library("ggplot2")
library("GGally")
library("gridExtra")
#Part B: Residuals and Transforms
#Exercise 1: Residuals Plot
#a - Obtain plot
#Obtain the Residuals vs Fitted Plot of the fitted model with an added horizontal line at
#y=0
#Do the points look randomly distributed about the line?
ToyotaPrices <- read.csv("C:/Users/aksha/Downloads/ToyotaPrices.csv")
names(ToyotaPrices)
## [1] "Id" "Price" "Age_08_04"
## [4] "Mfg_Month" "Mfg_Year" "KM"
## [7] "HP" "Automatic" "cc"
## [10] "Doors" "Cylinders" "Gears"
## [13] "Quarterly_Tax" "Weight" "Mfr_Guarantee"
## [16] "BOVAG_Guarantee" "Guarantee_Period" "ABS"
## [19] "Airbag_1" "Airbag_2" "Airco"
## [22] "Automatic_airco" "Boardcomputer" "CD_Player"
## [25] "Central_Lock" "Powered_Windows" "Power_Steering"
## [28] "Radio" "Mistlamps" "Sport_Model"
## [31] "Backseat_Divider" "Metallic_Rim" "Radio_cassette"
## [34] "Tow_Bar"
myData_PKWT = subset(ToyotaPrices, select = c(Price, KM, Weight, Tow_Bar))
#Exercise 1
fit = lm(Price~ KM + Weight + Tow_Bar, data= myData_PKWT)
plot(fit$fitted.values,fit$residuals)
abline(h=0,v=NULL)
#yes the points look randomly distributed about the line.
#Exercise 2
# b - Obtain plot using the z-scores of the resiudals
# Repeat the Residuals vs Fitted Plot using z-scores of the residuals.
# Add empirical rule horizontal lines at
# +2 and ???2. Use these lines to judge whether or not the residuals are normal or
# there are outliers. Point out any outliers. Point out any floor or ceiling effects. Do you think the residuals are normal?
x=fit$residuals
mean(x)
## [1] 1.60432e-12
y=(x-mean(x))/sd(x)
plot(y,fit$fitted.values)
abline(h=NULL,v=-2)
abline(h=NULL,v=2)
mod= fortify(fit)
plot1= qplot(.stdresid, data= mod , geom= "histogram")
plot2= qplot(.stdresid, data= mod , geom= "density")
plot3= qplot(sample=.stdresid, data= mod , geom= "qq") + geom_abline()
grid.arrange(plot1,plot2,plot3,nrow=1)
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
#The residuals normal and there are outliers that are present as well.
plot(floor(y),fit$fitted.values)
#If we have empirical rule between +2 and -2 then we have many outliers.
plot(ceiling(y),fit$fitted.values)
#If we have empirical rule betwwen +2 and -2 then we just have less outliers.
#Exercise 2
#2a
#a - The Plot
#Obtain the normal probability QQ-Plot of the residuals.
qqnorm(fit$residuals)
qqline(fit$residuals)
#2b - Normality
#Do the residuals look normal?
#the residuals look normal but there are some outliers
#Exercise 3
#3a - Obtain the composite goodness-of-fit plots
#Obtain the composite goodness-of-fit plots for the fitted model. What plots involve the residuals? Do the Residuals vs Fitted Plot and the Normal QQ-Plot look about the same as those obtained earlier?
plot(fit)
#Residuals vs Fitted Plots & Residuals vs leverage Plot involves residuals
#the Residuals vs Fitted Plot and the Normal QQ-PLot are the same as those obtained earlier
#3b-b - Outliers
#We examine the Residuals vs Leverage Plot in the composite goodness-of-fit plots. Outliers points will be identified by their row name. Are there any outliers? If so, what are their row names.
#Yes there are outliers
#602,961,222 are the row names of the outliers