U.S. Bank Loans

class: center, middle, inverse, title-slide

.title[
# U.S. Bank Loans
]
.subtitle[
## Sampling Strategies
]
.author[
### Tyler Battaglini & Ryan Lebo
]
.date[
### 2025-03-30
]

---

## Table of Contents

<li>Introduction</li>
<li>Variables</li>
<li>Missing Variables/Converting Variables</li>
<li>Variable Rework</li>
<li>Default Rates/Discretize GrApprv</li>
<li>Study Population/Sample Calculations</li>
<li>Sample Methods</li>
<li>Comparison of Methods</li>
<li>Conclusion</li>

</ul>

---

## Introduction

<li>EDA Bank Loan Data set</li>
<li>Combined Dataset</li>
<li>Data set provides data from SBA</li>

</ul>

---
## Variables

<li>Mis_Status</li>
<li>DisbursementGross</li>
<li>BalanceGross</li>
<li>ChgOffPrinGr</li>
<li>GrAppv</li>
<li>SBA_Appv</li>

</ul>

---
## Missing Variables/Converting Variables

<li>Looked for missing Mis_Status variables</li>
<li>Converted DisbursementGross, BalanceGross, ChgOffPrinGr, GrAppv, and SBA_Appv </li>

</ul>

---
## Variable Rework

<li>6 regional categories</li>
<li>Can see patterns</li>
<li>Easier for visualization</li>

</ul>

```

Mid-Atlantic      Midwest    Northeast    Southeast    Southwest      Unknown 
      142486       211424       133479       138304        85461         5733 
        West 
      182277 
```

---
## Default Rates/Discretize GrApprv

<li>Calculated default rates of SBA-backed loans</li>
<li>Compare regions</li>
<li>Easier to interpret</li>

</ul>

<table>
 <thead>
  <tr>
   <th style="text-align:left;"> BankRegion </th>
   <th style="text-align:right;"> Total_Loans </th>
   <th style="text-align:right;"> Defaults </th>
   <th style="text-align:right;"> Default_Rate </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> Mid-Atlantic </td>
   <td style="text-align:right;"> 142486 </td>
   <td style="text-align:right;"> 29375 </td>
   <td style="text-align:right;"> 20.616060 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Midwest </td>
   <td style="text-align:right;"> 211424 </td>
   <td style="text-align:right;"> 33263 </td>
   <td style="text-align:right;"> 15.732840 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Northeast </td>
   <td style="text-align:right;"> 133479 </td>
   <td style="text-align:right;"> 19692 </td>
   <td style="text-align:right;"> 14.752883 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Southeast </td>
   <td style="text-align:right;"> 138304 </td>
   <td style="text-align:right;"> 30791 </td>
   <td style="text-align:right;"> 22.263275 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Southwest </td>
   <td style="text-align:right;"> 85461 </td>
   <td style="text-align:right;"> 10167 </td>
   <td style="text-align:right;"> 11.896655 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Unknown </td>
   <td style="text-align:right;"> 5733 </td>
   <td style="text-align:right;"> 443 </td>
   <td style="text-align:right;"> 7.727193 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> West </td>
   <td style="text-align:right;"> 182277 </td>
   <td style="text-align:right;"> 33827 </td>
   <td style="text-align:right;"> 18.558019 </td>
  </tr>
</tbody>
</table>

---

## Default Rates/Discretize GrApprv

<li>Easier to interpret</li>
<li>Evenly Distributed</li>
<li>Split into 5 groups</li>

</ul>

```

Very Low       Low    Medium      High Very High 
   180997    179102    179575    179677    179813 
```

---

## Study Population/Sample Calculations

<li>Remove unknown group</li>
<li>Make calculation from sample</li>

</ul>

<table>
 <thead>
  <tr>
   <th style="text-align:right;"> Mid-Atlantic </th>
   <th style="text-align:right;"> Midwest </th>
   <th style="text-align:right;"> Northeast </th>
   <th style="text-align:right;"> Southeast </th>
   <th style="text-align:right;"> Southwest </th>
   <th style="text-align:right;"> West </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:right;"> 142486 </td>
   <td style="text-align:right;"> 211424 </td>
   <td style="text-align:right;"> 133479 </td>
   <td style="text-align:right;"> 138304 </td>
   <td style="text-align:right;"> 85461 </td>
   <td style="text-align:right;"> 182277 </td>
  </tr>
</tbody>
</table>
---

## Simple Random Sample

<li>Perform simple random sample</li>
<li>Assigned a unique index to each observation</li>
<li>Randomly selected 32,724 observations</li>

</ul>

<table>
 <thead>
  <tr>
   <th style="text-align:right;"> Size </th>
   <th style="text-align:right;"> Var.count </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:right;"> 32724 </td>
   <td style="text-align:right;"> 30 </td>
  </tr>
</tbody>
</table>

---

## Systematic Sampling

<li>Sample from intervals after a given starting point </li>
<li>Ensures representation throughout dataset </li>
<li>Reduces bias </li>

</ul>

<table>
 <thead>
  <tr>
   <th style="text-align:right;"> Size </th>
   <th style="text-align:right;"> Var.count </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:right;"> 33090 </td>
   <td style="text-align:right;"> 30 </td>
  </tr>
</tbody>
</table>

---

## Stratefied Sampling

<li>Ensures each region is equally represented </li>
<li>Improved accuracy </li>
<li>Reduces bias </li>

</ul>

<table>
 <thead>
  <tr>
   <th style="text-align:right;"> Mid-Atlantic </th>
   <th style="text-align:right;"> Midwest </th>
   <th style="text-align:right;"> Northeast </th>
   <th style="text-align:right;"> Southeast </th>
   <th style="text-align:right;"> Southwest </th>
   <th style="text-align:right;"> West </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:right;"> 5219 </td>
   <td style="text-align:right;"> 7744 </td>
   <td style="text-align:right;"> 4889 </td>
   <td style="text-align:right;"> 5066 </td>
   <td style="text-align:right;"> 3130 </td>
   <td style="text-align:right;"> 6676 </td>
  </tr>
</tbody>
</table>

---

## Cluster Sampling

<ul style="font-size: 1.6em; line-height: 1.6;"> 
<li>Cluster selection bias</li>
<li>Potential over/Under representation of population</li>
<li> Enhances comparability between groups</li>
</ul>

<table>
 <thead>
  <tr>
   <th style="text-align:right;"> Size </th>
   <th style="text-align:right;"> Var.count </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:right;"> 32305 </td>
   <td style="text-align:right;"> 29 </td>
  </tr>
</tbody>
</table>

---

<div style="display: flex; justify-content: center; align-items: center; height: 80vh; font-size: 50px;">
  Comparison of Methods
</div>

---

## Population-level Default Rates

<li>Population default rates will be used for comparison   </li>
<li>Rates relatively close to one another  </li>

</ul>

<table>
 <thead>
  <tr>
   <th style="text-align:left;">   </th>
   <th style="text-align:right;"> no.lab </th>
   <th style="text-align:right;"> default </th>
   <th style="text-align:right;"> no.default </th>
   <th style="text-align:right;"> default.rate </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> Mid-Atlantic </td>
   <td style="text-align:right;"> 141 </td>
   <td style="text-align:right;"> 29375 </td>
   <td style="text-align:right;"> 112970 </td>
   <td style="text-align:right;"> 20.6 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Midwest </td>
   <td style="text-align:right;"> 143 </td>
   <td style="text-align:right;"> 33263 </td>
   <td style="text-align:right;"> 178018 </td>
   <td style="text-align:right;"> 15.7 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Northeast </td>
   <td style="text-align:right;"> 1396 </td>
   <td style="text-align:right;"> 19692 </td>
   <td style="text-align:right;"> 112391 </td>
   <td style="text-align:right;"> 14.9 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Southeast </td>
   <td style="text-align:right;"> 99 </td>
   <td style="text-align:right;"> 30791 </td>
   <td style="text-align:right;"> 107414 </td>
   <td style="text-align:right;"> 22.3 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Southwest </td>
   <td style="text-align:right;"> 57 </td>
   <td style="text-align:right;"> 10167 </td>
   <td style="text-align:right;"> 75237 </td>
   <td style="text-align:right;"> 11.9 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Unknown </td>
   <td style="text-align:right;"> 54 </td>
   <td style="text-align:right;"> 443 </td>
   <td style="text-align:right;"> 5236 </td>
   <td style="text-align:right;"> 7.8 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> West </td>
   <td style="text-align:right;"> 107 </td>
   <td style="text-align:right;"> 33827 </td>
   <td style="text-align:right;"> 148343 </td>
   <td style="text-align:right;"> 18.6 </td>
  </tr>
</tbody>
</table>

---

## Region-specific Default Rates for Differing Samples

<li>Little to no variation between methods   </li>
<li>Almost equal to our default rate population </li>

</ul>

<table>
 <thead>
  <tr>
   <th style="text-align:left;">   </th>
   <th style="text-align:right;"> default.rate.pop </th>
   <th style="text-align:right;"> default.rate.srs </th>
   <th style="text-align:right;"> default.rate.sys </th>
   <th style="text-align:right;"> default.rate.str </th>
   <th style="text-align:right;"> default.rate.cluster </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> Northeast </td>
   <td style="text-align:right;"> 20.6 </td>
   <td style="text-align:right;"> 19.9 </td>
   <td style="text-align:right;"> 21.2 </td>
   <td style="text-align:right;"> 20.4 </td>
   <td style="text-align:right;"> 21.7 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Mid-Atlantic </td>
   <td style="text-align:right;"> 15.7 </td>
   <td style="text-align:right;"> 16.0 </td>
   <td style="text-align:right;"> 15.8 </td>
   <td style="text-align:right;"> 15.3 </td>
   <td style="text-align:right;"> 15.1 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Southeast </td>
   <td style="text-align:right;"> 14.9 </td>
   <td style="text-align:right;"> 15.1 </td>
   <td style="text-align:right;"> 14.7 </td>
   <td style="text-align:right;"> 14.4 </td>
   <td style="text-align:right;"> 15.6 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Southwest </td>
   <td style="text-align:right;"> 22.3 </td>
   <td style="text-align:right;"> 22.1 </td>
   <td style="text-align:right;"> 22.3 </td>
   <td style="text-align:right;"> 21.6 </td>
   <td style="text-align:right;"> 21.5 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Midwest </td>
   <td style="text-align:right;"> 11.9 </td>
   <td style="text-align:right;"> 11.3 </td>
   <td style="text-align:right;"> 11.8 </td>
   <td style="text-align:right;"> 11.8 </td>
   <td style="text-align:right;"> 12.9 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> West </td>
   <td style="text-align:right;"> 18.6 </td>
   <td style="text-align:right;"> 17.6 </td>
   <td style="text-align:right;"> 18.5 </td>
   <td style="text-align:right;"> 18.6 </td>
   <td style="text-align:right;"> 20.6 </td>
  </tr>
</tbody>
</table>

---

## Visualization

---

<div style="display: flex; justify-content: center; align-items: center; height: 80vh; font-size: 50px;">
  Conclusion
</div>

---

## Conclusion

<li> Stratified/Systematic sampling most accurate </li>
<li> Representative selection across methods </li>
<li> Default rates between differing sampling plans are similar to population default rates </li>
<li> Large sample could leads to random variation decreasing </li>

</ul>

---

## Limitations

<li> Economic Factors differ by region </li>
<li> Big economical shifts for the 30 years of the dataset</li>
<li> Densely populated areas could inflate rates for whole region </li>

</ul>

---

<div style="display: flex; justify-content: center; align-items: center; height: 80vh; font-size: 50px;">
  Thank You
</div>---

---

## Contributors

<li> Ryan Lebo - Slides Beginning to Simple Random Sampling  </li>
<li> Tyler Battaglini - Slides Systematic Sampling to Conclusion </li>

</ul>