean Paris is the management accountant at Ash Tree Bank, where the data science department is leading an initiative to predict whether loans will default or repay. The default rate in the training set is $25\%.$ After building a model on the training set that predicts whether a loan will default or repay, the data scientist applies it to the validation set of $4,000$ observations to evaluate its peffomance.

Read the requirements,

Kequirement $1.$ Help the data scientst complete the contusion matrixes below for arterent model tinesholds.

Start by completing the confusion matrix for the cutoff point $0\mathrm{.}40.$

$\backslash$table$[[,$Confusion Matrix $(0\mathrm{.}40),],[,,$Predicted Outcomes,Total$],[,,$Default,Repay$],[$Actual$,$Default,,,$],[$Outcomes$,$Repay,$1,740,1,260,3,000],[,$Total,$2,600||,,4,000]]$

Complete the confusion matrix for the cutoff point $0\mathrm{.}55.$

$\backslash$table$[[,$Confusion Matrix $(0\mathrm{.}55),],[,,$Predicted Outcomes,Total$],[,,$Default,Repay$],[$Actual$,$Default,$720,,1,000],[$Outcomes$,$Repay,,,$3,000],[,$Total,,$2800,]]$

Requirement $2.$ Assume that: Ash Tree Bank has $$1,000$ to invest in each loan of the validation sample. If Ash Tree Bank does not invest in a loan, it keeps the money in a risk$-$friee irvestment at $4\%$ a year for $3$ years $($ignore the time value of money$).$ If Ash Tree invests in a loan that eventually repays, it receives $8\%$ a year for $3$ years. If Ash Tree invests in a loan that everitually defauts, Ash Tree loses $55\%$ of the amount of the loan. Fill in the payoff matnix below. Which model threshold should Dean and the data scientist use?

Start by constuting the payroll matix. $($Enter a loss amount yith a minus sign or parentheses.$)$

$\backslash$table$[[,$Payoff Matrix$],[,$Predicted Outcomes$],[,$Default,Repay,$],[($Do Not Invest in Loan$),($Invest in Loan$),,],[\backslash$table$[[$Actual$],[$Outcomes$]],$Default,,$],[$Repay$,,]]$

Calculate the payoff at each cutoff probability.

Total payoff at cutoff $0\mathrm{.}40=$

Total payoff at cutoff $0\mathrm{.}55=$

Which model threshold should Dean and the data scientist use?

Which model theshold should Dean and the dala sciertist use?

Dean and the data scientists should use the cutoft value at because it results in the predicied pa$)$ off.

Requirements

Help the data scientist complete the confusion matrixes below for different model thresholds.

$\backslash$table$[[,$Confusion Matrix $(0\mathrm{.}40),,,$Confusion Matrix $(0\mathrm{.}55),],[,,\backslash$table$[[$Predicted$],[$Outcomes$]],$Total,,,$\backslash$table$[[$Predicted$],[$Outcomes$]],$Total$],[,,$Default,Repay,,,Default,Repay$],[$Actual$,$Default,,,,$\backslash$table$[[$Actual$],[$Outcomes$]],$Default,$720,,1,000],[$Outcomes$,$Repay,$1,740,1,260,3,000,$Repay,,,$3,000],[,$Total,$2,600,,4,000,,$Total,,$2,800,]]$

Assume that Ash Tree Bank has $$1,000$ to invest in each loan of the validation sample. If Ash Tree Bank does not invest in a loan, it keeps the money in a risk$-$free investment at $4\%$ a year for $3$ years $($ignore the time value of money$).$ If Ash Tree invests in a loan that eventually repays, it receives $8\%$ a year for $3$ years. If Ash Tree invests in a loan that eventually defaults,