Six Airlines Analysis
Himanshu Dwivedi
22 December 2017
Basic Analysis
airline = read.csv(paste("SixAirlinesDataV2.csv", sep=""))
attach(airline)
head(airline)## Airline Aircraft FlightDuration TravelMonth IsInternational SeatsEconomy
## 1 British Boeing 12.25 Jul International 122
## 2 British Boeing 12.25 Aug International 122
## 3 British Boeing 12.25 Sep International 122
## 4 British Boeing 12.25 Oct International 122
## 5 British Boeing 8.16 Aug International 122
## 6 British Boeing 8.16 Sep International 122
## SeatsPremium PitchEconomy PitchPremium WidthEconomy WidthPremium
## 1 40 31 38 18 19
## 2 40 31 38 18 19
## 3 40 31 38 18 19
## 4 40 31 38 18 19
## 5 40 31 38 18 19
## 6 40 31 38 18 19
## PriceEconomy PricePremium PriceRelative SeatsTotal PitchDifference
## 1 2707 3725 0.38 162 7
## 2 2707 3725 0.38 162 7
## 3 2707 3725 0.38 162 7
## 4 2707 3725 0.38 162 7
## 5 1793 2999 0.67 162 7
## 6 1793 2999 0.67 162 7
## WidthDifference PercentPremiumSeats
## 1 1 24.69
## 2 1 24.69
## 3 1 24.69
## 4 1 24.69
## 5 1 24.69
## 6 1 24.69str(airline)## 'data.frame': 458 obs. of 18 variables:
## $ Airline : Factor w/ 6 levels "AirFrance","British",..: 2 2 2 2 2 2 2 2 2 2 ...
## $ Aircraft : Factor w/ 2 levels "AirBus","Boeing": 2 2 2 2 2 2 2 2 2 2 ...
## $ FlightDuration : num 12.25 12.25 12.25 12.25 8.16 ...
## $ TravelMonth : Factor w/ 4 levels "Aug","Jul","Oct",..: 2 1 4 3 1 4 3 1 4 4 ...
## $ IsInternational : Factor w/ 2 levels "Domestic","International": 2 2 2 2 2 2 2 2 2 2 ...
## $ SeatsEconomy : int 122 122 122 122 122 122 122 122 122 122 ...
## $ SeatsPremium : int 40 40 40 40 40 40 40 40 40 40 ...
## $ PitchEconomy : int 31 31 31 31 31 31 31 31 31 31 ...
## $ PitchPremium : int 38 38 38 38 38 38 38 38 38 38 ...
## $ WidthEconomy : int 18 18 18 18 18 18 18 18 18 18 ...
## $ WidthPremium : int 19 19 19 19 19 19 19 19 19 19 ...
## $ PriceEconomy : int 2707 2707 2707 2707 1793 1793 1793 1476 1476 1705 ...
## $ PricePremium : int 3725 3725 3725 3725 2999 2999 2999 2997 2997 2989 ...
## $ PriceRelative : num 0.38 0.38 0.38 0.38 0.67 0.67 0.67 1.03 1.03 0.75 ...
## $ SeatsTotal : int 162 162 162 162 162 162 162 162 162 162 ...
## $ PitchDifference : int 7 7 7 7 7 7 7 7 7 7 ...
## $ WidthDifference : int 1 1 1 1 1 1 1 1 1 1 ...
## $ PercentPremiumSeats: num 24.7 24.7 24.7 24.7 24.7 ...summary(airline)## 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(Filter(is.numeric,airline))## vars n mean sd median trimmed mad min
## FlightDuration 1 458 7.58 3.54 7.79 7.57 4.81 1.25
## SeatsEconomy 2 458 202.31 76.37 185.00 194.64 85.99 78.00
## SeatsPremium 3 458 33.65 13.26 36.00 33.35 11.86 8.00
## PitchEconomy 4 458 31.22 0.66 31.00 31.26 0.00 30.00
## PitchPremium 5 458 37.91 1.31 38.00 38.05 0.00 34.00
## WidthEconomy 6 458 17.84 0.56 18.00 17.81 0.00 17.00
## WidthPremium 7 458 19.47 1.10 19.00 19.53 0.00 17.00
## PriceEconomy 8 458 1327.08 988.27 1242.00 1244.40 1159.39 65.00
## PricePremium 9 458 1845.26 1288.14 1737.00 1799.05 1845.84 86.00
## PriceRelative 10 458 0.49 0.45 0.36 0.42 0.41 0.02
## SeatsTotal 11 458 235.96 85.29 227.00 228.73 90.44 98.00
## PitchDifference 12 458 6.69 1.76 7.00 6.76 0.00 2.00
## WidthDifference 13 458 1.63 1.19 1.00 1.53 0.00 0.00
## PercentPremiumSeats 14 458 14.65 4.84 13.21 14.31 2.68 4.71
## max range skew kurtosis se
## FlightDuration 14.66 13.41 -0.07 -1.12 0.17
## 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 0.23Plots
par(mfrow= c(1,2))
hist(PriceEconomy, breaks = 10)
hist(PricePremium, breaks = 10)
par(mfrow= c(1,2))
hist(SeatsEconomy, breaks = 10)
hist(SeatsPremium, breaks = 10)
par(mfrow= c(1,2))
hist(WidthEconomy, breaks = 10)
hist(WidthPremium, breaks = 10)
par(mfrow= c(1,2))
hist(PitchEconomy, breaks = 10)
hist(PitchPremium, breaks = 10)
library(lattice)
bwplot(PriceRelative~Airline, main = "Relative price difference of different Airline" , xlab = "Airline")
bwplot(PriceRelative~Aircraft, main = "Relative price difference of different Aircraft" , xlab = "Aircraft")
bwplot(PriceRelative~TravelMonth, main = "Relative price difference of different Travel month" , xlab = "Travel Month")
bwplot(PriceRelative~IsInternational, main = "Relative price difference of different types of Airline" , xlab = "Airline")
library(car)
scatterplot(PriceRelative~FlightDuration, cex = 0.9, pch=19, main = " Relative price difference vs Flight Duration")
scatterplot(PriceRelative~PercentPremiumSeats, cex = 0.9, pch=19, main = " Relative price difference vs Percent Premium Seats")
library(RColorBrewer)
mycolors <- brewer.pal(6,"Set1")
names(mycolors) <- levels(Airline)
scatterplotMatrix(~PriceRelative+SeatsTotal+PitchDifference+WidthDifference|Airline, data=airline , reg.line="" , smoother="", col=mycolors, smoother.args=list(col="grey") , cex=0.9 , pch=c(15,16,17,18,19,1) , main="Scatter Plot of difference between price, seats, width and pitch",legend.plot= FALSE)
legend(x="topright", legend = levels(Airline), col=mycolors, pch=c(15,16,17,18,19,1), cex = 0.67)
Correlations
round(cor(Filter(is.numeric, airline)),2)## FlightDuration SeatsEconomy SeatsPremium PitchEconomy
## FlightDuration 1.00 0.20 0.16 0.29
## SeatsEconomy 0.20 1.00 0.63 0.14
## SeatsPremium 0.16 0.63 1.00 -0.03
## PitchEconomy 0.29 0.14 -0.03 1.00
## PitchPremium 0.10 0.12 0.00 -0.55
## WidthEconomy 0.46 0.37 0.46 0.29
## WidthPremium 0.10 0.10 0.00 -0.54
## PriceEconomy 0.57 0.13 0.11 0.37
## PricePremium 0.65 0.18 0.22 0.23
## PriceRelative 0.12 0.00 -0.10 -0.42
## SeatsTotal 0.20 0.99 0.72 0.12
## PitchDifference -0.04 0.04 0.02 -0.78
## WidthDifference -0.12 -0.08 -0.22 -0.64
## PercentPremiumSeats 0.06 -0.33 0.49 -0.10
## PitchPremium WidthEconomy WidthPremium PriceEconomy
## FlightDuration 0.10 0.46 0.10 0.57
## SeatsEconomy 0.12 0.37 0.10 0.13
## SeatsPremium 0.00 0.46 0.00 0.11
## PitchEconomy -0.55 0.29 -0.54 0.37
## PitchPremium 1.00 -0.02 0.75 0.05
## WidthEconomy -0.02 1.00 0.08 0.07
## WidthPremium 0.75 0.08 1.00 -0.06
## PriceEconomy 0.05 0.07 -0.06 1.00
## PricePremium 0.09 0.15 0.06 0.90
## PriceRelative 0.42 -0.04 0.50 -0.29
## SeatsTotal 0.11 0.41 0.09 0.13
## PitchDifference 0.95 -0.13 0.76 -0.10
## WidthDifference 0.70 -0.39 0.88 -0.08
## PercentPremiumSeats -0.18 0.23 -0.18 0.07
## PricePremium PriceRelative SeatsTotal PitchDifference
## FlightDuration 0.65 0.12 0.20 -0.04
## SeatsEconomy 0.18 0.00 0.99 0.04
## SeatsPremium 0.22 -0.10 0.72 0.02
## PitchEconomy 0.23 -0.42 0.12 -0.78
## PitchPremium 0.09 0.42 0.11 0.95
## WidthEconomy 0.15 -0.04 0.41 -0.13
## WidthPremium 0.06 0.50 0.09 0.76
## PriceEconomy 0.90 -0.29 0.13 -0.10
## PricePremium 1.00 0.03 0.19 -0.02
## PriceRelative 0.03 1.00 -0.01 0.47
## SeatsTotal 0.19 -0.01 1.00 0.03
## PitchDifference -0.02 0.47 0.03 1.00
## WidthDifference -0.01 0.49 -0.11 0.76
## PercentPremiumSeats 0.12 -0.16 -0.22 -0.09
## WidthDifference PercentPremiumSeats
## FlightDuration -0.12 0.06
## SeatsEconomy -0.08 -0.33
## SeatsPremium -0.22 0.49
## PitchEconomy -0.64 -0.10
## PitchPremium 0.70 -0.18
## WidthEconomy -0.39 0.23
## WidthPremium 0.88 -0.18
## PriceEconomy -0.08 0.07
## PricePremium -0.01 0.12
## PriceRelative 0.49 -0.16
## SeatsTotal -0.11 -0.22
## PitchDifference 0.76 -0.09
## WidthDifference 1.00 -0.28
## PercentPremiumSeats -0.28 1.00library(corrgram)
corrgram(airline, order = TRUE, lower.panel = panel.shade, upper.panel = panel.pie)
Regressions
t.test(PriceRelative, PercentPremiumSeats)##
## Welch Two Sample t-test
##
## data: PriceRelative and PercentPremiumSeats
## t = -62.302, df = 464.91, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -14.60477 -13.71164
## sample estimates:
## mean of x mean of y
## 0.4872052 14.6454148fit = lm(PriceRelative ~ FlightDuration+SeatsEconomy+SeatsPremium+WidthEconomy+WidthPremium+PitchEconomy+PitchPremium, data = airline)
summary(fit)##
## Call:
## lm(formula = PriceRelative ~ FlightDuration + SeatsEconomy +
## SeatsPremium + WidthEconomy + WidthPremium + PitchEconomy +
## PitchPremium, data = airline)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.86549 -0.25418 -0.07713 0.14522 1.34717
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.8912366 1.7209126 4.004 7.27e-05 ***
## FlightDuration 0.0278757 0.0058374 4.775 2.43e-06 ***
## SeatsEconomy 0.0007934 0.0003168 2.505 0.0126 *
## SeatsPremium -0.0076652 0.0019421 -3.947 9.19e-05 ***
## WidthEconomy -0.0050452 0.0415730 -0.121 0.9035
## WidthPremium 0.1256658 0.0259356 4.845 1.74e-06 ***
## PitchEconomy -0.2606111 0.0411633 -6.331 5.90e-10 ***
## PitchPremium -0.0194938 0.0212963 -0.915 0.3605
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3689 on 450 degrees of freedom
## Multiple R-squared: 0.3401, Adjusted R-squared: 0.3299
## F-statistic: 33.14 on 7 and 450 DF, p-value: < 2.2e-16coefficients(fit)## (Intercept) FlightDuration SeatsEconomy SeatsPremium WidthEconomy
## 6.891236561 0.027875683 0.000793419 -0.007665192 -0.005045239
## WidthPremium PitchEconomy PitchPremium
## 0.125665753 -0.260611105 -0.019493820Summary
Analysis of six different airlines gives us the following inference about the price difference between premium and economy class-
- Price difference between economy and premium class depends upon the six different types of Airlines ie more difference in Jet, Virgin and Singapore flights
- International flights have more price difference than Domestic ones
- It does NOT depends much upon the type of aircraft or the month of travel
- Price difference is positively correlated with pitch difference, width difference but not upon the total seats
- As given by T-test the null hypothesis ie Percent of Premium Seats is independent to relative price difference is FALSE (p-value < 0.05)
- Regression of the variables gives that relative price difference depends upon Flight duration, Premium seats, Premium width, Economy pitch and slightly upon Economy Seats
It does not depend upon Economy width and Premium pitch (p-value > 0.05)
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