Concussions_Variable_Selection.Rmd

---
title: "Project 3 Data Analytics"
author: "Skylar Furey"
output: pdf_document
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = T, comment = NA, message = FALSE,fig.width=7, fig.height=4)
```

```{r}
library(ISLR)
library(leaps)
Concussions <- read.csv("~/Desktop/Data Mining/STT450_R_Folder/Concussion.csv", header = TRUE)
Concussions$Position = as.factor(Concussions$Position)
Concussions$Team = as.factor(Concussions$Team)
Concussions$Season = as.factor(Concussions$Season)
Concussions$Winning_Team = as.factor(Concussions$Winning_Team)
```

## Best #

```{r}
regfit.full=regsubsets(Playtime_After~Playtime_Before+Winning_Team+Games_Missed,Concussions)
summary(regfit.full)
```

```{r}
reg.summary=summary(regfit.full)
reg.summary$rsq
```

```{r}
par(mfrow=c(2,2))
plot(reg.summary$adjr2,xlab="Number of Variables",ylab="Adjusted RSq",type="l")
which.max(reg.summary$adjr2)
points(2,reg.summary$adjr2[2], col="red",cex=2,pch=20)
plot(reg.summary$cp,xlab="Number of Variables",ylab="Cp",type='l')
which.min(reg.summary$cp)
points(2,reg.summary$cp[2],col="red",cex=2,pch=20)
which.min(reg.summary$bic)
plot(reg.summary$bic,xlab="Number of Variables",ylab="BIC",type='l')
points(2,reg.summary$bic[2],col="red",cex=2,pch=20)
```

```{r}
plot(regfit.full,scale="adjr2")
```

```{r}
plot(regfit.full,scale="Cp")
```

```{r}
plot(regfit.full,scale="bic")
```

## Forward #

```{r}
regfit.fwd=regsubsets(Playtime_After~Playtime_Before+Winning_Team+Games_Missed,Concussions,method="forward")
summary(regfit.fwd)
```

## Backward #

```{r}
regfit.bwd=regsubsets(Playtime_After~Playtime_Before+Winning_Team+Games_Missed,Concussions, method="backward")
summary(regfit.bwd)
```

## Coefficients #

```{r}
coef(regfit.full,3)
```
```{r}
coef(regfit.fwd,3)
```
```{r}
coef(regfit.bwd,3)
```