MINI PROJECT ON THE AIRLINE INDUSTRY
Devesh Patidar
Six <- read.csv(paste("SixAirlinesDataV2.csv", sep=""))
View(Six)
summary(Six)## 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. :24.69library(psych)
describe(Six)## vars n mean sd median trimmed mad min
## Airline* 1 458 3.01 1.65 2.00 2.89 1.48 1.00
## Aircraft* 2 458 1.67 0.47 2.00 1.71 0.00 1.00
## FlightDuration 3 458 7.58 3.54 7.79 7.57 4.81 1.25
## TravelMonth* 4 458 2.56 1.17 3.00 2.58 1.48 1.00
## IsInternational* 5 458 1.91 0.28 2.00 2.00 0.00 1.00
## SeatsEconomy 6 458 202.31 76.37 185.00 194.64 85.99 78.00
## SeatsPremium 7 458 33.65 13.26 36.00 33.35 11.86 8.00
## PitchEconomy 8 458 31.22 0.66 31.00 31.26 0.00 30.00
## PitchPremium 9 458 37.91 1.31 38.00 38.05 0.00 34.00
## WidthEconomy 10 458 17.84 0.56 18.00 17.81 0.00 17.00
## WidthPremium 11 458 19.47 1.10 19.00 19.53 0.00 17.00
## PriceEconomy 12 458 1327.08 988.27 1242.00 1244.40 1159.39 65.00
## PricePremium 13 458 1845.26 1288.14 1737.00 1799.05 1845.84 86.00
## PriceRelative 14 458 0.49 0.45 0.36 0.42 0.41 0.02
## SeatsTotal 15 458 235.96 85.29 227.00 228.73 90.44 98.00
## PitchDifference 16 458 6.69 1.76 7.00 6.76 0.00 2.00
## WidthDifference 17 458 1.63 1.19 1.00 1.53 0.00 0.00
## PercentPremiumSeats 18 458 14.65 4.84 13.21 14.31 2.68 4.71
## max range skew kurtosis se
## Airline* 6.00 5.00 0.61 -0.95 0.08
## Aircraft* 2.00 1.00 -0.72 -1.48 0.02
## FlightDuration 14.66 13.41 -0.07 -1.12 0.17
## TravelMonth* 4.00 3.00 -0.14 -1.46 0.05
## IsInternational* 2.00 1.00 -2.91 6.50 0.01
## SeatsEconomy 389.00 311.00 0.72 -0.36 3.57
## SeatsPremium 66.00 58.00 0.23 -0.46 0.62
## PitchEconomy 33.00 3.00 -0.03 -0.35 0.03
## PitchPremium 40.00 6.00 -1.51 3.52 0.06
## WidthEconomy 19.00 2.00 -0.04 -0.08 0.03
## WidthPremium 21.00 4.00 -0.08 -0.31 0.05
## PriceEconomy 3593.00 3528.00 0.51 -0.88 46.18
## PricePremium 7414.00 7328.00 0.50 0.43 60.19
## PriceRelative 1.89 1.87 1.17 0.72 0.02
## SeatsTotal 441.00 343.00 0.70 -0.53 3.99
## PitchDifference 10.00 8.00 -0.54 1.78 0.08
## WidthDifference 4.00 4.00 0.84 -0.53 0.06
## PercentPremiumSeats 24.69 19.98 0.71 0.28 0.23boxplot(Six)
attach(Six)Comparison of No. of Economy Seats to No. of Premium Seats
par(mfrow=c(1,2))
hist(SeatsEconomy,main="Economy Class Seats",col='blue')
hist(SeatsPremium, main="Premium Class Seats",col='blue')
par(mfrow=c(1,2))
boxplot(SeatsEconomy,col='blue',xlab="Economy Seats")
boxplot(SeatsPremium,col='blue', xlab="Premium Seats")
Comparison of Economy Seat Pitch with Premium Seat Pitch
par(mfrow=c(1,2))
hist(PitchEconomy,main="Economy Class Seat Pitch",col='blue')
hist(PitchPremium, main="Premium Class Seat Pitch",col='blue')
par(mfrow=c(1,2))
boxplot(PitchEconomy,col='blue',xlab="Pitch of Economy Seats")
boxplot(PitchPremium,col='blue', xlab="Pitch of Premium Seats")
Comparison of Economy Seat Width with Premium Seat Width
par(mfrow=c(1,2))
hist(WidthEconomy,main="Economy Class Seat Width",col='blue')
hist(WidthPremium, main="Premium Class Seat Width",col='blue')
par(mfrow=c(1,2))
boxplot(WidthEconomy,col='blue',xlab="Width of Economy Seats")
boxplot(WidthPremium,col='blue', xlab="Width of Premium Seats")
Comparison of Economy Seat Price with Premium Seat Price
par(mfrow=c(1,2))
hist(PriceEconomy,main="Economy Class Seat Price",col='blue')
hist(PricePremium, main="Premium Class Seat Price",col='blue')
par(mfrow=c(1,2))
boxplot(PriceEconomy,col='blue',xlab="Price of Economy Seats")
boxplot(PricePremium,col='blue', xlab="Price of Premium Seats")
library(car)##
## Attaching package: 'car'## The following object is masked from 'package:psych':
##
## logitScatterplot for Relative Price vs Percent Premium Seats
scatterplot(PriceRelative~PercentPremiumSeats,spread=FALSE, main="Relative Price vs Percent Premium Seats",xlab="Percent Premium Seats",ylab='Relative Price')
Scatterplot for Relative Price vs Width Difference
scatterplot(PriceRelative~WidthDifference,spread=FALSE, main="Relative Price vs Width Difference",xlab="Percent Premium Seats",ylab='Relative Price')
Scatterplot for Relative Price vs Pitch Difference
scatterplot(PriceRelative~PitchDifference,spread=FALSE, main="Relative Price vs Pitch Difference",xlab="Percent Premium Seats",ylab='Relative Price')
ScatterplotMatrix of Relative Price, Pitch Difference and Width Difference
scatterplotMatrix(~PriceRelative+PitchDifference+WidthDifference,data = Six, diagonal='histogram')
library(corrgram)
corrgram(Six,
main="Premium Class Analysis in Various Factors",
lower.panel=panel.shade, upper.panel=panel.pie,
diag.panel=panel.minmax, text.panel=panel.txt)
cor(Six[,6:18])## SeatsEconomy SeatsPremium PitchEconomy PitchPremium
## SeatsEconomy 1.000000000 0.625056587 0.14412692 0.119221250
## SeatsPremium 0.625056587 1.000000000 -0.03421296 0.004883123
## PitchEconomy 0.144126924 -0.034212963 1.00000000 -0.550606241
## PitchPremium 0.119221250 0.004883123 -0.55060624 1.000000000
## WidthEconomy 0.373670252 0.455782883 0.29448586 -0.023740873
## WidthPremium 0.102431959 -0.002717527 -0.53929285 0.750259029
## PriceEconomy 0.128167220 0.113642176 0.36866123 0.050384550
## PricePremium 0.177000928 0.217612376 0.22614179 0.088539147
## PriceRelative 0.003956939 -0.097196009 -0.42302204 0.417539056
## SeatsTotal 0.992607966 0.715171053 0.12373524 0.107512784
## PitchDifference 0.035318044 0.016365566 -0.78254993 0.950591466
## WidthDifference -0.080670148 -0.216168666 -0.63557430 0.703281797
## PercentPremiumSeats -0.330935223 0.485029771 -0.10280880 -0.175487414
## WidthEconomy WidthPremium PriceEconomy PricePremium
## SeatsEconomy 0.37367025 0.102431959 0.12816722 0.17700093
## SeatsPremium 0.45578288 -0.002717527 0.11364218 0.21761238
## PitchEconomy 0.29448586 -0.539292852 0.36866123 0.22614179
## PitchPremium -0.02374087 0.750259029 0.05038455 0.08853915
## WidthEconomy 1.00000000 0.081918728 0.06799061 0.15054837
## WidthPremium 0.08191873 1.000000000 -0.05704522 0.06402004
## PriceEconomy 0.06799061 -0.057045224 1.00000000 0.90138870
## PricePremium 0.15054837 0.064020043 0.90138870 1.00000000
## PriceRelative -0.04396116 0.504247591 -0.28856711 0.03184654
## SeatsTotal 0.40545860 0.091297500 0.13243313 0.19232533
## PitchDifference -0.12722421 0.760121272 -0.09952511 -0.01806629
## WidthDifference -0.39320512 0.884149655 -0.08449975 -0.01151218
## PercentPremiumSeats 0.22714172 -0.183312058 0.06532232 0.11639097
## PriceRelative SeatsTotal PitchDifference
## SeatsEconomy 0.003956939 0.99260797 0.03531804
## SeatsPremium -0.097196009 0.71517105 0.01636557
## PitchEconomy -0.423022038 0.12373524 -0.78254993
## PitchPremium 0.417539056 0.10751278 0.95059147
## WidthEconomy -0.043961160 0.40545860 -0.12722421
## WidthPremium 0.504247591 0.09129750 0.76012127
## PriceEconomy -0.288567110 0.13243313 -0.09952511
## PricePremium 0.031846537 0.19232533 -0.01806629
## PriceRelative 1.000000000 -0.01156894 0.46873025
## SeatsTotal -0.011568942 1.00000000 0.03416915
## PitchDifference 0.468730249 0.03416915 1.00000000
## WidthDifference 0.485802437 -0.10584398 0.76089108
## PercentPremiumSeats -0.161565556 -0.22091465 -0.09264869
## WidthDifference PercentPremiumSeats
## SeatsEconomy -0.08067015 -0.33093522
## SeatsPremium -0.21616867 0.48502977
## PitchEconomy -0.63557430 -0.10280880
## PitchPremium 0.70328180 -0.17548741
## WidthEconomy -0.39320512 0.22714172
## WidthPremium 0.88414965 -0.18331206
## PriceEconomy -0.08449975 0.06532232
## PricePremium -0.01151218 0.11639097
## PriceRelative 0.48580244 -0.16156556
## SeatsTotal -0.10584398 -0.22091465
## PitchDifference 0.76089108 -0.09264869
## WidthDifference 1.00000000 -0.27559416
## PercentPremiumSeats -0.27559416 1.00000000cor(PriceRelative,PitchDifference)## [1] 0.4687302cor(PriceRelative,WidthDifference)## [1] 0.4858024cor(PriceRelative,PricePremium)## [1] 0.03184654cor(PriceRelative, PriceEconomy)## [1] -0.2885671cor(PriceRelative,PercentPremiumSeats)## [1] -0.1615656Appropriate t-test
t.test(PriceRelative~Aircraft,Six)##
## Welch Two Sample t-test
##
## data: PriceRelative by Aircraft
## t = -2.6145, df = 363.72, p-value = 0.009306
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.18934647 -0.02678486
## sample estimates:
## mean in group AirBus mean in group Boeing
## 0.4147682 0.5228339Corr Test
cor.test(PriceRelative,PitchDifference,method="pearson")##
## Pearson's product-moment correlation
##
## data: PriceRelative and PitchDifference
## t = 11.331, df = 456, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.3940262 0.5372817
## sample estimates:
## cor
## 0.4687302cor.test(PriceRelative,WidthDifference,method="pearson")##
## Pearson's product-moment correlation
##
## data: PriceRelative and WidthDifference
## t = 11.869, df = 456, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.4125388 0.5528218
## sample estimates:
## cor
## 0.4858024cor.test(PriceRelative,SeatsEconomy,method="pearson")##
## Pearson's product-moment correlation
##
## data: PriceRelative and SeatsEconomy
## t = 0.084498, df = 456, p-value = 0.9327
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.08770167 0.09554911
## sample estimates:
## cor
## 0.003956939cor.test(PriceRelative,SeatsPremium,method="pearson")##
## Pearson's product-moment correlation
##
## data: PriceRelative and SeatsPremium
## t = -2.0854, df = 456, p-value = 0.03759
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.18715605 -0.00561924
## sample estimates:
## cor
## -0.09719601Regration Model
fit <- lm(PriceRelative ~ Airline+Aircraft+FlightDuration+TravelMonth+IsInternational+SeatsEconomy+SeatsPremium+PitchEconomy+PitchPremium+WidthEconomy+WidthPremium+PriceEconomy+PricePremium +PercentPremiumSeats+PitchDifference+WidthDifference+SeatsTotal, data =Six)
summary(fit)##
## Call:
## lm(formula = PriceRelative ~ Airline + Aircraft + FlightDuration +
## TravelMonth + IsInternational + SeatsEconomy + SeatsPremium +
## PitchEconomy + PitchPremium + WidthEconomy + WidthPremium +
## PriceEconomy + PricePremium + PercentPremiumSeats + PitchDifference +
## WidthDifference + SeatsTotal, data = Six)
##
## 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
## 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
## FlightDuration 2.613e-02 4.727e-03 5.526 5.63e-08 ***
## 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
## 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
## PriceEconomy -9.325e-04 3.318e-05 -28.105 < 2e-16 ***
## PricePremium 5.781e-04 2.294e-05 25.197 < 2e-16 ***
## 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
## ---
## 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-16The variables AirlineBritish, AirlineJet, AirlineSingapore, FlightDuration, TravelMonthOct, SeatsPremium, WidthEconomy, PriceEconomy and PricePremium are statically significant as their p-value < 0.05. Null hypothesis is rejected. The number of economy seats are much higher than the number of premium seats. We can also interpret that premium seats price has a positive effect on the relative price. From the above analysis the price of premium seats is greater than the price of economy seats due to more pitch and width in premium seats. Relative price mainly depends on the width of premium class seats and pitch difference.
fit<- lm(PriceRelative~PitchDifference+WidthDifference,Six)
summary(fit)##
## Call:
## lm(formula = PriceRelative ~ PitchDifference + WidthDifference,
## data = Six)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.84163 -0.28484 -0.07241 0.17698 1.18778
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.10514 0.08304 -1.266 0.206077
## PitchDifference 0.06019 0.01590 3.785 0.000174 ***
## WidthDifference 0.11621 0.02356 4.933 1.14e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3886 on 455 degrees of freedom
## Multiple R-squared: 0.2593, Adjusted R-squared: 0.2561
## F-statistic: 79.65 on 2 and 455 DF, p-value: < 2.2e-16We can reject the null hypothesis as both the p value are less than 0.05.It implies that both pitch difference and width difference have impact on relative price of the ticket.