Sampling loans by Region

class: center, middle, inverse, title-slide

.title[
# <font size="7" color="White">Sampling loans by Region</font>
]
.author[
### <font size="6" color="white"> Samantha Gouveia & Joshua Grant </font>
]
.date[
### <font color="white" size="5">3/26/24<br> </font> <font color="white" size="6"> STA490: Statistics Capstone </font>
]

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# <h2 align="center">Objective</h2>
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- Removing Values
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- Stratifying Populations
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- Sampling Techniques

- Random Samples
    
    - Systematic Samples
    
    - Stratified Samples
    
    - Clustered Samples

---

# <h2 align="center">Data Introduction</h2>

The data being using is from the U.S. Small Business Administration 
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It provides historical data from 1987 until 2014 
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There are 27 variables and 899,164 observations each representing a loan
</div>
</body>

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#  <h2 align="center">Remove missing values</h2>
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- We begin by removing any loans that are missing an MIS Status
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- Removing the missing MIS status values allows for the data to be equal for each of the samples
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- We find there are 155 MIS values missing

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# <h2 align="center">Map of Regions</h2>

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#  <h2 align="center">Stratifing the Population</h2>
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We stratify the population based on the region the loan is in 
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By stratifying the data into regions we have created 9 sub populations
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This will allow us to see a more accurate result due to there being smaller sample sizes

- New England 
- Mid-Atlantic
- South
- Great Lakes
- Midwest
- Pacific Coast
- Non Continental
- Rocky Mountain 
- Southwest

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# <h2 align="center"> Number of observations in each Region </h2>

|Region          |  Count|
|:---------------|------:|
|Great Lakes     | 247186|
|Mid-Atlantic    |  41134|
|Midwest         |  58146|
|New England     |  70023|
|Non Continental |   6014|
|Pacific Coast   | 164920|
|Rocky Mountain  |  60453|
|South           | 149001|
|Southwest       | 102132|

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# Cluster by Zip Code
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- We cluster by zip code using the entire study population. We will create clusters and select 9 of them to be used as the final study population.
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- When clustering by zip code it is important for the researchers to know we have a chance of getting no data from smaller areas as they may be picked less often.

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# Simple Random Sampling 
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- A simple random sample allows for each observation to have an equal chance of being chosen
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- A sample size of 100

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# Systematic Sample
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- A systematic sample uses a random sample from the population at a fixed interval of 50
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- By using the systematic sample there will be no influence over which loans are chosen allowing for the study to be unbiased.

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# Stratified Sample
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- A stratified sample will be done using the 9 regions we created earlier in the study.
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- A sample proportional to 10% of the total number loans in each region is taken per region. This keeps the proportion of observations from each region equal to that of the total population.

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# <h1 align="center">True Default Rate</h1>
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|Region          | True_Default_Rate|
|:---------------|-----------------:|
|Great Lakes     |         0.1718382|
|Mid-Atlantic    |         0.1999319|
|Midwest         |         0.1318749|
|New England     |         0.1178470|
|Non Continental |         0.1380113|
|Pacific Coast   |         0.1765462|
|Rocky Mountain  |         0.1507783|
|South           |         0.2175623|
|Southwest       |         0.1903713|

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# <h1 align="center">Sample Default Rate</h1>

<table>
 <thead>
  <tr>
   <th style="text-align:left;"> Region </th>
   <th style="text-align:right;"> Sample_Default_Rate </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> Great Lakes </td>
   <td style="text-align:right;"> 0.16 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Mid-Atlantic </td>
   <td style="text-align:right;"> 0.17 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Midwest </td>
   <td style="text-align:right;"> 0.11 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> New England </td>
   <td style="text-align:right;"> 0.10 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Non Continental </td>
   <td style="text-align:right;"> 0.15 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Pacific Coast </td>
   <td style="text-align:right;"> 0.13 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Rocky Mountain </td>
   <td style="text-align:right;"> 0.17 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> South </td>
   <td style="text-align:right;"> 0.24 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Southwest </td>
   <td style="text-align:right;"> 0.34 </td>
  </tr>
</tbody>
</table>
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# <h1 align="center">Comparison Table</h1>

|Region          | True_Default_Rate| Sample_Default_Rate|
|:---------------|-----------------:|-------------------:|
|Great Lakes     |         0.1718382|                0.16|
|Mid-Atlantic    |         0.1999319|                0.17|
|Midwest         |         0.1318749|                0.11|
|New England     |         0.1178470|                0.10|
|Non Continental |         0.1380113|                0.15|
|Pacific Coast   |         0.1765462|                0.13|
|Rocky Mountain  |         0.1507783|                0.17|
|South           |         0.2175623|                0.24|
|Southwest       |         0.1903713|                0.34|

---

```
## Using Region as id variables
```

![](project2slide--1-_files/figure-html/unnamed-chunk-13-1.png)
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<h2 align="center">Best Sampling method</h2>
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- Found Stratified yields best results
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- Guarantee all regions are weighted equally

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<h2 align="center">Conclusion</h2>
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- Throughout the study we have looked at the data provided by the U.S. Small Business Administration 
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- Used 4 different sampling methods to analysis loans
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- We compared the true default with defalut rate using stratified sampling 
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