Six Airlines
Sahil Garg
22 December 2017
Reading and Understanding the data
Read the data into R.
setwd("D:/manipal-year2/internship/IIML_dataAnalytics/Datasets")
air.df <- read.csv(paste("SixAirlinesDataV2.csv",sep=""))
View(air.df)
head(air.df)## 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 24.69Summarize data
Summarize the data to understand the mean, median, standard deviation of each variable.
summary(air.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. :24.69library(psych)
describe(air.df)## 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 0.23str(air.df)## '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 ...dim(air.df)## [1] 458 18colnames(air.df)## [1] "Airline" "Aircraft" "FlightDuration"
## [4] "TravelMonth" "IsInternational" "SeatsEconomy"
## [7] "SeatsPremium" "PitchEconomy" "PitchPremium"
## [10] "WidthEconomy" "WidthPremium" "PriceEconomy"
## [13] "PricePremium" "PriceRelative" "SeatsTotal"
## [16] "PitchDifference" "WidthDifference" "PercentPremiumSeats"Describe per airline data
describe(air.df[which(air.df$Airline=="Virgin"),][c(3,6:18)],skew =FALSE)## vars n mean sd min max range se
## FlightDuration 1 62 9.25 1.94 6.58 12.58 6.00 0.25
## SeatsEconomy 2 62 230.18 59.26 185.00 375.00 190.00 7.53
## SeatsPremium 3 62 42.53 10.23 35.00 66.00 31.00 1.30
## PitchEconomy 4 62 31.00 0.00 31.00 31.00 0.00 0.00
## PitchPremium 5 62 38.00 0.00 38.00 38.00 0.00 0.00
## WidthEconomy 6 62 18.00 0.00 18.00 18.00 0.00 0.00
## WidthPremium 7 62 21.00 0.00 21.00 21.00 0.00 0.00
## PriceEconomy 8 62 1603.53 532.90 540.00 2445.00 1905.00 67.68
## PricePremium 9 62 2721.69 809.55 594.00 3694.00 3100.00 102.81
## PriceRelative 10 62 0.76 0.48 0.10 1.82 1.72 0.06
## SeatsTotal 11 62 272.71 67.59 233.00 441.00 208.00 8.58
## PitchDifference 12 62 7.00 0.00 7.00 7.00 0.00 0.00
## WidthDifference 13 62 3.00 0.00 3.00 3.00 0.00 0.00
## PercentPremiumSeats 14 62 15.75 2.43 14.02 20.60 6.58 0.31describe(air.df[which(air.df$Airline=="British"),][c(3,6:18)],skew =
FALSE)## vars n mean sd min max range se
## FlightDuration 1 175 7.85 3.68 1.25 13.83 12.58 0.28
## SeatsEconomy 2 175 216.59 74.68 122.00 312.00 190.00 5.65
## SeatsPremium 3 175 43.18 9.57 24.00 56.00 32.00 0.72
## PitchEconomy 4 175 31.00 0.00 31.00 31.00 0.00 0.00
## PitchPremium 5 175 38.00 0.00 38.00 38.00 0.00 0.00
## WidthEconomy 6 175 18.00 0.00 18.00 18.00 0.00 0.00
## WidthPremium 7 175 19.00 0.00 19.00 19.00 0.00 0.00
## PriceEconomy 8 175 1293.48 781.46 65.00 3102.00 3037.00 59.07
## PricePremium 9 175 1937.03 1340.31 86.00 7414.00 7328.00 101.32
## PriceRelative 10 175 0.44 0.32 0.04 1.39 1.35 0.02
## SeatsTotal 11 175 259.77 80.55 162.00 367.00 205.00 6.09
## PitchDifference 12 175 7.00 0.00 7.00 7.00 0.00 0.00
## WidthDifference 13 175 1.00 0.00 1.00 1.00 0.00 0.00
## PercentPremiumSeats 14 175 17.79 5.19 10.57 24.69 14.12 0.39describe(air.df[which(air.df$Airline=="Jet"),][c(3,6:18)],skew =
FALSE)## vars n mean sd min max range se
## FlightDuration 1 61 4.14 2.07 2.50 9.50 7.00 0.26
## SeatsEconomy 2 61 140.31 16.57 124.00 162.00 38.00 2.12
## SeatsPremium 3 61 15.66 6.50 8.00 28.00 20.00 0.83
## PitchEconomy 4 61 30.23 0.64 30.00 32.00 2.00 0.08
## PitchPremium 5 61 39.77 0.64 38.00 40.00 2.00 0.08
## WidthEconomy 6 61 17.11 0.32 17.00 18.00 1.00 0.04
## WidthPremium 7 61 20.77 0.64 19.00 21.00 2.00 0.08
## PriceEconomy 8 61 276.16 154.52 108.00 676.00 568.00 19.78
## PricePremium 9 61 483.36 185.17 228.00 931.00 703.00 23.71
## PriceRelative 10 61 0.94 0.49 0.12 1.89 1.77 0.06
## SeatsTotal 11 61 155.97 14.40 140.00 170.00 30.00 1.84
## PitchDifference 12 61 9.54 1.29 6.00 10.00 4.00 0.16
## WidthDifference 13 61 3.66 0.96 1.00 4.00 3.00 0.12
## PercentPremiumSeats 14 61 10.17 4.10 4.71 16.87 12.16 0.52describe(air.df[which(air.df$Airline=="AirFrance"),][c(3,6:18)],skew =
FALSE)## vars n mean sd min max range se
## FlightDuration 1 74 8.99 1.62 6.83 13.00 6.17 0.19
## SeatsEconomy 2 74 214.46 88.24 147.00 389.00 242.00 10.26
## SeatsPremium 3 74 26.70 6.20 21.00 38.00 17.00 0.72
## PitchEconomy 4 74 32.00 0.00 32.00 32.00 0.00 0.00
## PitchPremium 5 74 38.00 0.00 38.00 38.00 0.00 0.00
## WidthEconomy 6 74 17.57 0.50 17.00 18.00 1.00 0.06
## WidthPremium 7 74 19.00 0.00 19.00 19.00 0.00 0.00
## PriceEconomy 8 74 2769.78 749.67 630.00 3593.00 2963.00 87.15
## PricePremium 9 74 3065.22 543.21 1611.00 3972.00 2361.00 63.15
## PriceRelative 10 74 0.20 0.41 0.02 1.64 1.62 0.05
## SeatsTotal 11 74 241.16 94.24 168.00 427.00 259.00 10.96
## PitchDifference 12 74 6.00 0.00 6.00 6.00 0.00 0.00
## WidthDifference 13 74 1.43 0.50 1.00 2.00 1.00 0.06
## PercentPremiumSeats 14 74 11.59 1.42 8.90 12.50 3.60 0.16describe(air.df[which(air.df$Airline=="Delta"),][c(3,6:18)],skew =FALSE)## vars n mean sd min max range se
## FlightDuration 1 46 4.03 2.24 1.57 9.50 7.93 0.33
## SeatsEconomy 2 46 137.22 44.93 78.00 233.00 155.00 6.62
## SeatsPremium 3 46 22.57 6.79 18.00 38.00 20.00 1.00
## PitchEconomy 4 46 31.72 0.66 31.00 33.00 2.00 0.10
## PitchPremium 5 46 34.72 1.34 34.00 38.00 4.00 0.20
## WidthEconomy 6 46 17.39 0.49 17.00 18.00 1.00 0.07
## WidthPremium 7 46 17.78 1.33 17.00 21.00 4.00 0.20
## PriceEconomy 8 46 560.93 547.65 158.00 1999.00 1841.00 80.75
## PricePremium 9 46 684.67 790.56 173.00 2765.00 2592.00 116.56
## PriceRelative 10 46 0.12 0.11 0.03 0.46 0.43 0.02
## SeatsTotal 11 46 159.78 50.97 98.00 271.00 173.00 7.52
## PitchDifference 12 46 3.00 1.63 2.00 7.00 5.00 0.24
## WidthDifference 13 46 0.39 1.02 0.00 3.00 3.00 0.15
## PercentPremiumSeats 14 46 14.48 2.86 12.50 20.41 7.91 0.42describe(air.df[which(air.df$Airline=="Singapore"),][c(3,6:18)],skew =FALSE)## vars n mean sd min max range se
## FlightDuration 1 40 10.48 3.58 3.83 14.66 10.83 0.57
## SeatsEconomy 2 40 243.60 73.92 184.00 333.00 149.00 11.69
## SeatsPremium 3 40 31.20 3.97 28.00 36.00 8.00 0.63
## PitchEconomy 4 40 32.00 0.00 32.00 32.00 0.00 0.00
## PitchPremium 5 40 38.00 0.00 38.00 38.00 0.00 0.00
## WidthEconomy 6 40 19.00 0.00 19.00 19.00 0.00 0.00
## WidthPremium 7 40 20.00 0.00 20.00 20.00 0.00 0.00
## PriceEconomy 8 40 860.25 349.42 505.00 1431.00 926.00 55.25
## PricePremium 9 40 1239.92 359.13 619.00 1947.00 1328.00 56.78
## PriceRelative 10 40 0.53 0.35 0.09 1.11 1.02 0.06
## SeatsTotal 11 40 274.80 77.89 212.00 369.00 157.00 12.32
## PitchDifference 12 40 6.00 0.00 6.00 6.00 0.00 0.00
## WidthDifference 13 40 1.00 0.00 1.00 1.00 0.00 0.00
## PercentPremiumSeats 14 40 11.83 1.71 9.76 13.21 3.45 0.27Aggregating prices
Find the mean prices for economy and premium classes for each of the airlines.
aggregate(air.df$PricePremium,by=list(airline=air.df$Airline),mean)## airline x
## 1 AirFrance 3065.2162
## 2 British 1937.0286
## 3 Delta 684.6739
## 4 Jet 483.3607
## 5 Singapore 1239.9250
## 6 Virgin 2721.6935aggregate(air.df$PriceEconomy,by=list(airline=air.df$Airline),mean)## airline x
## 1 AirFrance 2769.7838
## 2 British 1293.4800
## 3 Delta 560.9348
## 4 Jet 276.1639
## 5 Singapore 860.2500
## 6 Virgin 1603.5323Summary of certain important columns
Find the summary for economy and premium classes for each of the airlines.
summary(air.df$SeatsEconomy)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 78.0 133.0 185.0 202.3 243.0 389.0summary(air.df$SeatsPremium)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 8.00 21.00 36.00 33.65 40.00 66.00summary(air.df$SeatsTotal)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 98 166 227 236 279 441summary(air.df$PriceEconomy)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 65 413 1242 1327 1909 3593summary(air.df$PricePremium)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 86.0 528.8 1737.0 1845.3 2989.0 7414.0summary(air.df$PitchDifference)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 2.000 6.000 7.000 6.688 7.000 10.000summary(air.df$WidthDifference)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.000 1.000 1.000 1.633 3.000 4.000Creating Histograms
hist(air.df$SeatsEconomy, breaks = 5)
hist(air.df$SeatsPremium, breaks = 5)
hist(air.df$SeatsTotal, breaks = 5)
hist(air.df$FlightDuration, breaks = 5)
hist(air.df$PitchEconomy, breaks = 5)
hist(air.df$PitchPremium, breaks = 5)
hist(air.df$PitchDifference, breaks = 5)
hist(air.df$WidthEconomy, breaks = 5)
hist(air.df$WidthPremium, breaks = 5)
hist(air.df$WidthDifference, breaks = 5)
hist(air.df$PriceEconomy, breaks = 5)
hist(air.df$PricePremium, breaks = 5)
hist(air.df$PriceRelative, breaks = 5)
hist(air.df$PercentPremiumSeats, breaks = 5)
Creating Box Plots
boxplot(air.df$SeatsEconomy, horizontal = T)
boxplot(air.df$SeatsPremium, horizontal = T)
boxplot(air.df$SeatsTotal,horizontal = T)
boxplot(air.df$FlightDuration, horizontal = T)
boxplot(air.df$PitchEconomy, horizontal = T)
boxplot(air.df$PitchPremium, horizontal = T)
boxplot(air.df$PitchDifference, horizontal = T)
boxplot(air.df$WidthEconomy, horizontal = T)
boxplot(air.df$WidthPremium, horizontal = T)
boxplot(air.df$WidthDifference, horizontal = T)
boxplot(air.df$PriceEconomy, horizontal = T)
boxplot(air.df$PricePremium, horizontal = T)
boxplot(air.df$PriceRelative, horizontal = T)
boxplot(air.df$PercentPremiumSeats, horizontal = T)
Finding some statistics about the data
aggregate(air.df$PriceRelative, by = list(air.df$Airline), mean)## Group.1 x
## 1 AirFrance 0.2047297
## 2 British 0.4375429
## 3 Delta 0.1250000
## 4 Jet 0.9396721
## 5 Singapore 0.5297500
## 6 Virgin 0.7606452aggregate(air.df$WidthDifference, by = list(air.df$Airline), mean)## Group.1 x
## 1 AirFrance 1.4324324
## 2 British 1.0000000
## 3 Delta 0.3913043
## 4 Jet 3.6557377
## 5 Singapore 1.0000000
## 6 Virgin 3.0000000aggregate(air.df$PitchDifference, by = list(air.df$Airline), mean)## Group.1 x
## 1 AirFrance 6.000000
## 2 British 7.000000
## 3 Delta 3.000000
## 4 Jet 9.540984
## 5 Singapore 6.000000
## 6 Virgin 7.000000Getting some statistics about Categorical Variables
table(air.df$Airline)##
## AirFrance British Delta Jet Singapore Virgin
## 74 175 46 61 40 62table(air.df$Aircraft)##
## AirBus Boeing
## 151 307table(air.df$TravelMonth)##
## Aug Jul Oct Sep
## 127 75 127 129table(air.df$IsInternational)##
## Domestic International
## 40 418table(air.df$TravelMonth)##
## Aug Jul Oct Sep
## 127 75 127 129Finding some relations
xtabs(~air.df$Airline+air.df$TravelMonth)## air.df$TravelMonth
## air.df$Airline Aug Jul Oct Sep
## AirFrance 20 12 20 22
## British 52 16 53 54
## Delta 12 10 13 11
## Jet 16 15 15 15
## Singapore 11 8 10 11
## Virgin 16 14 16 16xtabs(~air.df$Airline+air.df$PitchDifference)## air.df$PitchDifference
## air.df$Airline 2 3 6 7 10
## AirFrance 0 0 74 0 0
## British 0 0 0 175 0
## Delta 24 16 0 6 0
## Jet 0 0 7 0 54
## Singapore 0 0 40 0 0
## Virgin 0 0 0 62 0xtabs(~air.df$Airline+air.df$WidthDifference)## air.df$WidthDifference
## air.df$Airline 0 1 2 3 4
## AirFrance 0 42 32 0 0
## British 0 175 0 0 0
## Delta 40 0 0 6 0
## Jet 0 7 0 0 54
## Singapore 0 40 0 0 0
## Virgin 0 0 0 62 0Drawing Scatterplots and other graphs
attach(air.df)
pairs(formula = ~ Aircraft + Airline+ PricePremium + PercentPremiumSeats )
pairs(formula = ~ PriceEconomy + PitchEconomy + WidthEconomy)
pairs(formula = ~ PricePremium + PitchPremium + WidthPremium)
pairs(formula = ~ PriceRelative + WidthDifference + PitchDifference)
library(car)
scatterplot(PriceRelative, WidthDifference)
scatterplot(PriceRelative, PitchDifference)
scatterplot(PriceRelative, FlightDuration)
scatterplot(PriceRelative, SeatsEconomy)
scatterplot(PriceRelative, SeatsPremium)
airPricePitch <- table(PriceRelative, PitchDifference)
barplot(airPricePitch, main = "Price Difference With Respect to Legspace Difference", xlab = "Amount of Legspace", ylab = "Price Difference")
airPriceWidth <- table(PriceRelative, WidthDifference)
barplot(airPriceWidth, main = "Price Difference With Respect to Width Difference", xlab = "Amount of Width", ylab = "Price Difference")
library(lattice)
bwplot(Airline ~ PriceRelative, horizontal=TRUE)
Finding Correlation and covariance Matrix
cor(air.df[,c(3,6:17)])## 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
## 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
## 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
## WidthDifference
## FlightDuration -0.11856070
## SeatsEconomy -0.08067015
## SeatsPremium -0.21616867
## PitchEconomy -0.63557430
## PitchPremium 0.70328180
## WidthEconomy -0.39320512
## WidthPremium 0.88414965
## PriceEconomy -0.08449975
## PricePremium -0.01151218
## PriceRelative 0.48580244
## SeatsTotal -0.10584398
## PitchDifference 0.76089108
## WidthDifference 1.00000000cov(air.df[,c(3,6:17)])## FlightDuration SeatsEconomy SeatsPremium PitchEconomy
## FlightDuration 12.5462183 52.9194291 7.57372426 0.6817421
## SeatsEconomy 52.9194291 5832.9154300 633.07060954 7.2117665
## SeatsPremium 7.5737243 633.0706095 175.86521648 -0.2972586
## PitchEconomy 0.6817421 7.2117665 -0.29725856 0.4292471
## PitchPremium 0.4477835 11.9637325 0.08508595 -0.4739855
## WidthEconomy 0.9014224 15.9105138 3.36977440 0.1075650
## WidthPremium 0.4019845 8.5832800 -0.03954019 -0.3876621
## PriceEconomy 1983.5401655 9673.7944684 1489.38359627 238.7031905
## PricePremium 2959.9783043 17413.2541733 3717.36428960 190.8517195
## PriceRelative 0.1932368 0.1361699 -0.58078765 -0.1248808
## SeatsTotal 60.4931534 6465.9860396 808.93582602 6.9145079
## PitchDifference -0.2339587 4.7519660 0.38234451 -0.9032326
## WidthDifference -0.4994380 -7.3272338 -3.40931459 -0.4952271
## PitchPremium WidthEconomy WidthPremium PriceEconomy
## FlightDuration 0.44778348 0.90142242 0.40198446 1983.54017
## SeatsEconomy 11.96373253 15.91051379 8.58327998 9673.79447
## SeatsPremium 0.08508595 3.36977440 -0.03954019 1489.38360
## PitchEconomy -0.47398546 0.10756500 -0.38766208 238.70319
## PitchPremium 1.72639580 -0.01739081 1.08157435 65.42513
## WidthEconomy -0.01739081 0.31081765 0.05010845 37.46095
## WidthPremium 1.08157435 0.05010845 1.20378776 -61.85450
## PriceEconomy 65.42513354 37.46095191 -61.85450011 976684.06198
## PricePremium 149.85356368 108.11611707 90.47997668 1147494.76801
## PriceRelative 0.24719874 -0.01104335 0.24928593 -128.49992
## SeatsTotal 12.04881848 19.28028819 8.54373979 11163.17806
## PitchDifference 2.20038126 -0.12495581 1.46923643 -173.27806
## WidthDifference 1.09896515 -0.26070920 1.15367930 -99.31545
## PricePremium PriceRelative SeatsTotal PitchDifference
## FlightDuration 2959.97830 0.19323683 60.4931534 -0.2339587
## SeatsEconomy 17413.25417 0.13616991 6465.9860396 4.7519660
## SeatsPremium 3717.36429 -0.58078765 808.9358260 0.3823445
## PitchEconomy 190.85172 -0.12488080 6.9145079 -0.9032326
## PitchPremium 149.85356 0.24719874 12.0488185 2.2003813
## WidthEconomy 108.11612 -0.01104335 19.2802882 -0.1249558
## WidthPremium 90.47998 0.24928593 8.5437398 1.4692364
## PriceEconomy 1147494.76801 -128.49991725 11163.1780647 -173.2780570
## PricePremium 1659293.11947 18.48428836 21130.6184629 -40.9981558
## PriceRelative 18.48429 0.20302893 -0.4446177 0.3720795
## SeatsTotal 21130.61846 -0.44461774 7274.9218656 5.1343105
## PitchDifference -40.99816 0.37207954 5.1343105 3.1036138
## WidthDifference -17.63614 0.26032928 -10.7365484 1.5941922
## WidthDifference
## FlightDuration -0.4994380
## SeatsEconomy -7.3272338
## SeatsPremium -3.4093146
## PitchEconomy -0.4952271
## PitchPremium 1.0989652
## WidthEconomy -0.2607092
## WidthPremium 1.1536793
## PriceEconomy -99.3154520
## PricePremium -17.6361404
## PriceRelative 0.2603293
## SeatsTotal -10.7365484
## PitchDifference 1.5941922
## WidthDifference 1.4143885round(cor(air.df[,c(3,6:17)]),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
## 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
## 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
## WidthDifference
## FlightDuration -0.12
## SeatsEconomy -0.08
## SeatsPremium -0.22
## PitchEconomy -0.64
## PitchPremium 0.70
## WidthEconomy -0.39
## WidthPremium 0.88
## PriceEconomy -0.08
## PricePremium -0.01
## PriceRelative 0.49
## SeatsTotal -0.11
## PitchDifference 0.76
## WidthDifference 1.00Plots to find changes with flight durations
plot(FlightDuration,PriceEconomy,
main="Flight duration vs Economy Price",
xlab="flight duration",
ylab = "Economy Price")
abline(lm(PriceEconomy~FlightDuration),
col="blue")
plot(FlightDuration,PricePremium,
main="Flight duration vs Premium Price",
xlab="flight duration",
ylab = "Economy Price")
abline(lm(PricePremium~FlightDuration),
col="blue")
plot(PitchDifference,PriceRelative,main = "Analysis of Pitch with price Difference")
abline(lm(PriceRelative~PitchDifference),col="blue")
plot(WidthDifference,PriceRelative,main = "Analysis of width with price Difference")
abline(lm(PriceRelative~WidthDifference),col="blue")
Drawing Corrgram
library(corrgram)
corrgram(air.df, order=TRUE, lower.panel=panel.shade,
upper.panel=panel.pie, text.panel=panel.txt,
main="Corrgram of airlines data")
Finding Correlations
cor(PriceRelative,FlightDuration)## [1] 0.121075cor(PriceRelative,SeatsEconomy)## [1] 0.003956939cor(PriceRelative,SeatsPremium)## [1] -0.09719601cor(PriceRelative,WidthEconomy)## [1] -0.04396116cor(PriceRelative,WidthPremium)## [1] 0.5042476cor(PriceRelative,PitchEconomy)## [1] -0.423022cor(PriceRelative,PitchPremium)## [1] 0.4175391Insights and formulation of Hypothesis
We can observe the following insights -
The flight prices are related directly with flight duration and timing.
The width and pitch is higher in the premium aircrafts as compared to the economy ones, providing more comfort.
There are a large number of economy seats, accounting to about 90 percent of the total seats.
Prices are directly correlated with pitch difference and width difference.
More the number of economy seats, lesser is the percentage premium seats.
The graph clearly represents high correlation between the above discussed variables which were further investigated using regression
Hypothesis -
The prices of premium and economy seats are positively increase with flight duration, increase in width diference and pitch difference as well as depending on whether the flight is international or domestic.
The relative prices of premium and economy class are directly correlated with the pitch difference and width difference.
Running T-Tests
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
## 0.4687302cor.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
## 0.4858024cor.test(PriceRelative,FlightDuration)##
## Pearson's product-moment correlation
##
## data: PriceRelative and FlightDuration
## t = 2.6046, df = 456, p-value = 0.009498
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.02977856 0.21036806
## sample estimates:
## cor
## 0.121075cor.test(PriceRelative,SeatsTotal)##
## Pearson's product-moment correlation
##
## data: PriceRelative and SeatsTotal
## t = -0.24706, df = 456, p-value = 0.805
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.10308648 0.08014282
## sample estimates:
## cor
## -0.01156894cor.test(PriceRelative,SeatsEconomy)##
## Pearson's product-moment correlation
##
## data: PriceRelative and SeatsEconomy
## t = 0.084498, df = 456, p-value = 0.9327
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.08770167 0.09554911
## sample estimates:
## cor
## 0.003956939cor.test(PriceRelative,SeatsPremium)##
## Pearson's product-moment correlation
##
## data: PriceRelative and SeatsPremium
## t = -2.0854, df = 456, p-value = 0.03759
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.18715605 -0.00561924
## sample estimates:
## cor
## -0.09719601cor.test(PriceRelative,PercentPremiumSeats)##
## Pearson's product-moment correlation
##
## data: PriceRelative and PercentPremiumSeats
## t = -3.496, df = 456, p-value = 0.0005185
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.24949885 -0.07098966
## sample estimates:
## cor
## -0.1615656corr.test(air.df[,c(3,6:18)])## Call:corr.test(x = air.df[, c(3, 6:18)])
## Correlation matrix
## 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 1.00
## Sample Size
## [1] 458
## Probability values (Entries above the diagonal are adjusted for multiple tests.)
## FlightDuration SeatsEconomy SeatsPremium PitchEconomy
## FlightDuration 0.00 0.00 0.02 0.00
## SeatsEconomy 0.00 0.00 0.00 0.09
## SeatsPremium 0.00 0.00 0.00 1.00
## PitchEconomy 0.00 0.00 0.47 0.00
## PitchPremium 0.04 0.01 0.92 0.00
## WidthEconomy 0.00 0.00 0.00 0.00
## WidthPremium 0.03 0.03 0.95 0.00
## PriceEconomy 0.00 0.01 0.01 0.00
## PricePremium 0.00 0.00 0.00 0.00
## PriceRelative 0.01 0.93 0.04 0.00
## SeatsTotal 0.00 0.00 0.00 0.01
## PitchDifference 0.42 0.45 0.73 0.00
## WidthDifference 0.01 0.08 0.00 0.00
## PercentPremiumSeats 0.20 0.00 0.00 0.03
## PitchPremium WidthEconomy WidthPremium PriceEconomy
## FlightDuration 1.00 0.00 0.86 0.00
## SeatsEconomy 0.41 0.00 0.86 0.25
## SeatsPremium 1.00 0.00 1.00 0.52
## PitchEconomy 0.00 0.00 0.00 0.00
## PitchPremium 0.00 1.00 0.00 1.00
## WidthEconomy 0.61 0.00 1.00 1.00
## WidthPremium 0.00 0.08 0.00 1.00
## PriceEconomy 0.28 0.15 0.22 0.00
## PricePremium 0.06 0.00 0.17 0.00
## PriceRelative 0.00 0.35 0.00 0.00
## SeatsTotal 0.02 0.00 0.05 0.00
## PitchDifference 0.00 0.01 0.00 0.03
## WidthDifference 0.00 0.00 0.00 0.07
## PercentPremiumSeats 0.00 0.00 0.00 0.16
## PricePremium PriceRelative SeatsTotal PitchDifference
## FlightDuration 0.00 0.37 0.00 1.00
## SeatsEconomy 0.01 1.00 0.00 1.00
## SeatsPremium 0.00 1.00 0.00 1.00
## PitchEconomy 0.00 0.00 0.32 0.00
## PitchPremium 1.00 0.00 0.73 0.00
## WidthEconomy 0.06 1.00 0.00 0.26
## WidthPremium 1.00 0.00 1.00 0.00
## PriceEconomy 0.00 0.00 0.19 0.96
## PricePremium 0.00 1.00 0.00 1.00
## PriceRelative 0.50 0.00 1.00 0.00
## SeatsTotal 0.00 0.80 0.00 1.00
## PitchDifference 0.70 0.00 0.47 0.00
## WidthDifference 0.81 0.00 0.02 0.00
## PercentPremiumSeats 0.01 0.00 0.00 0.05
## WidthDifference PercentPremiumSeats
## FlightDuration 0.41 1.00
## SeatsEconomy 1.00 0.00
## SeatsPremium 0.00 0.00
## PitchEconomy 0.00 0.86
## PitchPremium 0.00 0.01
## WidthEconomy 0.00 0.00
## WidthPremium 0.00 0.00
## PriceEconomy 1.00 1.00
## PricePremium 1.00 0.46
## PriceRelative 0.00 0.02
## SeatsTotal 0.78 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 optionThese tests, using the p-values, show that the relative prices of the Premium and Economy flight are related by difference in pitch and width as well as flight duration, rejecting the null hypothesis. There is also a positive relation between percent premium seats and the prices.
Formulating a Regression Model
Dependent variable - PriceRelative Independent cariables - PitchDifference, WidthDifference, PercentPremiumSeats and Flight Duration
Fiting the linear model using all variables
fitt <- lm(formula = air.df$PriceRelative~., data = air.df)
summary(fitt)##
## Call:
## lm(formula = air.df$PriceRelative ~ ., data = air.df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.76373 -0.08269 0.00438 0.08002 0.84672
##
## Coefficients: (3 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.993e-01 2.948e+00 -0.135 0.892302
## AirlineBritish -3.971e-01 1.107e-01 -3.586 0.000373 ***
## AirlineDelta -3.865e-01 2.203e-01 -1.755 0.080020 .
## AirlineJet -2.584e-01 9.594e-02 -2.693 0.007354 **
## AirlineSingapore -3.535e-01 1.297e-01 -2.725 0.006685 **
## AirlineVirgin -3.575e-01 2.031e-01 -1.761 0.078997 .
## AircraftBoeing 4.003e-02 2.968e-02 1.349 0.178089
## FlightDuration 2.613e-02 4.727e-03 5.526 5.63e-08 ***
## TravelMonthJul 2.111e-02 3.145e-02 0.671 0.502475
## TravelMonthOct 2.778e-02 2.670e-02 1.041 0.298619
## TravelMonthSep -6.617e-03 2.664e-02 -0.248 0.803924
## IsInternationalInternational 2.785e-02 2.502e-01 0.111 0.911400
## SeatsEconomy 8.090e-04 5.462e-04 1.481 0.139313
## SeatsPremium -7.374e-03 3.615e-03 -2.040 0.041967 *
## PitchEconomy -1.756e-02 7.994e-02 -0.220 0.826207
## PitchPremium 5.960e-02 9.165e-02 0.650 0.515823
## WidthEconomy -9.207e-02 5.266e-02 -1.748 0.081085 .
## WidthPremium 4.904e-02 1.365e-01 0.359 0.719527
## PriceEconomy -9.325e-04 3.318e-05 -28.105 < 2e-16 ***
## PricePremium 5.781e-04 2.294e-05 25.197 < 2e-16 ***
## SeatsTotal NA NA NA NA
## PitchDifference NA NA NA NA
## WidthDifference NA NA NA NA
## PercentPremiumSeats 1.114e-02 7.653e-03 1.456 0.146197
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2123 on 437 degrees of freedom
## Multiple R-squared: 0.7878, Adjusted R-squared: 0.7781
## F-statistic: 81.12 on 20 and 437 DF, p-value: < 2.2e-16Fiting linear model according to our requirement
fitt <- lm(formula = air.df$PriceRelative~ PitchDifference+WidthDifference+FlightDuration+PercentPremiumSeats, data = air.df)
summary(fitt)##
## Call:
## lm(formula = air.df$PriceRelative ~ PitchDifference + WidthDifference +
## FlightDuration + PercentPremiumSeats, data = air.df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.79439 -0.29424 -0.03427 0.16197 1.13688
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.179033 0.101492 -1.764 0.07840 .
## PitchDifference 0.059311 0.015921 3.725 0.00022 ***
## WidthDifference 0.118140 0.024555 4.811 2.05e-06 ***
## FlightDuration 0.021707 0.005085 4.269 2.39e-05 ***
## PercentPremiumSeats -0.005999 0.003898 -1.539 0.12454
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.381 on 453 degrees of freedom
## Multiple R-squared: 0.2913, Adjusted R-squared: 0.285
## F-statistic: 46.54 on 4 and 453 DF, p-value: < 2.2e-16coefficients(fitt)## (Intercept) PitchDifference WidthDifference
## -0.179033482 0.059310975 0.118140211
## FlightDuration PercentPremiumSeats
## 0.021707245 -0.005999062confint(fitt)## 2.5 % 97.5 %
## (Intercept) -0.37848675 0.020419787
## PitchDifference 0.02802222 0.090599731
## WidthDifference 0.06988357 0.166396852
## FlightDuration 0.01171405 0.031700439
## PercentPremiumSeats -0.01366032 0.001662193fitted(fitt)## 1 2 3 4 5
## 0.472080459 0.472080459 0.472080459 0.472080459 0.383297829
## 6 7 8 9 10
## 0.383297829 0.383297829 0.347263803 0.347263803 0.455800026
## 11 12 13 14 15
## 0.455800026 0.455800026 0.455800026 0.457536605 0.457536605
## 16 17 18 19 20
## 0.457536605 0.405005073 0.405005073 0.405005073 0.352690614
## 21 22 23 24 25
## 0.352690614 0.352690614 0.350736962 0.350736962 0.350736962
## 26 27 28 29 30
## 0.396105103 0.396105103 0.396105103 0.312749284 0.312749284
## 31 32 33 34 35
## 0.312749284 0.289305460 0.289305460 0.289305460 0.289305460
## 36 37 38 39 40
## 0.499214515 0.499214515 0.499214515 0.289305460 0.289305460
## 41 42 43 44 45
## 0.289305460 0.289305460 0.323602906 0.323602906 0.323602906
## 46 47 48 49 50
## 0.385251481 0.385251481 0.385251481 0.482934081 0.482934081
## 51 52 53 54 55
## 0.482934081 0.354462677 0.453881857 0.453881857 0.453881857
## 56 57 58 59 60
## 0.345345635 0.345345635 0.345345635 0.484706145 0.474937885
## 61 62 63 64 65
## 0.484706145 0.640641256 0.640641256 0.640641256 0.640641256
## 66 67 68 69 70
## 0.658658269 0.658658269 0.658658269 0.658658269 0.620670591
## 71 72 73 74 75
## 0.620670591 0.620670591 0.635214445 -0.078824489 -0.072963533
## 76 77 78 79 80
## -0.078824489 -0.079909852 -0.072963533 -0.085553735 -0.073614751
## 81 82 83 84 85
## -0.073614751 0.390181604 0.390181604 0.390181604 0.390181604
## 86 87 88 89 90
## 0.406462037 0.406462037 0.406462037 0.406462037 0.852291252
## 91 92 93 94 95
## 0.852291252 0.852291252 0.852291252 0.852291252 0.852291252
## 96 97 98 99 100
## 0.852291252 0.852291252 -0.066683231 0.504390812 0.504390812
## 101 102 103 104 105
## 0.504390812 0.504390812 0.490064030 0.490064030 0.490064030
## 106 107 108 109 110
## 0.490064030 0.546068721 0.546068721 0.546068721 0.504390812
## 111 112 113 114 115
## 0.504390812 0.504390812 0.350703520 0.339849898 0.339849898
## 116 117 118 119 120
## 0.314452422 0.332686507 0.332686507 0.339849898 0.319879233
## 121 122 123 124 125
## 0.314452422 0.314452422 0.314452422 0.332686507 0.301862220
## 126 127 128 129 130
## 0.339849898 0.359820563 0.314452422 0.359820563 0.301862220
## 131 132 133 134 135
## 0.314452422 0.339849898 0.350703520 0.323569465 0.359820563
## 136 137 138 139 140
## 0.289272018 0.350703520 0.289272018 0.314452422 0.301862220
## 141 142 143 144 145
## 0.301862220 0.289272018 0.289272018 0.289272018 0.339849898
## 146 147 148 149 150
## 0.323569465 0.291008598 0.291008598 0.289272018 0.316672075
## 151 152 153 154 155
## 0.291008598 0.005905413 0.009812717 0.005905413 0.009812717
## 156 157 158 159 160
## 0.744664568 0.744664568 0.744664568 0.744664568 0.762681581
## 161 162 163 164 165
## 0.762681581 0.762681581 0.762681581 0.715876813 0.715876813
## 166 167 168 169 170
## 0.715876813 0.715876813 0.735547525 0.735547525 0.735547525
## 171 172 173 174 175
## 0.735547525 0.726430482 0.773535203 0.734110898 0.734110898
## 176 177 178 179 180
## 0.734110898 0.734110898 0.773535203 0.746401147 0.666735560
## 181 182 183 184 185
## 0.666735560 0.666735560 0.666735560 0.773535203 0.687278476
## 186 187 188 189 190
## 0.687278476 0.712675952 0.712675952 0.712675952 0.687278476
## 191 192 193 194 195
## 0.656454188 0.656454188 0.656454188 0.656454188 0.649290798
## 196 197 198 199 200
## 0.649290798 0.649290798 0.649290798 0.732429544 0.732429544
## 201 202 203 204 205
## 0.732429544 0.752400209 0.752400209 0.667307811 0.667307811
## 206 207 208 209 210
## 0.667307811 0.667307811 0.660144420 0.674688274 0.674688274
## 211 212 213 214 215
## 0.674688274 0.426203128 0.426203128 0.426203128 0.400805652
## 216 217 218 219 220
## 0.400805652 0.400805652 0.400805652 0.400805652 0.400805652
## 221 222 223 224 225
## 0.400805652 0.400805652 0.379098407 0.379098407 0.379098407
## 226 227 228 229 230
## 0.368244785 0.368244785 0.413395854 0.413395854 0.413395854
## 231 232 233 234 235
## 0.395378841 0.419256810 0.419256810 0.420776317 0.420776317
## 236 237 238 239 240
## 0.418822665 0.418822665 0.420776317 0.420776317 0.502868071
## 241 242 243 244 245
## 0.502868071 0.502868071 0.515675345 0.515675345 0.515675345
## 246 247 248 249 250
## 0.492014449 0.492014449 0.492014449 0.492014449 0.463143813
## 251 252 253 254 255
## 0.463143813 0.463143813 0.524575315 0.524575315 0.524575315
## 256 257 258 259 260
## 0.524575315 0.479424247 0.479424247 0.479424247 0.470307204
## 261 262 263 264 265
## 0.464880393 0.464880393 0.464880393 0.434273178 0.434273178
## 266 267 268 269 270
## 0.434273178 0.470307204 0.430582947 0.430582947 0.430582947
## 271 272 273 274 275
## 0.524575315 0.524575315 0.524575315 0.524575315 0.470307204
## 276 277 278 279 280
## 0.517411925 0.517411925 0.517411925 0.430582947 0.517411925
## 281 282 283 284 285
## -0.042492801 -0.043144018 -0.034895265 -0.034461120 -0.034244048
## 286 287 288 289 290
## 0.022155808 0.022155808 0.022155808 -0.040756221 -0.043144018
## 291 292 293 294 295
## -0.039236714 0.022155808 -0.042926946 -0.039887931 -0.095858670
## 296 297 298 299 300
## -0.096310174 -0.089580928 -0.081966034 -0.081966034 -0.034895265
## 301 302 303 304 305
## -0.075236788 -0.099349188 -0.098915043 -0.101319433 -0.083051396
## 306 307 308 309 310
## -0.099566261 -0.101319433 0.426203128 0.426203128 0.426203128
## 311 312 313 314 315
## 0.413395854 0.413395854 0.426203128 0.413395854 0.517672742
## 316 317 318 319 320
## 0.517672742 0.517672742 0.517672742 0.485111876 0.485111876
## 321 322 323 324 325
## 0.485111876 0.450814429 0.450814429 0.450814429 0.533953176
## 326 327 328 329 330
## 0.533953176 0.533953176 0.425416953 0.425416953 0.425416953
## 331 332 333 334 335
## 0.298863717 0.298863717 0.298863717 0.298863717 0.492492339
## 336 337 338 339 340
## 0.492492339 0.492492339 0.492492339 0.520265657 0.520265657
## 341 342 343 344 345
## 0.520265657 0.502248644 0.487704790 0.529382700 0.529382700
## 346 347 348 349 350
## 0.529382700 0.505721803 0.487704790 0.487704790 0.545663133
## 351 352 353 354 355
## 0.545663133 0.545663133 0.545663133 0.508635305 0.508635305
## 356 357 358 359 360
## 0.508635305 0.510371885 0.543709481 0.543709481 0.543709481
## 361 362 363 364 365
## 0.595464283 0.595464283 0.597977593 0.597977593 0.597977593
## 366 367 368 369 370
## 0.597977593 0.591084662 0.591084662 0.591084662 0.580231040
## 371 372 373 374 375
## 0.580231040 0.580231040 0.484285019 0.484285019 0.484285019
## 376 377 378 379 380
## 0.498828873 0.498828873 0.498828873 0.888616381 0.888616381
## 381 382 383 384 385
## 0.888616381 0.888616381 0.888616381 0.908369974 0.908369974
## 386 387 388 389 390
## 0.906633394 0.872335948 0.872335948 0.872335948 0.875809107
## 391 392 393 394 395
## 0.875809107 0.875809107 0.908369974 0.888616381 0.906633394
## 396 397 398 399 400
## 0.908369974 0.908369974 0.872335948 0.875809107 0.912060205
## 401 402 403 404 405
## 0.912060205 0.912060205 0.912060205 0.888616381 0.888616381
## 406 407 408 409 410
## 0.503119231 0.503119231 0.503119231 0.503119231 0.525779305
## 411 412 413 414 415
## 0.525779305 0.525779305 0.525779305 0.370138361 0.370138361
## 416 417 418 419 420
## 0.370138361 0.370138361 0.511235451 0.511235451 0.511235451
## 421 422 423 424 425
## 0.511235451 0.377518824 0.377518824 0.377518824 0.377518824
## 426 427 428 429 430
## 0.523775107 0.523775107 0.404385262 0.404385262 0.472980155
## 431 432 433 434 435
## 0.472980155 0.472980155 0.424138855 0.426092507 0.426092507
## 436 437 438 439 440
## 0.426092507 0.491214241 0.491214241 0.523775107 0.981244537
## 441 442 443 444 445
## 0.926976426 0.926976426 0.981244537 0.981244537 0.981244537
## 446 447 448 449 450
## 0.981244537 0.981244537 0.926976426 0.914386224 0.914386224
## 451 452 453 454 455
## 0.914386224 0.926976426 0.914386224 0.914386224 0.914386224
## 456 457 458
## 0.914386224 0.928930078 0.914386224Since the p-value<2.2e-16,it is safe to reject the null hypothesis and it can be observed that the variables are related.
The model can be written as - PriceRelative = 0.059311PitchDifference + 0.118140WidthDifference + 0.021707FlightDuration + -0.005999PercentPremiumSeats + intercept
Result and Conclusion
The difference in prices of premium and economy airline tickets depends on the factors width and pitch of the seats of the airlines, as well as the flight duration and percentage of premium seats.
The price increases with increase in width, pitch and flight duration. The price decreases with increase in percentage of premium seats.