Regression Analaysis - SW Airlines Fare estimation

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Regression Analysis of Southwest Airlines Data to predict fares

The goal of the analysis is to predict the airfares for new routes

library(ggplot2) library(car) library(MASS) library(corrplot)

air_train<-read.csv(“E:\ISB\Term 2 - SA2\Assignment\airfares_train.csv”,header=TRUE)

air_test<-read.csv(“E:\ISB\Term 2 - SA2\Assignment\airfares_test.csv”,header=TRUE)

attach(air_train) colnames(air_train)

air_train

To check how many observations we have

nrow(air_train) version par(mfrow=c(1, 2)) boxplot(air_train\(COUPON, main="COUPON") #boxplot(air_train\)NEW, main=“NEW”) boxplot(air_train\(HI, main="HI") par(mfrow=c(3, 2)) boxplot(air_train\)S_INCOME, main=“S_INCOME”) boxplot(air_train\(E_INCOME, main="E_INCOME") boxplot(air_train\)S_POP, main=“S_POP”) boxplot(air_train\(E_POP, main="E_POP") boxplot(air_train\)DISTANCE, main=“DISTANCE”) par(mfrow=c(1, 2)) boxplot(air_train\(FARE, main="FARE") boxplot(air_train\)PAX, main=“PAX”)

dat <- data.frame(x = air_train\(FARE) ggplot(dat, aes(x=air_train\)FARE)) + geom_density(fill=“violet”)

Try logarithamic transformation of fare to see the normal distribution

dat <- data.frame(x = log(air_train\(FARE)) ggplot(dat, aes(x=log(air_train\)FARE))) + geom_density(fill=“violet”)

Impose Normal distribution on current one to see the over lap

norm<-rnorm(510, mean=mean(air_train\(FARE), sd=sd(air_train\)FARE)) dat <- data.frame(cond = factor(rep(c(“FARE”,“Normal”), each=510)), x = c(air_train$FARE,norm)) ggplot(dat, aes(x, fill=cond)) + geom_density(alpha=.3)

Impose Normal distribution on Logarithmic Graph

lnorm<-rnorm(510, mean=mean(log(air_train\(FARE)), sd=sd(log(air_train\)FARE))) dat <- data.frame(cond = factor(rep(c(“LFARE”,“Log Normal”), each=510)), x = c(log(air_train$FARE),lnorm)) ggplot(dat, aes(x, fill=cond)) + geom_density(alpha=.3)

scplotdata <- air_train[, sapply(air_train, is.numeric)]

pairs(scplotdata,col=“dodgerblue4”,pch=20)

Correlation Matrix

mcor<-round(cor(scplotdata),2) mcor library(corrplot) png(height=1200, width=1500, pointsize=20, file=“Correlation Matrix2.jpg”) corrplot(mcor)

updateR

model_1<-lm(air_train\(FARE ~ air_train\)COUPON+airlines_train\(NEW+air_train\)HI+ air_train\(S_INCOME+air_train\)E_INCOME+ air_train\(S_POP+air_train\)E_POP+air_train\(DISTANCE+ air_train\)PAX) summary(model_1)

qqPlot(model_1, main=“QQ Plot of residuals: Model_3”)

residual1 <- studres(model_1) hist(residual1, freq=FALSE, main=“Distribution of Studentized Residuals:Model_3”) xfit1<-seq(min(residual1),max(residual1),length=40) yfit1<-dnorm(xfit1) lines(xfit1, yfit1)

residualPlot(model_1, id.n=5)

residualPlots(model_1, id.n=5)

Transformations