Airline Pricing Analysis
Madhurish Gupta
December 23, 2017
Reading Dataset
airlines <- read.csv('SixAirlinesDataV2.csv')Summarising data
summary(airlines)## 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. :24.69Describing Data
library(psych)## Warning: package 'psych' was built under R version 3.4.3describe(airlines)## 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
boxplot(airlines$FlightDuration,
main="FlightDuration",
xlab="Number")
boxplot(airlines$SeatsEconomy,
main="SeatsEconomy",
xlab="Number")
boxplot(airlines$SeatsPremium,
main="SeatsPremium",
xlab="Number")
boxplot(airlines$PitchEconomy,
main="PitchEconomy",
xlab="Number")
boxplot(airlines$PitchPremium,
main="PitchPremium",
xlab="Number")
boxplot(airlines$WidthEconomy,
main="WidthEconomy",
xlab="Number")
boxplot(airlines$WidthPremium,
main="WidthPremium",
xlab="Number")
boxplot(airlines$PriceEconomy,
main="PriceEconomy",
xlab="Number")
boxplot(airlines$PricePremium,
main="PricePremium",
xlab="Number")
boxplot(airlines$PriceRelative,
main="PriceRelative",
xlab="Number")
boxplot(airlines$SeatsTotal,
main="SeatsTotal",
xlab="Number")
boxplot(airlines$PitchDifference,
main="PitchDifference",
xlab="Number")
boxplot(airlines$WidthDifference,
main="WidthDifference",
xlab="Number")
boxplot(airlines$PercentPremiumSeats,
main="PercentPremiumSeats",
xlab="Number")
#BarPlots
counts <- table(airlines$FlightDuration)
barplot(counts, main="Analising",
xlab="Flight Duration")
#ScatterPlot
pairs(~ FlightDuration + SeatsEconomy
+ SeatsPremium + PitchEconomy + PitchPremium + WidthEconomy + WidthPremium + PriceEconomy + PricePremium + PriceRelative + SeatsTotal + PitchDifference + WidthDifference + PercentPremiumSeats
,data=airlines, main="Simple Scatterplot Matrix")
#Corrgram
library(corrgram)## Warning: package 'corrgram' was built under R version 3.4.3corrgram(airlines, order=TRUE, lower.panel=panel.shade,
upper.panel=panel.pie, text.panel=panel.txt,
main="Car Milage Data in PC2/PC1 Order")
library(corpcor)
library(tseries)## Warning: package 'tseries' was built under R version 3.4.3al <- as.matrix(airlines[,c(3,6:18)])
covmat = cov(al)
covmat## FlightDuration SeatsEconomy SeatsPremium
## FlightDuration 12.5462183 52.9194291 7.57372426
## SeatsEconomy 52.9194291 5832.9154300 633.07060954
## SeatsPremium 7.5737243 633.0706095 175.86521648
## PitchEconomy 0.6817421 7.2117665 -0.29725856
## PitchPremium 0.4477835 11.9637325 0.08508595
## WidthEconomy 0.9014224 15.9105138 3.36977440
## WidthPremium 0.4019845 8.5832800 -0.03954019
## PriceEconomy 1983.5401655 9673.7944684 1489.38359627
## PricePremium 2959.9783043 17413.2541733 3717.36428960
## PriceRelative 0.1932368 0.1361699 -0.58078765
## SeatsTotal 60.4931534 6465.9860396 808.93582602
## PitchDifference -0.2339587 4.7519660 0.38234451
## WidthDifference -0.4994380 -7.3272338 -3.40931459
## PercentPremiumSeats 1.0379912 -122.3914537 31.14753127
## PitchEconomy PitchPremium WidthEconomy WidthPremium
## FlightDuration 0.6817421 0.44778348 0.90142242 0.40198446
## SeatsEconomy 7.2117665 11.96373253 15.91051379 8.58327998
## SeatsPremium -0.2972586 0.08508595 3.36977440 -0.03954019
## PitchEconomy 0.4292471 -0.47398546 0.10756500 -0.38766208
## PitchPremium -0.4739855 1.72639580 -0.01739081 1.08157435
## WidthEconomy 0.1075650 -0.01739081 0.31081765 0.05010845
## WidthPremium -0.3876621 1.08157435 0.05010845 1.20378776
## PriceEconomy 238.7031905 65.42513354 37.46095191 -61.85450011
## PricePremium 190.8517195 149.85356368 108.11611707 90.47997668
## PriceRelative -0.1248808 0.24719874 -0.01104335 0.24928593
## SeatsTotal 6.9145079 12.04881848 19.28028819 8.54373979
## PitchDifference -0.9032326 2.20038126 -0.12495581 1.46923643
## WidthDifference -0.4952271 1.09896515 -0.26070920 1.15367930
## PercentPremiumSeats -0.3261739 -1.11655834 0.61321816 -0.97393787
## PriceEconomy PricePremium PriceRelative
## FlightDuration 1983.54017 2959.97830 0.19323683
## SeatsEconomy 9673.79447 17413.25417 0.13616991
## SeatsPremium 1489.38360 3717.36429 -0.58078765
## PitchEconomy 238.70319 190.85172 -0.12488080
## PitchPremium 65.42513 149.85356 0.24719874
## WidthEconomy 37.46095 108.11612 -0.01104335
## WidthPremium -61.85450 90.47998 0.24928593
## PriceEconomy 976684.06198 1147494.76801 -128.49991725
## PricePremium 1147494.76801 1659293.11947 18.48428836
## PriceRelative -128.49992 18.48429 0.20302893
## SeatsTotal 11163.17806 21130.61846 -0.44461774
## PitchDifference -173.27806 -40.99816 0.37207954
## WidthDifference -99.31545 -17.63614 0.26032928
## PercentPremiumSeats 312.61077 726.01582 -0.35252750
## SeatsTotal PitchDifference WidthDifference
## FlightDuration 60.4931534 -0.2339587 -0.4994380
## SeatsEconomy 6465.9860396 4.7519660 -7.3272338
## SeatsPremium 808.9358260 0.3823445 -3.4093146
## PitchEconomy 6.9145079 -0.9032326 -0.4952271
## PitchPremium 12.0488185 2.2003813 1.0989652
## WidthEconomy 19.2802882 -0.1249558 -0.2607092
## WidthPremium 8.5437398 1.4692364 1.1536793
## PriceEconomy 11163.1780647 -173.2780570 -99.3154520
## PricePremium 21130.6184629 -40.9981558 -17.6361404
## PriceRelative -0.4446177 0.3720795 0.2603293
## SeatsTotal 7274.9218656 5.1343105 -10.7365484
## PitchDifference 5.1343105 3.1036138 1.5941922
## WidthDifference -10.7365484 1.5941922 1.4143885
## PercentPremiumSeats -91.2439224 -0.7903844 -1.5871560
## PercentPremiumSeats
## FlightDuration 1.0379912
## SeatsEconomy -122.3914537
## SeatsPremium 31.1475313
## PitchEconomy -0.3261739
## PitchPremium -1.1165583
## WidthEconomy 0.6132182
## WidthPremium -0.9739379
## PriceEconomy 312.6107669
## PricePremium 726.0158229
## PriceRelative -0.3525275
## SeatsTotal -91.2439224
## PitchDifference -0.7903844
## WidthDifference -1.5871560
## PercentPremiumSeats 23.4493343cov2cor(covmat)## FlightDuration SeatsEconomy SeatsPremium PitchEconomy
## FlightDuration 1.00000000 0.195621187 0.161236400 0.29377174
## SeatsEconomy 0.19562119 1.000000000 0.625056587 0.14412692
## SeatsPremium 0.16123640 0.625056587 1.000000000 -0.03421296
## PitchEconomy 0.29377174 0.144126924 -0.034212963 1.00000000
## PitchPremium 0.09621471 0.119221250 0.004883123 -0.55060624
## WidthEconomy 0.45647720 0.373670252 0.455782883 0.29448586
## WidthPremium 0.10343747 0.102431959 -0.002717527 -0.53929285
## PriceEconomy 0.56664039 0.128167220 0.113642176 0.36866123
## PricePremium 0.64873981 0.177000928 0.217612376 0.22614179
## PriceRelative 0.12107501 0.003956939 -0.097196009 -0.42302204
## SeatsTotal 0.20023299 0.992607966 0.715171053 0.12373524
## PitchDifference -0.03749288 0.035318044 0.016365566 -0.78254993
## WidthDifference -0.11856070 -0.080670148 -0.216168666 -0.63557430
## PercentPremiumSeats 0.06051625 -0.330935223 0.485029771 -0.10280880
## PitchPremium WidthEconomy WidthPremium PriceEconomy
## FlightDuration 0.096214708 0.45647720 0.103437469 0.56664039
## SeatsEconomy 0.119221250 0.37367025 0.102431959 0.12816722
## SeatsPremium 0.004883123 0.45578288 -0.002717527 0.11364218
## PitchEconomy -0.550606241 0.29448586 -0.539292852 0.36866123
## PitchPremium 1.000000000 -0.02374087 0.750259029 0.05038455
## WidthEconomy -0.023740873 1.00000000 0.081918728 0.06799061
## WidthPremium 0.750259029 0.08191873 1.000000000 -0.05704522
## PriceEconomy 0.050384550 0.06799061 -0.057045224 1.00000000
## PricePremium 0.088539147 0.15054837 0.064020043 0.90138870
## PriceRelative 0.417539056 -0.04396116 0.504247591 -0.28856711
## SeatsTotal 0.107512784 0.40545860 0.091297500 0.13243313
## PitchDifference 0.950591466 -0.12722421 0.760121272 -0.09952511
## WidthDifference 0.703281797 -0.39320512 0.884149655 -0.08449975
## PercentPremiumSeats -0.175487414 0.22714172 -0.183312058 0.06532232
## PricePremium PriceRelative SeatsTotal PitchDifference
## FlightDuration 0.64873981 0.121075014 0.20023299 -0.03749288
## SeatsEconomy 0.17700093 0.003956939 0.99260797 0.03531804
## SeatsPremium 0.21761238 -0.097196009 0.71517105 0.01636557
## PitchEconomy 0.22614179 -0.423022038 0.12373524 -0.78254993
## PitchPremium 0.08853915 0.417539056 0.10751278 0.95059147
## WidthEconomy 0.15054837 -0.043961160 0.40545860 -0.12722421
## WidthPremium 0.06402004 0.504247591 0.09129750 0.76012127
## PriceEconomy 0.90138870 -0.288567110 0.13243313 -0.09952511
## PricePremium 1.00000000 0.031846537 0.19232533 -0.01806629
## PriceRelative 0.03184654 1.000000000 -0.01156894 0.46873025
## SeatsTotal 0.19232533 -0.011568942 1.00000000 0.03416915
## PitchDifference -0.01806629 0.468730249 0.03416915 1.00000000
## WidthDifference -0.01151218 0.485802437 -0.10584398 0.76089108
## PercentPremiumSeats 0.11639097 -0.161565556 -0.22091465 -0.09264869
## WidthDifference PercentPremiumSeats
## FlightDuration -0.11856070 0.06051625
## 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 1.00000000Linear Regression Model
a <- lm( formula = PriceRelative ~ SeatsEconomy +SeatsPremium+ PitchEconomy+ PitchPremium+ WidthEconomy+ WidthPremium+ PriceEconomy+ PricePremium+
FlightDuration+SeatsTotal +PitchDifference+ WidthDifference +PercentPremiumSeats , data = airlines)
summary(a)##
## Call:
## lm(formula = PriceRelative ~ SeatsEconomy + SeatsPremium + PitchEconomy +
## PitchPremium + WidthEconomy + WidthPremium + PriceEconomy +
## PricePremium + FlightDuration + SeatsTotal + PitchDifference +
## WidthDifference + PercentPremiumSeats, data = airlines)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.77611 -0.10464 0.00752 0.07428 0.84432
##
## Coefficients: (3 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -5.091e+00 1.108e+00 -4.594 5.66e-06 ***
## SeatsEconomy 1.768e-03 5.264e-04 3.358 0.000851 ***
## SeatsPremium -1.501e-02 3.131e-03 -4.793 2.25e-06 ***
## PitchEconomy 1.085e-01 2.824e-02 3.840 0.000141 ***
## PitchPremium 1.151e-01 1.349e-02 8.530 2.28e-16 ***
## WidthEconomy -1.998e-01 2.878e-02 -6.940 1.39e-11 ***
## WidthPremium 5.969e-02 1.602e-02 3.725 0.000220 ***
## PriceEconomy -8.462e-04 2.939e-05 -28.788 < 2e-16 ***
## PricePremium 5.500e-04 2.253e-05 24.410 < 2e-16 ***
## FlightDuration 2.163e-02 4.490e-03 4.817 2.00e-06 ***
## SeatsTotal NA NA NA NA
## PitchDifference NA NA NA NA
## WidthDifference NA NA NA NA
## PercentPremiumSeats 2.211e-02 7.480e-03 2.956 0.003285 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2187 on 447 degrees of freedom
## Multiple R-squared: 0.7695, Adjusted R-squared: 0.7643
## F-statistic: 149.2 on 10 and 447 DF, p-value: < 2.2e-16