U.S. Bank Loans

class: center, middle, inverse, title-slide

.title[
# U.S. Bank Loans
]
.subtitle[
## Sampling Strategies
]
.author[
### Tyler Battaglini & Ryan Lebo
]
.date[
### 2025-03-27
]

---

## 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>

|BankRegion   | Total_Loans| Defaults| Default_Rate|
|:------------|-----------:|--------:|------------:|
|Mid-Atlantic |      142486|    29375|    20.616060|
|Midwest      |      211424|    33263|    15.732840|
|Northeast    |      133479|    19692|    14.752883|
|Southeast    |      138304|    30791|    22.263275|
|Southwest    |       85461|    10167|    11.896655|
|Unknown      |        5733|      443|     7.727193|
|West         |      182277|    33827|    18.558019|

---

## 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>

| Mid-Atlantic| Midwest| Northeast| Southeast| Southwest|   West|
|------------:|-------:|---------:|---------:|---------:|------:|
|       142486|  211424|    133479|    138304|     85461| 182277|
---

## 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>

|  Size| Var.count|
|-----:|---------:|
| 32724|        30|

---

## Systematic Sampling

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

</ul>

|  Size| Var.count|
|-----:|---------:|
| 33090|        30|

---

## Stratefied Sampling

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

</ul>

| Mid-Atlantic| Midwest| Northeast| Southeast| Southwest| West|
|------------:|-------:|---------:|---------:|---------:|----:|
|         5219|    7744|      4889|      5066|      3130| 6676|

---

## 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>

|  Size| Var.count|
|-----:|---------:|
| 32305|        29|

---

<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>

|             | no.lab| default| no.default| default.rate|
|:------------|------:|-------:|----------:|------------:|
|Mid-Atlantic |    141|   29375|     112970|         20.6|
|Midwest      |    143|   33263|     178018|         15.7|
|Northeast    |   1396|   19692|     112391|         14.9|
|Southeast    |     99|   30791|     107414|         22.3|
|Southwest    |     57|   10167|      75237|         11.9|
|Unknown      |     54|     443|       5236|          7.8|
|West         |    107|   33827|     148343|         18.6|

---

## 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>

|             | default.rate.pop| default.rate.srs| default.rate.sys| default.rate.str| default.rate.cluster|
|:------------|----------------:|----------------:|----------------:|----------------:|--------------------:|
|Northeast    |             20.6|             21.0|             20.6|             20.8|                 21.7|
|Mid-Atlantic |             15.7|             15.6|             15.3|             16.2|                 15.1|
|Southeast    |             14.9|             14.3|             14.7|             15.2|                 15.6|
|Southwest    |             22.3|             22.4|             22.6|             22.3|                 21.5|
|Midwest      |             11.9|             11.9|             12.7|             13.4|                 12.9|
|West         |             18.6|             18.5|             19.0|             18.6|                 20.6|

---

## 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>