SixAirlines
Ashutosh Kumar
January 19, 2018
sixAirlines <- read.csv(paste("SixAirlinesDataV2.csv", sep=""))
View(sixAirlines)library(psych)
summary(sixAirlines)## 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(corrplot)## corrplot 0.84 loadedlibrary(corrgram)
str(sixAirlines)## '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 ...boxplot(sixAirlines$SeatsEconomy, xlab= "Seats Economy", ylab = "Seats Economy", main= "Seats Economy distribution", horizontal = TRUE)
boxplot(sixAirlines$SeatsPremium, xlab= "Seats Premium", ylab = "Seats Premium", main= "Seats Premium distribution", horizontal = TRUE)
boxplot(sixAirlines$PitchEconomy, xlab= "Pitch Economy", ylab = "Pitch Economy", main= "Pitch Economy distribution", horizontal = TRUE)
boxplot(sixAirlines$PitchPremium, xlab= "PitchPremium", ylab = "PitchPremium", main= "PitchPremium distribution", horizontal = TRUE)
boxplot(sixAirlines$WidthEconomy, xlab= "WidthEconomy", ylab = "WidthEconomy", main= "WidthEconomy distribution", horizontal = TRUE)
boxplot(sixAirlines$WidthPremium, xlab= "WidthPremium", ylab = "WidthPremium", main= "WidthPremium distribution", horizontal = TRUE)
boxplot(sixAirlines$WidthPremium, xlab= "WidthPremium", ylab = "WidthPremium", main= "WidthPremium distribution", horizontal = TRUE)
boxplot(sixAirlines$PricePremium , xlab= "PricePremium ", ylab = "PricePremium ", main= "PricePremium distribution", horizontal = TRUE)
boxplot(sixAirlines$PriceRelative, xlab= "PriceRelative", ylab = "PriceRelative", main= "PriceRelative distribution", horizontal = TRUE)
boxplot(sixAirlines$SeatsTotal, xlab= "SeatsTotal", ylab = "SeatsTotal", main= "SeatsTotal distribution", horizontal = TRUE)
boxplot(sixAirlines$PitchDifference, xlab= "PitchDifference", ylab = "PitchDifference", main= "PitchDifference distribution", horizontal = TRUE)
boxplot(sixAirlines$WidthDifference, xlab= "WidthDifference", ylab = "WidthDifference", main= "WidthDifference distribution", horizontal = TRUE)
boxplot(sixAirlines$PercentPremiumSeats, xlab= "PercentPremiumSeats", ylab = "PercentPremiumSeats", main= "PercentPremiumSeats distribution", horizontal = TRUE)
plot(x=sixAirlines$SeatsEconomy,y=sixAirlines$PitchEconomy, xlab= "Seats Economy", ylab = "Pitch Economy")
plot(x=sixAirlines$SeatsPremium,y=sixAirlines$PitchPremium, xlab= "Seats Premium", ylab = "Pitch Premium")
plot(x=sixAirlines$SeatsEconomy,y=sixAirlines$WidthEconomy, xlab= "Seats Economy", ylab = "Width Economy")
plot(x=sixAirlines$SeatsPremium,y=sixAirlines$WidthPremium, xlab= "Seats Premium", ylab = "Width Premmium")
plot(x=sixAirlines$PitchEconomy,y=sixAirlines$PriceEconomy, xlab= "Pitch Economy", ylab = "Price Economy")
plot(x=sixAirlines$PitchPremium,y=sixAirlines$PricePremium, xlab= "Pitch Premium", ylab = "Price Premium")
plot(x=sixAirlines$WidthEconomy,y=sixAirlines$PriceEconomy, xlab= "Width Economy", ylab = "Price Economy")
plot(x=sixAirlines$WidthPremium,y=sixAirlines$PricePremium, xlab= "Width Premium", ylab = "Price Premium")
plot(x=sixAirlines$PitchDifference,y=sixAirlines$PriceRelative, xlab= "Pitch Difference", ylab = "Price Relative")
plot(x=sixAirlines$WidthDifference,y=sixAirlines$PriceRelative, xlab= "Width Difference", ylab = "Price Relative")
plot(x=sixAirlines$PercentPremiumSeats,y=sixAirlines$PriceRelative, xlab= "Percent premium Seats", ylab = "Price Relative")
library(corrplot)
library(corrgram)
mytable <- sixAirlines[,6:18]
cov(mytable)## SeatsEconomy SeatsPremium PitchEconomy PitchPremium
## SeatsEconomy 5832.9154300 633.07060954 7.2117665 11.96373253
## SeatsPremium 633.0706095 175.86521648 -0.2972586 0.08508595
## PitchEconomy 7.2117665 -0.29725856 0.4292471 -0.47398546
## PitchPremium 11.9637325 0.08508595 -0.4739855 1.72639580
## WidthEconomy 15.9105138 3.36977440 0.1075650 -0.01739081
## WidthPremium 8.5832800 -0.03954019 -0.3876621 1.08157435
## PriceEconomy 9673.7944684 1489.38359627 238.7031905 65.42513354
## PricePremium 17413.2541733 3717.36428960 190.8517195 149.85356368
## PriceRelative 0.1361699 -0.58078765 -0.1248808 0.24719874
## SeatsTotal 6465.9860396 808.93582602 6.9145079 12.04881848
## PitchDifference 4.7519660 0.38234451 -0.9032326 2.20038126
## WidthDifference -7.3272338 -3.40931459 -0.4952271 1.09896515
## PercentPremiumSeats -122.3914537 31.14753127 -0.3261739 -1.11655834
## WidthEconomy WidthPremium PriceEconomy PricePremium
## SeatsEconomy 15.91051379 8.58327998 9673.79447 17413.25417
## SeatsPremium 3.36977440 -0.03954019 1489.38360 3717.36429
## PitchEconomy 0.10756500 -0.38766208 238.70319 190.85172
## PitchPremium -0.01739081 1.08157435 65.42513 149.85356
## WidthEconomy 0.31081765 0.05010845 37.46095 108.11612
## WidthPremium 0.05010845 1.20378776 -61.85450 90.47998
## PriceEconomy 37.46095191 -61.85450011 976684.06198 1147494.76801
## PricePremium 108.11611707 90.47997668 1147494.76801 1659293.11947
## PriceRelative -0.01104335 0.24928593 -128.49992 18.48429
## SeatsTotal 19.28028819 8.54373979 11163.17806 21130.61846
## PitchDifference -0.12495581 1.46923643 -173.27806 -40.99816
## WidthDifference -0.26070920 1.15367930 -99.31545 -17.63614
## PercentPremiumSeats 0.61321816 -0.97393787 312.61077 726.01582
## PriceRelative SeatsTotal PitchDifference
## SeatsEconomy 0.13616991 6465.9860396 4.7519660
## SeatsPremium -0.58078765 808.9358260 0.3823445
## PitchEconomy -0.12488080 6.9145079 -0.9032326
## PitchPremium 0.24719874 12.0488185 2.2003813
## WidthEconomy -0.01104335 19.2802882 -0.1249558
## WidthPremium 0.24928593 8.5437398 1.4692364
## PriceEconomy -128.49991725 11163.1780647 -173.2780570
## PricePremium 18.48428836 21130.6184629 -40.9981558
## PriceRelative 0.20302893 -0.4446177 0.3720795
## SeatsTotal -0.44461774 7274.9218656 5.1343105
## PitchDifference 0.37207954 5.1343105 3.1036138
## WidthDifference 0.26032928 -10.7365484 1.5941922
## PercentPremiumSeats -0.35252750 -91.2439224 -0.7903844
## WidthDifference PercentPremiumSeats
## SeatsEconomy -7.3272338 -122.3914537
## SeatsPremium -3.4093146 31.1475313
## PitchEconomy -0.4952271 -0.3261739
## PitchPremium 1.0989652 -1.1165583
## WidthEconomy -0.2607092 0.6132182
## WidthPremium 1.1536793 -0.9739379
## PriceEconomy -99.3154520 312.6107669
## PricePremium -17.6361404 726.0158229
## PriceRelative 0.2603293 -0.3525275
## SeatsTotal -10.7365484 -91.2439224
## PitchDifference 1.5941922 -0.7903844
## WidthDifference 1.4143885 -1.5871560
## PercentPremiumSeats -1.5871560 23.4493343cor(mytable)## 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 1.00000000corr.test(mytable, use= "complete")## Call:corr.test(x = mytable, use = "complete")
## Correlation matrix
## SeatsEconomy SeatsPremium PitchEconomy PitchPremium
## SeatsEconomy 1.00 0.63 0.14 0.12
## SeatsPremium 0.63 1.00 -0.03 0.00
## PitchEconomy 0.14 -0.03 1.00 -0.55
## PitchPremium 0.12 0.00 -0.55 1.00
## WidthEconomy 0.37 0.46 0.29 -0.02
## WidthPremium 0.10 0.00 -0.54 0.75
## PriceEconomy 0.13 0.11 0.37 0.05
## PricePremium 0.18 0.22 0.23 0.09
## PriceRelative 0.00 -0.10 -0.42 0.42
## SeatsTotal 0.99 0.72 0.12 0.11
## PitchDifference 0.04 0.02 -0.78 0.95
## WidthDifference -0.08 -0.22 -0.64 0.70
## PercentPremiumSeats -0.33 0.49 -0.10 -0.18
## WidthEconomy WidthPremium PriceEconomy PricePremium
## SeatsEconomy 0.37 0.10 0.13 0.18
## SeatsPremium 0.46 0.00 0.11 0.22
## PitchEconomy 0.29 -0.54 0.37 0.23
## PitchPremium -0.02 0.75 0.05 0.09
## WidthEconomy 1.00 0.08 0.07 0.15
## WidthPremium 0.08 1.00 -0.06 0.06
## PriceEconomy 0.07 -0.06 1.00 0.90
## PricePremium 0.15 0.06 0.90 1.00
## PriceRelative -0.04 0.50 -0.29 0.03
## SeatsTotal 0.41 0.09 0.13 0.19
## PitchDifference -0.13 0.76 -0.10 -0.02
## WidthDifference -0.39 0.88 -0.08 -0.01
## PercentPremiumSeats 0.23 -0.18 0.07 0.12
## PriceRelative SeatsTotal PitchDifference
## SeatsEconomy 0.00 0.99 0.04
## SeatsPremium -0.10 0.72 0.02
## PitchEconomy -0.42 0.12 -0.78
## PitchPremium 0.42 0.11 0.95
## WidthEconomy -0.04 0.41 -0.13
## WidthPremium 0.50 0.09 0.76
## PriceEconomy -0.29 0.13 -0.10
## PricePremium 0.03 0.19 -0.02
## PriceRelative 1.00 -0.01 0.47
## SeatsTotal -0.01 1.00 0.03
## PitchDifference 0.47 0.03 1.00
## WidthDifference 0.49 -0.11 0.76
## PercentPremiumSeats -0.16 -0.22 -0.09
## WidthDifference PercentPremiumSeats
## 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 1.00
## Sample Size
## [1] 458
## Probability values (Entries above the diagonal are adjusted for multiple tests.)
## SeatsEconomy SeatsPremium PitchEconomy PitchPremium
## SeatsEconomy 0.00 0.00 0.08 0.35
## SeatsPremium 0.00 0.00 1.00 1.00
## PitchEconomy 0.00 0.47 0.00 0.00
## PitchPremium 0.01 0.92 0.00 0.00
## WidthEconomy 0.00 0.00 0.00 0.61
## WidthPremium 0.03 0.95 0.00 0.00
## PriceEconomy 0.01 0.01 0.00 0.28
## PricePremium 0.00 0.00 0.00 0.06
## PriceRelative 0.93 0.04 0.00 0.00
## SeatsTotal 0.00 0.00 0.01 0.02
## PitchDifference 0.45 0.73 0.00 0.00
## WidthDifference 0.08 0.00 0.00 0.00
## PercentPremiumSeats 0.00 0.00 0.03 0.00
## WidthEconomy WidthPremium PriceEconomy PricePremium
## SeatsEconomy 0.00 0.78 0.22 0.01
## SeatsPremium 0.00 1.00 0.46 0.00
## PitchEconomy 0.00 0.00 0.00 0.00
## PitchPremium 1.00 0.00 1.00 1.00
## WidthEconomy 0.00 1.00 1.00 0.05
## WidthPremium 0.08 0.00 1.00 1.00
## PriceEconomy 0.15 0.22 0.00 0.00
## PricePremium 0.00 0.17 0.00 0.00
## PriceRelative 0.35 0.00 0.00 0.50
## SeatsTotal 0.00 0.05 0.00 0.00
## PitchDifference 0.01 0.00 0.03 0.70
## WidthDifference 0.00 0.00 0.07 0.81
## PercentPremiumSeats 0.00 0.00 0.16 0.01
## PriceRelative SeatsTotal PitchDifference
## SeatsEconomy 1.00 0.00 1.00
## SeatsPremium 0.94 0.00 1.00
## PitchEconomy 0.00 0.27 0.00
## PitchPremium 0.00 0.64 0.00
## WidthEconomy 1.00 0.00 0.22
## WidthPremium 0.00 1.00 0.00
## PriceEconomy 0.00 0.17 0.86
## PricePremium 1.00 0.00 1.00
## PriceRelative 0.00 1.00 0.00
## SeatsTotal 0.80 0.00 1.00
## PitchDifference 0.00 0.47 0.00
## WidthDifference 0.00 0.02 0.00
## PercentPremiumSeats 0.00 0.00 0.05
## WidthDifference PercentPremiumSeats
## SeatsEconomy 1.00 0.00
## SeatsPremium 0.00 0.00
## PitchEconomy 0.00 0.78
## PitchPremium 0.00 0.01
## WidthEconomy 0.00 0.00
## WidthPremium 0.00 0.00
## PriceEconomy 1.00 1.00
## PricePremium 1.00 0.41
## PriceRelative 0.00 0.02
## SeatsTotal 0.68 0.00
## PitchDifference 0.00 1.00
## WidthDifference 0.00 0.00
## PercentPremiumSeats 0.00 0.00
##
## To see confidence intervals of the correlations, print with the short=FALSE optioncorrgram(mytable, order= TRUE, lower.panel = panel.shade, upper.panel=panel.pie, text.panel = panel.txt,main="Corrgram of sixAirlines intercorrelation")
H1: There is greater relative difference between the Economy and Premium class, in International flight vs that of domestic flights. So the null-hypothesis is: There is no significant difference between the relative price of Economy class and premium class in case of International flights vs that of Domestic flights.
t.test(PriceRelative ~ IsInternational , data= sixAirlines)##
## Welch Two Sample t-test
##
## data: PriceRelative by IsInternational
## t = -19.451, df = 446.12, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.4855215 -0.3964139
## sample estimates:
## mean in group Domestic mean in group International
## 0.0847500 0.5257177As p is less than 0.05, we reject the null hypothesis, and say that indeed,“There is greater relative difference between the Economy and Premium class, in International flight vs that of domestic flights”. Null hypothesis: There is no significant difference between the Economy seat price in case of Beoing vs Airbus aircrafts.
t.test(PriceEconomy ~ Aircraft, data= sixAirlines)##
## Welch Two Sample t-test
##
## data: PriceEconomy by Aircraft
## t = 0.64317, df = 289.45, p-value = 0.5206
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -131.7801 259.7135
## sample estimates:
## mean in group AirBus mean in group Boeing
## 1369.954 1305.987As the value of p > 0.05, we cannot reject the null hpothesis.And we say that, there is no significant difference between the Economy seat price in case of Beoing vs Airbus aircrafts. Null hypothesis: There is no significant difference between the Premium seat price in case of Beoing vs Airbus aircrafts.
t.test(PricePremium ~ Aircraft, data= sixAirlines)##
## Welch Two Sample t-test
##
## data: PricePremium by Aircraft
## t = 0.28645, df = 310.38, p-value = 0.7747
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -212.2929 284.6350
## sample estimates:
## mean in group AirBus mean in group Boeing
## 1869.503 1833.332As the value of p > 0.05, we cannot reject the null hpothesis.And we say that, there is no significant difference between the premium seat price in case of Beoing vs Airbus aircrafts. Null hypothesis: There is no significant difference between the PriceRelative in case of Beoing vs Airbus aircrafts.
t.test(PriceRelative ~ Aircraft, data= sixAirlines)##
## 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 0.5228339As the value of p < 0.05, we reject the null hpothesis.And we say that, there is a significant difference between the PriceRelative in case of Beoing vs Airbus aircrafts.
model <- lm(PriceEconomy ~ SeatsEconomy + PitchEconomy + WidthEconomy, data = mytable)
summary(model)##
## Call:
## lm(formula = PriceEconomy ~ SeatsEconomy + PitchEconomy + WidthEconomy,
## data = mytable)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2209.23 -762.84 -39.25 727.96 1922.01
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.414e+04 2.250e+03 -6.283 7.79e-10 ***
## SeatsEconomy 1.352e+00 6.051e-01 2.234 0.0260 *
## PitchEconomy 5.700e+02 6.846e+01 8.325 1.00e-15 ***
## WidthEconomy -1.459e+02 8.584e+01 -1.700 0.0898 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 915.7 on 454 degrees of freedom
## Multiple R-squared: 0.1471, Adjusted R-squared: 0.1415
## F-statistic: 26.1 on 3 and 454 DF, p-value: 1.366e-15Inference: The width between the seats decreases the price of an economoy seat, this is because more the width, lesser the number of seats in the airplane for this class, and hence lesser the priceEconomy achievable.
model <- lm(PricePremium~ SeatsPremium + PitchPremium + WidthPremium, data = mytable)
summary(model)##
## Call:
## lm(formula = PricePremium ~ SeatsPremium + PitchPremium + WidthPremium,
## data = mytable)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2219.2 -936.9 -120.4 1078.6 5762.8
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2127.171 1736.937 -1.225 0.221
## SeatsPremium 21.095 4.432 4.760 2.61e-06 ***
## PitchPremium 87.481 67.656 1.293 0.197
## WidthPremium -2.744 81.021 -0.034 0.973
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1256 on 454 degrees of freedom
## Multiple R-squared: 0.05501, Adjusted R-squared: 0.04877
## F-statistic: 8.809 on 3 and 454 DF, p-value: 1.094e-05Inference: The width between the seats decreases the price of an Premium seat, this is because more the width, lesser the number of seats in the airplane for this class, and hence lesser the pricePremium achievable.The effect is more pronounced in Premium class as compared to the economy class.
model <- lm(PriceRelative ~ PitchDifference + WidthDifference, data= mytable)
summary(model)##
## Call:
## lm(formula = PriceRelative ~ PitchDifference + WidthDifference,
## data = mytable)
##
## 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-16Inference: Greater the value of PitchDifference and WidthDifference, greater is the relative price difference of the Economy and Premium class seats.
model <- lm(PriceEconomy ~ . , data= mytable)
summary(model)##
## Call:
## lm(formula = PriceEconomy ~ ., data = mytable)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1249.84 -85.09 2.48 117.87 581.01
##
## Coefficients: (3 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -9.816e+03 9.529e+02 -10.301 < 2e-16 ***
## SeatsEconomy 2.190e+00 5.015e-01 4.366 1.57e-05 ***
## SeatsPremium -1.761e+01 2.966e+00 -5.939 5.77e-09 ***
## PitchEconomy 2.451e+02 2.497e+01 9.816 < 2e-16 ***
## PitchPremium 1.471e+02 1.212e+01 12.136 < 2e-16 ***
## WidthEconomy -2.055e+02 2.458e+01 -8.360 8.01e-16 ***
## WidthPremium 1.942e+01 1.560e+01 1.246 0.214
## PricePremium 6.730e-01 8.749e-03 76.926 < 2e-16 ***
## PriceRelative -7.528e+02 2.642e+01 -28.492 < 2e-16 ***
## SeatsTotal NA NA NA NA
## PitchDifference NA NA NA NA
## WidthDifference NA NA NA NA
## PercentPremiumSeats 3.259e+01 7.090e+00 4.597 5.59e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 210.2 on 448 degrees of freedom
## Multiple R-squared: 0.9557, Adjusted R-squared: 0.9548
## F-statistic: 1073 on 9 and 448 DF, p-value: < 2.2e-16Inference: A significant inference is the relation that PriceEconomy and PricePremium factos hold, in the sense that the value of PriceEconomy is increased ‘6’ times when there is a unit change of PricePremium, but in the other case , the value of PricePremium is increased only ‘1.38’ times when there is a unit increase in the value of PriceEconomy.
model <- lm(PricePremium ~ . , data= mytable)
summary(model)##
## Call:
## lm(formula = PricePremium ~ ., data = mytable)
##
## Residuals:
## Min 1Q Median 3Q Max
## -884.43 -137.82 -5.22 95.60 2154.66
##
## Coefficients: (3 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.064e+04 1.433e+03 7.424 5.76e-13 ***
## SeatsEconomy -2.479e+00 7.242e-01 -3.422 0.000678 ***
## SeatsPremium 2.285e+01 4.279e+00 5.340 1.48e-07 ***
## PitchEconomy -2.575e+02 3.751e+01 -6.867 2.20e-11 ***
## PitchPremium -1.866e+02 1.797e+01 -10.384 < 2e-16 ***
## WidthEconomy 2.457e+02 3.604e+01 6.817 3.01e-11 ***
## WidthPremium -9.399e+00 2.238e+01 -0.420 0.674650
## PriceEconomy 1.381e+00 1.796e-02 76.926 < 2e-16 ***
## PriceRelative 1.067e+03 3.858e+01 27.660 < 2e-16 ***
## SeatsTotal NA NA NA NA
## PitchDifference NA NA NA NA
## WidthDifference NA NA NA NA
## PercentPremiumSeats -3.398e+01 1.027e+01 -3.309 0.001012 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 301.1 on 448 degrees of freedom
## Multiple R-squared: 0.9464, Adjusted R-squared: 0.9454
## F-statistic: 879.7 on 9 and 448 DF, p-value: < 2.2e-16Inference: Greater seats in the Premium class, lesser is the value of the PriceEconomy, and vice-versa.
model <- lm(PriceRelative ~ . , data= mytable)
summary(model)##
## Call:
## lm(formula = PriceRelative ~ ., data = mytable)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.86630 -0.10024 -0.00421 0.07693 0.83219
##
## Coefficients: (3 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -6.658e+00 1.085e+00 -6.135 1.88e-09 ***
## SeatsEconomy 1.892e-03 5.387e-04 3.513 0.000488 ***
## SeatsPremium -1.660e-02 3.190e-03 -5.206 2.95e-07 ***
## PitchEconomy 1.232e-01 2.877e-02 4.281 2.27e-05 ***
## PitchPremium 1.223e-01 1.373e-02 8.904 < 2e-16 ***
## WidthEconomy -1.474e-01 2.731e-02 -5.398 1.09e-07 ***
## WidthPremium 5.990e-02 1.642e-02 3.649 0.000294 ***
## PriceEconomy -8.559e-04 3.004e-05 -28.492 < 2e-16 ***
## PricePremium 5.911e-04 2.137e-05 27.660 < 2e-16 ***
## SeatsTotal NA NA NA NA
## PitchDifference NA NA NA NA
## WidthDifference NA NA NA NA
## PercentPremiumSeats 2.389e-02 7.654e-03 3.121 0.001920 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2241 on 448 degrees of freedom
## Multiple R-squared: 0.7575, Adjusted R-squared: 0.7527
## F-statistic: 155.5 on 9 and 448 DF, p-value: < 2.2e-16Inference: The ‘negative’ effect on PriceRelative is put most by the PriceEconomy, and it is almost ‘8’ times. This inference can infact be well validated by the formula where the term of PriceEconomy is in the denominator, and that’s how increasing the value of PriceEconomy decreases the value of PriceRelative.