Airlines
Adithya Nataraj G
22 December 2017
setwd("C:\\Users\\Adithya Nataraj\\Downloads")
air.df<-read.csv(paste("SixAirlinesDataV2.csv",sep =""))
View(air.df)
summary(air.df)## Airline Aircraft FlightDuration TravelMonth
## AirFrance: 74 AirBus:151 Min. : 1.250 Aug:127
## British :175 Boeing:307 1st Qu.: 4.260 Jul: 75
## Delta : 46 Median : 7.790 Oct:127
## Jet : 61 Mean : 7.578 Sep:129
## Singapore: 40 3rd Qu.:10.620
## Virgin : 62 Max. :14.660
## IsInternational SeatsEconomy SeatsPremium PitchEconomy
## Domestic : 40 Min. : 78.0 Min. : 8.00 Min. :30.00
## International:418 1st Qu.:133.0 1st Qu.:21.00 1st Qu.:31.00
## Median :185.0 Median :36.00 Median :31.00
## Mean :202.3 Mean :33.65 Mean :31.22
## 3rd Qu.:243.0 3rd Qu.:40.00 3rd Qu.:32.00
## Max. :389.0 Max. :66.00 Max. :33.00
## PitchPremium WidthEconomy WidthPremium PriceEconomy
## Min. :34.00 Min. :17.00 Min. :17.00 Min. : 65
## 1st Qu.:38.00 1st Qu.:18.00 1st Qu.:19.00 1st Qu.: 413
## Median :38.00 Median :18.00 Median :19.00 Median :1242
## Mean :37.91 Mean :17.84 Mean :19.47 Mean :1327
## 3rd Qu.:38.00 3rd Qu.:18.00 3rd Qu.:21.00 3rd Qu.:1909
## Max. :40.00 Max. :19.00 Max. :21.00 Max. :3593
## PricePremium PriceRelative SeatsTotal PitchDifference
## Min. : 86.0 Min. :0.0200 Min. : 98 Min. : 2.000
## 1st Qu.: 528.8 1st Qu.:0.1000 1st Qu.:166 1st Qu.: 6.000
## Median :1737.0 Median :0.3650 Median :227 Median : 7.000
## Mean :1845.3 Mean :0.4872 Mean :236 Mean : 6.688
## 3rd Qu.:2989.0 3rd Qu.:0.7400 3rd Qu.:279 3rd Qu.: 7.000
## Max. :7414.0 Max. :1.8900 Max. :441 Max. :10.000
## WidthDifference PercentPremiumSeats
## Min. :0.000 Min. : 4.71
## 1st Qu.:1.000 1st Qu.:12.28
## Median :1.000 Median :13.21
## Mean :1.633 Mean :14.65
## 3rd Qu.:3.000 3rd Qu.:15.36
## Max. :4.000 Max. :24.69Boxplots of the Variables
boxplot(air.df$FlightDuration, main="Duration of Flight")
boxplot(air.df$SeatsEconomy, main="Number of Economy Seats in the Aircraft")
boxplot(air.df$SeatsPremium, main="Number of Premium Economy Seats in the Aircraft")
boxplot(air.df$PitchEconomy, main="Distance between two consecutive Economy Seats")
boxplot(air.df$PitchPremium, main="Distance between two consecutive Premium Economy Seats")
boxplot(air.df$WidthEconomy, main="Width between armrests of an Economy Seat")
boxplot(air.df$WidthPremium, main="Width between armrests of a Premium Economy Seat")
boxplot(air.df$PriceEconomy, main="Price of Economy Seat")
boxplot(air.df$PricePremium, main="Price of Premium Economy Seat")
Various Scatterplots from the data
plot(air.df$Airline, air.df$SeatsEconomy, main="Airline vs No. of seats in Economy Class")
plot(air.df$Airline, air.df$SeatsPremium, main="Airline vs No. of seats in PremiumClass")
plot(air.df$Airline, air.df$TravelMonth, main="Airline vs Month of Travel")
plot(air.df$Airline, air.df$Aircraft, main="Airline vs Aircraft")
plot(air.df$Airline, air.df$SeatsTotal, main="Airline vs Total no. of seats")
plot(air.df$Airline, air.df$IsInternational, main="Airline vs Type of flight(Int. or Dom.)")
plot(air.df$Aircraft, air.df$IsInternational, main="Aircraft vs Type of flight(Int. or Dom.)")
plot(air.df$Airline, air.df$FlightDuration, main="Airline vs Duration of flight")
plot(air.df$Aircraft, air.df$FlightDuration, main="Aircraft vs Duration of flight")
plot(air.df$Airline, air.df$PriceEconomy, main="Airline vs Price of Economy Class ticket")
plot(air.df$Aircraft, air.df$PriceEconomy, main="Aircraft vs Price of Economy Class ticket")
plot(air.df$Airline, air.df$PricePremium, main="Airline vs Price of Premium Class ticket")
plot(air.df$Aircraft, air.df$PricePremium, main="Aircraft vs Price of Premium Class ticket")
Correlation Matrix of all the numerical variables
library(corrplot) ## corrplot 0.84 loadedcorrplot(corr=cor(air.df[ , c(3,6:18)], use="complete.obs"),
method ="ellipse")
Corrgram of all the variables
library(corrgram)
corrgram(air.df, order=TRUE,
main="Corrgram of all the Variables",
lower.panel=panel.shade, upper.panel=panel.pie,
diag.panel=panel.minmax, text.panel=panel.txt) 
Null hypothesis: The price of Economy ticket and Premium ticket are the same.
t.test(air.df$PriceEconomy, air.df$PricePremium)##
## Welch Two Sample t-test
##
## data: air.df$PriceEconomy and air.df$PricePremium
## t = -6.8304, df = 856.56, p-value = 1.605e-11
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -667.0831 -369.2793
## sample estimates:
## mean of x mean of y
## 1327.076 1845.258We can see that the p-value is lesser than 0.05 and hence the null hyphothesis is rejected. There is a significant difference between the Economy ticket price and Premium ticket price. Premium ticket price is more than Economy ticket price.
regr <- lm(PriceRelative ~ PriceEconomy + PricePremium + FlightDuration + SeatsEconomy + SeatsPremium + PitchEconomy + PitchPremium + WidthEconomy + WidthPremium + PercentPremiumSeats + PitchDifference + WidthDifference + SeatsTotal + Airline + Aircraft + TravelMonth + IsInternational, data = air.df)
summary(regr)##
## Call:
## lm(formula = PriceRelative ~ PriceEconomy + PricePremium + FlightDuration +
## SeatsEconomy + SeatsPremium + PitchEconomy + PitchPremium +
## WidthEconomy + WidthPremium + PercentPremiumSeats + PitchDifference +
## WidthDifference + SeatsTotal + Airline + Aircraft + TravelMonth +
## IsInternational, data = air.df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.76373 -0.08269 0.00438 0.08002 0.84672
##
## Coefficients: (3 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.993e-01 2.948e+00 -0.135 0.892302
## PriceEconomy -9.325e-04 3.318e-05 -28.105 < 2e-16 ***
## PricePremium 5.781e-04 2.294e-05 25.197 < 2e-16 ***
## FlightDuration 2.613e-02 4.727e-03 5.526 5.63e-08 ***
## SeatsEconomy 8.090e-04 5.462e-04 1.481 0.139313
## SeatsPremium -7.374e-03 3.615e-03 -2.040 0.041967 *
## PitchEconomy -1.756e-02 7.994e-02 -0.220 0.826207
## PitchPremium 5.960e-02 9.165e-02 0.650 0.515823
## WidthEconomy -9.207e-02 5.266e-02 -1.748 0.081085 .
## WidthPremium 4.904e-02 1.365e-01 0.359 0.719527
## PercentPremiumSeats 1.114e-02 7.653e-03 1.456 0.146197
## PitchDifference NA NA NA NA
## WidthDifference NA NA NA NA
## SeatsTotal NA NA NA NA
## AirlineBritish -3.971e-01 1.107e-01 -3.586 0.000373 ***
## AirlineDelta -3.865e-01 2.203e-01 -1.755 0.080020 .
## AirlineJet -2.584e-01 9.594e-02 -2.693 0.007354 **
## AirlineSingapore -3.535e-01 1.297e-01 -2.725 0.006685 **
## AirlineVirgin -3.575e-01 2.031e-01 -1.761 0.078997 .
## AircraftBoeing 4.003e-02 2.968e-02 1.349 0.178089
## TravelMonthJul 2.111e-02 3.145e-02 0.671 0.502475
## TravelMonthOct 2.778e-02 2.670e-02 1.041 0.298619
## TravelMonthSep -6.617e-03 2.664e-02 -0.248 0.803924
## IsInternationalInternational 2.785e-02 2.502e-01 0.111 0.911400
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2123 on 437 degrees of freedom
## Multiple R-squared: 0.7878, Adjusted R-squared: 0.7781
## F-statistic: 81.12 on 20 and 437 DF, p-value: < 2.2e-16regr$coefficients## (Intercept) PriceEconomy
## -0.3993377527 -0.0009324897
## PricePremium FlightDuration
## 0.0005781041 0.0261250335
## SeatsEconomy SeatsPremium
## 0.0008089538 -0.0073744940
## PitchEconomy PitchPremium
## -0.0175636803 0.0596015823
## WidthEconomy WidthPremium
## -0.0920739338 0.0490357851
## PercentPremiumSeats PitchDifference
## 0.0111406012 NA
## WidthDifference SeatsTotal
## NA NA
## AirlineBritish AirlineDelta
## -0.3971066460 -0.3865140546
## AirlineJet AirlineSingapore
## -0.2583533203 -0.3534833629
## AirlineVirgin AircraftBoeing
## -0.3575114105 0.0400301547
## TravelMonthJul TravelMonthOct
## 0.0211075134 0.0277808779
## TravelMonthSep IsInternationalInternational
## -0.0066168064 0.0278544004confint(regr)## 2.5 % 97.5 %
## (Intercept) -6.1929433320 5.3942678265
## PriceEconomy -0.0009976989 -0.0008672805
## PricePremium 0.0005330119 0.0006231963
## FlightDuration 0.0168339700 0.0354160970
## SeatsEconomy -0.0002645551 0.0018824627
## SeatsPremium -0.0144799061 -0.0002690820
## PitchEconomy -0.1746859016 0.1395585411
## PitchPremium -0.1205254829 0.2397286476
## WidthEconomy -0.1955718265 0.0114239588
## WidthPremium -0.2191781676 0.3172497379
## PercentPremiumSeats -0.0039009458 0.0261821482
## PitchDifference NA NA
## WidthDifference NA NA
## SeatsTotal NA NA
## AirlineBritish -0.6147350632 -0.1794782288
## AirlineDelta -0.8194540321 0.0464259229
## AirlineJet -0.4469062306 -0.0698004100
## AirlineSingapore -0.6084196676 -0.0985470581
## AirlineVirgin -0.7566003059 0.0415774849
## AircraftBoeing -0.0182983856 0.0983586951
## TravelMonthJul -0.0407034449 0.0829184718
## TravelMonthOct -0.0246876236 0.0802493793
## TravelMonthSep -0.0589659858 0.0457323729
## IsInternationalInternational -0.4638526936 0.5195614944Variables PriceEconomy, PricePremium, FlightDuration, AirlineBritish, AirlineJet, AirlineSingapore, SeatsPremium are Statistically significant with p<0.05.
Variables SeatsEconomy, PitchEconomy, PitchPremium, WidthEconomy, WidthPremium, AirlineDelta, AirlineVirgin, Travels Months - Jul, Oct and Sep are statistically insignificant with p>0.05.
The expected change in PriceRelative if the Price Economy changes by 1 rupee is -0.0009324897. The expected change in PriceRelative if the Price Premium changes by 1 rupee is 0.0005781041. The expected change in PriceRelative if the Flight Duration changes by 0.01hrs is 0.0261250335. The expected change in PriceRelative if the Economy Seats change by 1 is 0.0008089538. The expected change in PriceRelative if the PRemium Seats change by 1 is -0.0073744940. The expected change in PriceRelative if the width of an Economy seat changes by 1 is -0.0920739338. The expected change in PriceRelative if the width of a Premium seat changes by 1 is 0.0490357851.
It can be said from the regression analysis and correlation matrices that some variables are related more than the others. Flight duration was more linked to the price of a premium ticket than that of an economy ticket price. Total seats(Economy seats + Premium seats) was more linked to the number of economy seats than the number of premium seats. From this we can conclude that the number of economy seats far exceeded the number of premium seats in any airplane. Price relative ie. (PricePremium - PriceEconomy) / PriceEconomy changed in such a way according to the beta coefficients trend such that a positive change in Premium price had a positive effect on the relative price and a positive change in Economy price had a negative effect on the relative price. This analysis proves to be true due to the fact that the Economy price is only inversely related to the relative price and the premium price is directly related would only shoot up the value of the denominator. Further it can be seen that the relative price is never negative, hence the price of an economy ticket is lesser than that of a Premium ticket.