#Multiple Regression (Multiple_regress.txt)

#Y,   the number of people employed;
#X1,  the index;
#X2,  the percentage price deflation;
#X3,  the GNP in millions of dollars;
#X4,  the number of unemployed in thousands;
#X5,  the number of people employed by the military;
#X6,  the number of people over 14;
#X7,  the year.

## Define the directory where the data set is
setwd("/run/media/marcos/OS/UFMG/Disciplinas/mlg_mestrado/slides/analise de residuos/R/")

## Load the data set and prepare for use
data <- read.table("Multiple_regress.txt")
dimnames(data)[[2]] <- c("X1","X2","X3","X4","X5","X6","X7","Y")
data <- as.data.frame(data)

## Fit a multiple linear regression with the data
fit <- lm(Y~X2+X3+X4+X5+X6+X7, data=data)

X <- model.matrix(fit)

## Print the summary of the output of fit
summary(fit)

# CIs for model parameters
confint(fit, level=0.95)

## Plot Q-Q normal plot of the residuals
qqnorm(residuals(fit))

## Plot the residual x predicted value to validate the hypothesis
plot(x=predict(fit),y=residuals(fit))

## Perform the normal Shapiro-Wilk test for the residuals
shapiro.test(residuals(fit))


# Other useful functions
coefficients(fit) # model coefficients
confint(fit, level=0.95) # CIs for model parameters
fitted(fit) # predicted values
residuals(fit) # residuals
residuals(fit)/sqrt(sum(residuals(fit)^2)/(length(residuals(fit))-ncol(X)) # standadized residuals
rstandard(fit) # internaly studentized residuals
rstudent(fit) # externaly studentized residuals 
anova(fit) # anova table
vcov(fit) # covariance matrix for model parameters
influence(fit) # regression diagnostics
influence.measures(fit) # Table with the main influence measures
hatvalues(fit) # for the hat matrix diagonals
covratio(fit)
dffits(fit) #DFFITS
dfbetas(fit) #DFBETAS
cooks.distance(fit) #Cook's Distance

##For SAS anova table
source("SASAnova.R")
SASanova(fit)

##For VIF 
library("car")
vif(fit)

## Perform breush-pagan test for hetereocedascity
library(lmtest)
bptest(fit)

## Perform white test for hetereocedascity
library(bstats)
white.test(fit)