Bank Loan

class: center, middle, inverse, title-slide

.title[
# Bank Loan
]
.subtitle[
## Sampling Strategies
]
.author[
### Tyler Battaglini & Ryan Lebo
]
.date[
### 2025-03-24
]

---

<h1 align="center"> Table of Contents</h1>
<BR>

.pull-left[
- Introduction
- Variables
- Missing Variables/Converting Variables
- Variable Rework
- Default Rates/Discretize GrApprv
- Study Population/Sample Calculations
- Sample Methods
- Comparison of Methods
- Conclusion

]

---

<h1 align = "center"> Introduction <font color="orange"></font></h1>
<BR>
.pull-left[
- EDA Bank Loan Data set
- Data set provides ()

]

---
<h1 align = "center"> Variables <font color="orange"></font></h1>
<BR>

- Mis_Status
- DisbursementGross
- BalanceGross
- ChgOffPrinGr
- GrAppv
- SBA_Appv

---
<h1 align = "center"> Missing Variables/Converting Variables <font color="orange"></font></h1>
<BR>

- Looked for missing Mis_Status variables
- Converted DisbursementGross, BalanceGross, ChgOffPrinGr, GrAppv, and SBA_Appv

---
## Variable Rework

- 4 regional categories
- Can see patterns
- Easier for visualization

```

Midwest Northeast     South   Unknown      West 
   269885    150560    275751      1730    201238 
```

---
<h1 align = "center">  Default Rates/Discretize GrApprv <font color="orange"></font></h1>
<BR>

- Calculated default rates of SBA-backed loans
- Compare regions
- Easier to interpret
- Evenly distributed

```
# A tibble: 5 × 4
  BankRegion Total_Loans Defaults Default_Rate
  <chr>            <int>    <int>        <dbl>
1 Midwest         269885    42537        15.8 
2 Northeast       150560    21021        14.0 
3 South           275751    58751        21.3 
4 Unknown           1730      106         6.13
5 West            201238    35143        17.5 
```

```

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

---

<h1 align = "center"> Study Population/Sample Calculations <font color="orange"></font></h1>
<BR>

- Remove unknown group
- Make calculation from sample

```

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

## Simple Random Sample

- Perform simple random sample
- Assigned a unique index to each observation
- Randomly selected 32,724 observations

---

## 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|
|-----:|---------:|
| 33239|        30|

---

## Stratefied Sampling

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

</ul>

| Midwest| Northeast| South| West|
|-------:|---------:|-----:|----:|
|    9841|      5490| 10055| 7338|

---

## SBA_Appr Curves

---

<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|
|:---------|------:|-------:|----------:|------------:|
|Midwest   |    174|   42537|     227174|         15.8|
|Northeast |   1427|   21021|     128112|         14.1|
|South     |    227|   58751|     216773|         21.3|
|Unknown   |     54|     106|       1570|          6.3|
|West      |    115|   35143|     165980|         17.5|

---

##  Region-Specific Default Rates based on SRS

<li>Little to no variation between methods   </li>
<li>Increased and decreased rates </li>

</ul>

|          | default.rate.pop| default.rate.srs|
|:---------|----------------:|----------------:|
|Midwest   |             15.8|             15.7|
|Northeast |             14.1|             13.2|
|South     |             21.3|             21.6|
|West      |             17.5|             16.7|

---

## Region-specific Rates- Systematics Sample

<li>Little to no variation between methods  </li>
<li>Three of our rates increased </li>

</ul>

|          | default.rate.pop| default.rate.srs| default.rate.sys|
|:---------|----------------:|----------------:|----------------:|
|Midwest   |             15.8|             15.7|             15.6|
|Northeast |             14.1|             13.2|             13.9|
|South     |             21.3|             21.6|             21.6|
|West      |             17.5|             16.7|             17.0|

---

## Region-specific Default Rates- Stratified Sample

<li>Again 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|
|:---------|----------------:|----------------:|----------------:|----------------:|
|Northeast |             15.8|             15.7|             15.6|             16.7|
|Midwest   |             14.1|             13.2|             13.9|             13.6|
|South     |             21.3|             21.6|             21.6|             20.8|
|West      |             17.5|             16.7|             17.0|             17.5|

---

## Visualization

---

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

---

## Conclusion

<li>Default rates between differing sampling plans are similar to population default rates </li>
<li> Systematic sample slightly overestimates most regions </li>
<li> Stratified performs the best regarding accuracy </li>
<li> South consistently has the highest default rates across sampling methods </li>

</ul>

---

## Limitations

<li> Economic Factors differ by region </li>
<li> Wide regions with bigger and/or more states could skew data for that region </li>
<li> Distribution of wealth between regions </li>

</ul>

---

## Contributors

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

</ul>