Airline
Prasunn
19 ??????????????? 2018
air.df<-read.csv(paste("SixAirlinesDataV2.csv",sep=""))
View(air.df)Summary
library(psych)
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. :24.69str(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 ...Mean of Premium price based on airlines
aggregate(air.df$PricePremium~air.df$Airline,FUN=mean)## air.df$Airline air.df$PricePremium
## 1 AirFrance 3065.2162
## 2 British 1937.0286
## 3 Delta 684.6739
## 4 Jet 483.3607
## 5 Singapore 1239.9250
## 6 Virgin 2721.6935Mean Pitch Diffence based on different airlines
aggregate(air.df$PitchDifference~air.df$Airline,FUN = mean)## air.df$Airline air.df$PitchDifference
## 1 AirFrance 6.000000
## 2 British 7.000000
## 3 Delta 3.000000
## 4 Jet 9.540984
## 5 Singapore 6.000000
## 6 Virgin 7.000000Mean width differece based on different airlines
aggregate(air.df$WidthDifference~air.df$Airline,FUN = mean)## air.df$Airline air.df$WidthDifference
## 1 AirFrance 1.4324324
## 2 British 1.0000000
## 3 Delta 0.3913043
## 4 Jet 3.6557377
## 5 Singapore 1.0000000
## 6 Virgin 3.0000000Distribution of Relative pricing of different airlines
library(lattice)
histogram(air.df$PriceRelative,main = "Distribution pitch diff", col="light blue" )
Boxplot comparing no of Premium economy seats based on airlines
boxplot(air.df$SeatsPremium~air.df$Airline,ylab="Airlines",xlab="#Premium Class seats",col="light blue",horizontal=TRUE)
Boxplot comparing price of Premium economy seats based on airlines
boxplot(PricePremium~Airline, data =air.df, ylab = "Airlines", xlab = "Premium economy price", col = "light blue",horizontal=TRUE)
Some hypothesis we can get are 1.price is relatively dependent on width difference 2.price is relatively dependent on pitch difference 3.price is relatively is dependent on flight duration Checking corelation and scatterplot of price relative vs width difference
library(car)##
## Attaching package: 'car'## The following object is masked from 'package:psych':
##
## logitcor.test(air.df$PriceRelative,air.df$WidthDifference)##
## Pearson's product-moment correlation
##
## data: air.df$PriceRelative and air.df$WidthDifference
## t = 11.869, df = 456, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.4125388 0.5528218
## sample estimates:
## cor
## 0.4858024scatterplot(air.df$PriceRelative , air.df$WidthDifference, main="Price Relative vs width difference")
The correlation test coefficent shows that hypothesis 1 holds good.Width diff has dependence on price relative. Checking corelation and scatterplot of price relative vs width difference
cor.test(air.df$PriceRelative,air.df$PitchDifference)##
## Pearson's product-moment correlation
##
## data: air.df$PriceRelative and air.df$PitchDifference
## t = 11.331, df = 456, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.3940262 0.5372817
## sample estimates:
## cor
## 0.4687302scatterplot(air.df$PriceRelative ,air.df$PitchDifference, main="Price Relative vs pitch difference" )
The correlation test coefficent shows that hypothesis 2 holds good .Pitch diff has dependence on price relative. Scatterplot matirx between price relative/pitch difference/width difference
scatterplotMatrix(~ air.df$PriceRelative + air.df$PitchDifference + air.df$WidthDifference)
Checking corelation and scatterplot of price relative vs width difference
cor.test(air.df$PriceRelative,air.df$FlightDuration)##
## Pearson's product-moment correlation
##
## data: air.df$PriceRelative and air.df$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
## 0.121075scatterplot(air.df$PriceRelative ,air.df$FlightDuration, main="Price Relative vs flight duration" )
The correlation test coefficient is low for this .This shows that hypothesis 3 does not holds good and price doesn’t have significant dependence on flight duration.
Corrgram
library(corrgram)
corrgram(air.df,main="Corrgram",upper.panel = panel.pie)
From the above hypothesis we canconsider only hypothesis 1 & 2.So,to use linear regression we take “Y” as Price Relative ,“x1” as pitch diff and “x2” as width diff
fit <- lm(air.df$PriceRelative ~ air.df$WidthDifference + air.df$PitchDifference)
summary(fit)##
## Call:
## lm(formula = air.df$PriceRelative ~ air.df$WidthDifference +
## air.df$PitchDifference)
##
## 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
## air.df$WidthDifference 0.11621 0.02356 4.933 1.14e-06 ***
## air.df$PitchDifference 0.06019 0.01590 3.785 0.000174 ***
## ---
## 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-16The p value is very small So our hypothesis 1 and 2 holds good . This implies that the price relative of a aircraft depends upon the pitch difference and width difference. So the factor that play a role in creating the difference in pricing between economy and premium class seats are: 1.Pitch difference 2.Width difference