Private College Acceptance

class: center, middle, inverse, title-slide

.title[
# <font color="black">Private College Acceptance</font>
]
.subtitle[
## <font color="black">Multiple linear Regression</font>
]
.author[
### <font color="black">Samantha Gouveia</font>
]
.date[
### <font color="black">r Sys.Date().</font>
]

---

<h1 align="center"> Data Introduction.</h1>

The case study focuses on 777 private and public colleges with 8 predictors

Response variable:
>Private

Predictors: 
>Application

>Acceptance

>Enrollment

>Top 10 percent

>Top 25 percent

>Grad rate

---

<h1 align="center">Objective</h1>

<br>
> <font size = 6> Find which predictor variables are the most influential in predicting acceptence to a private college.</font><br>
<br>
<br>

> <font size = 6> Explore the correltation between variables and determine which model will preform the best.</font>

---

<h1 align="center">Pairwise Scatterplot</h1>
![](Xarin_files/figure-html/pairwise scatterplot-1.png)
---
<h1 align="center">Dummy Variables</h1>
.left-column[
<font size = 5>Create two histograms due to their high correlation<br>

to determine which will be used in the predictor models.</font>

>Accept

>Application

]

.right-column[
![](Xarin_files/figure-html/unnamed-chunk-1-1.png)
]

---
<h1 align="center">Prediction Error</h1>
.left-column[
<font size = 5> Create 3 candidate models to find the prediction errors.</font>

> Full model

> Reduced model

> Step-wise model

]

.right-column[

```
## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
```

<table>
<caption>Average of prediction errors of candidate models</caption>
 <thead>
  <tr>
   <th style="text-align:right;"> PE1 </th>
   <th style="text-align:right;"> PE2 </th>
   <th style="text-align:right;"> PE3 </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:right;"> 0.916129 </td>
   <td style="text-align:right;"> 0.916129 </td>
   <td style="text-align:right;"> 0.9129032 </td>
  </tr>
</tbody>
</table>
]

---
<h1 align="center">Accuracy</h1>

<br>
<font size = 6>We see the actual accuracy of the final model to be 0.741<br><br>

The step-wise model will be used as the final model due to having the lowest prediction error and number of variables
</font>

---

<h1 align="center">ROC Curve</h1>

.left-column[

<font size = 5,<div style = "text-align: center;">The ROC Curve shows the aggregate measure of performance across all 3 classification thresholds</font></div>
]

.right-column[
<div style = "text-align: center;">

]

![](Xarin_files/figure-html/unnamed-chunk-7-1.png)
]
---
<h1 align="center">ROC Curve Analysis</h1>
<br><br>
<font size = 6,h1 align="center"> Find the Full model and Step-wise model have the same AUC</font></h1><br>
<br>
<br>

<font size = 6,h1 align="center"> We  see the reduced model will be the worst predictior model</font></h1>

---
<h1 align="center">Conclusion</h1>
<br>

<font size = 6,h1 align="center">The stepwise model is our best predictor model</font></h1><br>
<br>

<font size = 6,h1 align="center">We have a high prediction rate</font></h1><br>
<br>

<font size = 6,h1 align="center">We have a high accuracy</font></h1><br>
---

<h1 align="center">Refernces</h1>
Gupta, Y. (2019, October 28). US College Data. Kaggle. https://www.kaggle.com/datasets/yashgpt/us-college-data

---

# Thanks!

Slides created via the R packages:

[**xaringan**](https://github.com/yihui/xaringan)<br>
[gadenbuie/xaringanthemer](https://github.com/gadenbuie/xaringanthemer)