Regression_split.Rmd

---
title: "Regression_Training_Test"
author: "Andrea Huerfano"
date: "September 21, 2019"
output: pdf_document
header-includes:
- \usepackage{float}
- \floatplacement{figure}{H}
---

```{r, warning=FALSE, message=FALSE, results=FALSE}
rm(list = ls(all.names = TRUE))
Packages <- c("GLMsData", "dplyr","GGally", "MASS", "zoo", "lmtest") 
lapply(Packages, library, character.only = TRUE)
set.seed(3)
source("Macros_Normal.txt")
```


```{r, message=FALSE, warning=FALSE}
AIS_f<-data(AIS)
```


This file is one of the regression analysis papers. Here you can find:

+ Plots
+ Correlations
+ Identifying the best model
+ Influence and leverage points
+ Residuals examination
+ Variance examination

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```

```{r}
colnames(AIS)
atletas<-subset(AIS,select = c("Sex","LBM", "Ht", "Wt", "BMI", "SSF"))
summary(atletas)
```
```{r}
ggpairs(atletas, columns = 1:ncol(atletas), title = "atlethes' variables behavior",
  axisLabels = "show", mapping = aes(colour=Sex,alpha = 5),
  upper = list(continuous = wrap("cor", size =3)), 
  lower = list(continuous = wrap("points", alpha = 0.9,    size=0.3)))
```

```{r}
fit <- lm(LBM ~ 1+Ht+Wt+BMI+SSF, data=atletas) ##No va sex pq no es cuanti
Correlaciones(fit,2,1,4,"")
```

```{r, fig.height=7,fig.pos='h'}
Correlaciones.parcial(fit,4,1,1,"")
```

```{r}

train_index <- sample(1:nrow(atletas), 0.8 * nrow(atletas))
test_index <- setdiff(1:nrow(atletas), train_index)
# Build X_train and X_test
X_train <- atletas[train_index,]
X_test <- atletas[test_index,]

```


```{r}
cor(X_train[,2:ncol(X_train)])
```
```{r, warning=FALSE, message=FALSE}
fit <- lm(LBM ~ 1 + Sex+Ht+Wt+BMI+log(SSF), data=X_train)
stepAIC(fit)

```
```{r}
fit2<-lm(formula = LBM ~ Sex + Wt + BMI + log(SSF),data = X_train)
summary(fit2)
```


```{r, echo=FALSE, fig.height=6,fig.pos='h'}
######## Leverage #####################################

#par(mfrow=c(6,1))
Leverage <- Leverage.normal(fit2,3,"")

######## Residuos #####################################
residuos <- Residuos.normal(fit2,3,"")

######## Influencia #####################################
influence <- Influence.normal(fit2,2,2,3,"")


######## QQ Plot y sus bandas de confianza ########
qqplot.normal(fit2,500,0.01,3,"")
```


```{r}
######## Evaluando homogeneidad de la varianza ########
######## Test de Breusch-pagan ########
bptest(fit2) ##Nula es homocedasticidad

```
 The Breusch-pagan's  test to examine the homogenicity in the variance is not rejected with a significant level of 5% 
```{r}
######## Evaluando NO correlación de los errores ########
######## Test de Durbin-Watson ########
dwtest(fit2)
```
 The autocorrelation between residuals is rejected at significant level of 5%
 
```{r}
Residual<-fit2$residuals
rev<-as.data.frame(cbind(X_train$Wt,X_train$BMI,log(X_train$SSF),Residual))
colnames(rev)=c("Wt", "BMI", "SSF", "Residual")
ggplot(data=rev,aes(BMI,Residual))+geom_point()
ggplot(data=rev,aes(Wt,Residual))+geom_point()
ggplot(data=rev,aes(SSF,Residual))+geom_point()

```
```{r}
rev<-predict(fit2,X_test,type = "response")
 X_test$predicted.classes<- round(rev,2) 
 X_test$indica<-'test'
 X_train$predicted.classes<- round(fit2$fitted.values,2) 
 X_train$indica<-'train'
 head(X_test,3)
 tail(X_test,3)
```
```{r}
error<-X_test$LBM-X_test$predicted.classes
sqrt(mean(error^2))
quantile(error)
boxplot(error)
sd(error)
```
 
 
```{r}
inside<-X_train$LBM-fit2$fitted.values
sqrt(mean(error^2))/sqrt(mean(inside^2))
quantile(inside)
boxplot(inside)
sd(inside)
```
 
 
```{r}
total<-rbind(X_train,X_test)
colnames(total)
ggplot(total,aes(LBM,predicted.classes, color=indica))+geom_point()
```