THE AIRLINE INDUSTRY
Raj Kapoor
19 January 2018
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# Analysis of Airline Ticket Pricing
# NAME: RAJ KAPOOR GUPTA
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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 loaded## corrplot 0.84 loaded
library(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")
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 0.5257177t.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 1305.987t.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 1833.332t.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 0.5228339model <- 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-15model <- 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-05model <- 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-16model <- 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-16model <- 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-16model <- 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-16Note that the echo = FALSE parameter was added to the code chunk to prevent printing of the R code that generated the plot.