SixAirlines
Charanjeet Singh
February 16, 2018
1. Reading the Data
setwd("C:/Users/CJ With HP/Desktop/IIM Lucknow/Datasets")
airlines.df <- read.csv(paste("SixAirlinesDataV2.csv",sep = ""))
attach(airlines.df)2. Displaying summary statistics
summary(airlines.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. :24.69The dependent parameter on which we are going to work upon will be PriceRelative i.e. Relative difference in the price between Economy Tickets and Premium Tickets.
3. Creating a correlation Matrix
round(cor(airlines.df[,c(3,6:18)]),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 1.00We would be using boxplots and aggregate method to govern the relationship between PriceRelative and Categorical Variables.
4.Governing relation between PriceRelative and IsInternational
boxplot(PriceRelative~IsInternational)
aggregate(PriceRelative,by=list(IsInternational),mean)## Group.1 x
## 1 Domestic 0.0847500
## 2 International 0.5257177Conclusion: The relative price is 52% higher in case of International flights compared to only 8% higher in Domestic flights.
5.Governing relation between PriceRelative and Airline
boxplot(PriceRelative~Airline)
aggregate(PriceRelative,by=list(Airline),mean)## Group.1 x
## 1 AirFrance 0.2047297
## 2 British 0.4375429
## 3 Delta 0.1250000
## 4 Jet 0.9396721
## 5 Singapore 0.5297500
## 6 Virgin 0.7606452Conclusion: Jet Airwarys charge the highest relative price i.e. nearly 93% followed by Virgin and Singapore Airlines.
6.Governing relation between PriceRelative and Aircraft
boxplot(PriceRelative~Aircraft)
aggregate(PriceRelative,by=list(Aircraft),mean)## Group.1 x
## 1 AirBus 0.4147682
## 2 Boeing 0.5228339Conclusion: Boeing Aircraft has a higher relative price i.e. 52.28% compared to Airbus 41%.
7.Governing relation between PriceRelative and TravelMonth
boxplot(PriceRelative~TravelMonth)
aggregate(PriceRelative,by=list(TravelMonth,Airline),mean)## Group.1 Group.2 x
## 1 Aug AirFrance 0.16600000
## 2 Jul AirFrance 0.08583333
## 3 Oct AirFrance 0.27700000
## 4 Sep AirFrance 0.23909091
## 5 Aug British 0.42884615
## 6 Jul British 0.40875000
## 7 Oct British 0.47584906
## 8 Sep British 0.41685185
## 9 Aug Delta 0.14333333
## 10 Jul Delta 0.06400000
## 11 Oct Delta 0.14076923
## 12 Sep Delta 0.14181818
## 13 Aug Jet 0.94500000
## 14 Jul Jet 0.91000000
## 15 Oct Jet 1.08666667
## 16 Sep Jet 0.81666667
## 17 Aug Singapore 0.53090909
## 18 Jul Singapore 0.58875000
## 19 Oct Singapore 0.50800000
## 20 Sep Singapore 0.50545455
## 21 Aug Virgin 0.76437500
## 22 Jul Virgin 0.77357143
## 23 Oct Virgin 0.76062500
## 24 Sep Virgin 0.74562500Conclusion: The relative price is nearly same across each month for each Airline, with the rates in October being a little higher.
Now,we would be comparing Relative Price with continous varibales.
8. Governing relation between PriceRelative and WidthDifference
boxplot(PriceRelative~WidthDifference)
cor.test(PriceRelative,WidthDifference)##
## 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
## 0.48580249. Governing relation between PriceRelative and PitchDifference
boxplot(PriceRelative~PitchDifference)
cor.test(PriceRelative,PitchDifference)##
## 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
## 0.4687302Conclusion: Width Difference and Pitch Difference are highly correlated with Relative Price.
10. Running Regression to check the Hypothesis whether Relative Price is statistically determined by the independent Variables or not.
fit<- lm(PriceRelative~SeatsPremium + PercentPremiumSeats + WidthDifference + PitchDifference + FlightDuration)
summary(fit)##
## Call:
## lm(formula = PriceRelative ~ SeatsPremium + PercentPremiumSeats +
## WidthDifference + PitchDifference + FlightDuration)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.81065 -0.30092 -0.04026 0.15425 1.13516
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.172716 0.101757 -1.697 0.090322 .
## SeatsPremium -0.001436 0.001600 -0.897 0.370012
## PercentPremiumSeats -0.004351 0.004310 -1.009 0.313316
## WidthDifference 0.113092 0.025197 4.488 9.12e-06 ***
## PitchDifference 0.062545 0.016327 3.831 0.000146 ***
## FlightDuration 0.022297 0.005128 4.348 1.70e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3811 on 452 degrees of freedom
## Multiple R-squared: 0.2925, Adjusted R-squared: 0.2847
## F-statistic: 37.38 on 5 and 452 DF, p-value: < 2.2e-16Conclusion: The relative Price is strongly determined by the three continous variables namely WidthDifference, Pitch Difference and Flight Duration, and the variables are positively correlated to the Relative Price. Howerver number of premium seats or percentage of premium seats are not statically significant in the determination of Relative Price.
Therefore Answer to the Question:
What factors explain the difference in price between an economy ticket and a premium-economy airline ticket? is:
The type of Airline, Aircraft, the month of travel, the domestic or the international travel are the categorical factors which determine the difference in price between an economy ticket and a premium-economy airline ticket. Similary, The relative Price is strongly determined by the three continous variables namely WidthDifference, Pitch Difference and Flight Duration.