Admission_Prediction_v1.Rmd

---
title: "College Admission Prediction"
author: "Deo Ivan Mareza"
date: "`14 February 2020`"
output:
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    df_print: paged
    highlight: breezedark
    theme: cosmo
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    toc: yes
---
# INTRODUCTION

In this exercise, I want to predict someone's `chance of admission` to a university of their choice using linear regression method based on other variables.
<br><br>
I will use MSE and RMSE as a measure of my model's accuracy.
<br>

 

<br>

# DATA PREPARATION


Library packages that I'm using
```{r,warning=FALSE, results='hide',message=FALSE}

library(tidyverse)
library(GGally)
library(MLmetrics)
library(car)
library(lmtest)
library(stringr)

```

Reading the data
```{r,warning=FALSE, results='hide',message=FALSE}

admission <- read_csv("data_input/Admission_Predict_Ver1.1.csv")

```

Checking the data

```{r, results='asis'}
knitr::kable(head(admission, 10))

```

<br>
<font size = "5">
The Data Explains : <br><br>
</font>
1. GRE Scores ( out of 340 ) <br>
2. TOEFL Scores ( out of 120 ) <br>
3. University Rating ( out of 5 ) <br>
4. Statement of Purpose and Letter of Recommendation Strength ( out of 5 ) <br>
5. Undergraduate GPA ( out of 10 ) <br>
6. Research Experience ( either 0 or 1 ) <br>
7. Chance of Admit ( ranging from 0 to 1 )

<br>

I'm changing the column names to something more code-friendly & our research column from numeric to a logical TRUE and FALSE
```{r}

names(admission) <- str_replace_all(str_to_lower(names(admission)), " ", "_")
admission[,"research"] <- as.logical(as.integer( unlist(admission[,"research"])))

```


## Separating Data to Train and Test

In order to test the model on later stage, I'll separate the dataset into 2, training and testing data with a ratio 8:2. 

```{r}

admission_train <- admission[1:400,]
admission_test <- admission[401:ncol(admission),]

```

<br>

# DATA ANALYSIS

Checking if any of the variables are linearly related to each other.

```{r, warning=FALSE,}

ggcorr(admission_train, label = T, hjust = .7, layout.exp = 1, label_size = 4, cex = 3)

```



Seeing that all variablers have a good correlation with each other except the serial number, I think we can move to modelling and exclude the serial number in our model.
<br>

# MODELLING

I'll make a linear model with the name `model_admission`
```{r}

model_admission <- lm(formula = chance_of_admit ~ gre_score + toefl_score + 
    university_rating + lor + cgpa + research, data = admission_train)

summary(model_admission)


```

I think I'm pretty happy with the resulting R squared and t value. The university rating has a lower t value but I personally think that it's an important variable, so I'll keep it inside the linear model. 

<br>


## Checking Our Assumption

### Normality


```{r}

hist(model_admission$residuals)
shapiro.test(model_admission$residuals)

```


### Homoscedacity


```{r}

plot(model_admission$fitted.values, model_admission$residuals)
abline(h = 0, col = "red")
bptest(model_admission)

```

Based on our bp test, there seemed to be abit of a pattern here, but looking at the graph, I think it's still acceptable.


### Multicolinearity

```{r}

vif(model_admission)

```

It seemed that our predictor variable does not correlate strongly with each other.

<br><br>

### Initial MSE and RMSE with training data

```{r}

MSE(y_pred = model_admission$fitted.values, y_true = admission_train$chance_of_admit)
RMSE(y_pred = model_admission$fitted.values, y_true = admission_train$chance_of_admit)


```

<br>

# PREDICTION

Using the model I've built, I will try to test it with the `admission_test` dataset that we've split before.
```{r}

admission_test$chance_admit_predict <- round(predict(object = model_admission, newdata = admission_test),2)

```

### MSE and RMSE value with test data
```{r}

MSE(y_pred = admission_test$chance_admit_predict, y_true = admission_test$chance_of_admit)
RMSE(y_pred = admission_test$chance_admit_predict, y_true = admission_test$chance_of_admit)

```
<br>

# CONCLUSION

Considering that our range of data is between `0.34` and `0.97`, I think my model have achieved a pretty good prediction result with average error value of `0.063`.

<br>

# CREDITS



The data is kindly provided by : Mohan S Acharya, Asfia Armaan, Aneeta S Antony : A Comparison of Regression Models for Prediction of Graduate Admissions, IEEE International Conference on Computational Intelligence in Data Science 2019