Flights
Siddhant Vats
January 21, 2018
Reading and viewinf data:
air.df <- read.csv(paste("SixAirlinesDataV2.csv", sep=""))
View(air.df)Getting Summary stats:
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. :24.69Converting into factor variables:
air.df$Airline<-factor(air.df$Airline)
air.df$Aircraft <- factor(air.df$Aircraft)
air.df$TravelMonth <- factor(air.df$TravelMonth)
air.df$IsInternational <- factor(air.df$IsInternational)Plotting each variable indiviually:
plot(air.df$Airline)
plot(air.df$Airline)
plot(air.df$Aircraft)
plot(air.df$TravelMonth)
plot(air.df$IsInternational)
hist(air.df$FlightDuration,main = "Distribution of Flight Duration",xlab ="Flight Duration",ylab = "Frequency")
hist(air.df$SeatsEconomy,main = "Distribution of number of seats of economy class",xlab = "Number of Economy Seat",ylab = "Frequency")
hist(air.df$SeatsPremium, main = "Distribution of number of seats of premium class", xlab= "Seat in Premium class",ylab = "Frequency")
hist(air.df$PitchEconomy,main = "Distribution of pitch of economy class seats",xlab="Pitch of economy class seats",ylab = "Frequency")
hist(air.df$PitchPremium,main = "Distribution of pitch of premium class seats",xlab = "Pitch of premium class seats",ylab = "Frequency")
hist(air.df$WidthEconomy,main = "Distribution of width of economic class seats",xlab = "Width of Economy class seats",ylab = "Frequency")
hist(air.df$WidthPremium,main = "Distribution of width of premium class seats",xlab="Width of Premium class seats",ylab = "Frequency")
hist(air.df$PriceEconomy,main = "Distribution of price in economy class seats",xlab = "Price of economy class seats",ylab = "Frequency")
hist(air.df$PricePremium,main = "Distribution of price in premium class seats",xlab = "Price of premium class seats",ylab = "Frequency")
hist(air.df$PriceRelative,main = "Distribution of Relative price",xlab = "Relative(PricePremium - PriceEconomy) / PriceEconomy",ylab = "Frequency")
hist(air.df$SeatsTotal,main = "Distribution of total seats(Economy + premium)",xlab = "Total seats",ylab = "Frequency")
hist(air.df$PitchDifference,main = "Distribution of Pitch difference",xlab = "Pitch difference",ylab = "Frequency")
hist(air.df$WidthDifference,main = "Distribution of Width difference",xlab = "Width difference",ylab = "Frequency")
hist(air.df$PercentPremiumSeats,main = "Distribution of Percentage of premium seats",xlab ="Percentage of premium seats" ,ylab = "Frequency")
Plotting Corrgram to get the correlation between the matrix:
library(corrgram)
corrgram(air.df, order=TRUE, lower.panel=panel.shade,
upper.panel=panel.pie, text.panel=panel.txt,
main="Corrgram of store variables")
Generating correlation matrix:
cor(air.df[,c(3,6:18)])## FlightDuration SeatsEconomy SeatsPremium PitchEconomy
## FlightDuration 1.00000000 0.195621187 0.161236400 0.29377174
## SeatsEconomy 0.19562119 1.000000000 0.625056587 0.14412692
## SeatsPremium 0.16123640 0.625056587 1.000000000 -0.03421296
## PitchEconomy 0.29377174 0.144126924 -0.034212963 1.00000000
## PitchPremium 0.09621471 0.119221250 0.004883123 -0.55060624
## WidthEconomy 0.45647720 0.373670252 0.455782883 0.29448586
## WidthPremium 0.10343747 0.102431959 -0.002717527 -0.53929285
## PriceEconomy 0.56664039 0.128167220 0.113642176 0.36866123
## PricePremium 0.64873981 0.177000928 0.217612376 0.22614179
## PriceRelative 0.12107501 0.003956939 -0.097196009 -0.42302204
## SeatsTotal 0.20023299 0.992607966 0.715171053 0.12373524
## PitchDifference -0.03749288 0.035318044 0.016365566 -0.78254993
## WidthDifference -0.11856070 -0.080670148 -0.216168666 -0.63557430
## PercentPremiumSeats 0.06051625 -0.330935223 0.485029771 -0.10280880
## PitchPremium WidthEconomy WidthPremium PriceEconomy
## FlightDuration 0.096214708 0.45647720 0.103437469 0.56664039
## SeatsEconomy 0.119221250 0.37367025 0.102431959 0.12816722
## SeatsPremium 0.004883123 0.45578288 -0.002717527 0.11364218
## PitchEconomy -0.550606241 0.29448586 -0.539292852 0.36866123
## PitchPremium 1.000000000 -0.02374087 0.750259029 0.05038455
## WidthEconomy -0.023740873 1.00000000 0.081918728 0.06799061
## WidthPremium 0.750259029 0.08191873 1.000000000 -0.05704522
## PriceEconomy 0.050384550 0.06799061 -0.057045224 1.00000000
## PricePremium 0.088539147 0.15054837 0.064020043 0.90138870
## PriceRelative 0.417539056 -0.04396116 0.504247591 -0.28856711
## SeatsTotal 0.107512784 0.40545860 0.091297500 0.13243313
## PitchDifference 0.950591466 -0.12722421 0.760121272 -0.09952511
## WidthDifference 0.703281797 -0.39320512 0.884149655 -0.08449975
## PercentPremiumSeats -0.175487414 0.22714172 -0.183312058 0.06532232
## PricePremium PriceRelative SeatsTotal PitchDifference
## FlightDuration 0.64873981 0.121075014 0.20023299 -0.03749288
## SeatsEconomy 0.17700093 0.003956939 0.99260797 0.03531804
## SeatsPremium 0.21761238 -0.097196009 0.71517105 0.01636557
## PitchEconomy 0.22614179 -0.423022038 0.12373524 -0.78254993
## PitchPremium 0.08853915 0.417539056 0.10751278 0.95059147
## WidthEconomy 0.15054837 -0.043961160 0.40545860 -0.12722421
## WidthPremium 0.06402004 0.504247591 0.09129750 0.76012127
## PriceEconomy 0.90138870 -0.288567110 0.13243313 -0.09952511
## PricePremium 1.00000000 0.031846537 0.19232533 -0.01806629
## PriceRelative 0.03184654 1.000000000 -0.01156894 0.46873025
## SeatsTotal 0.19232533 -0.011568942 1.00000000 0.03416915
## PitchDifference -0.01806629 0.468730249 0.03416915 1.00000000
## WidthDifference -0.01151218 0.485802437 -0.10584398 0.76089108
## PercentPremiumSeats 0.11639097 -0.161565556 -0.22091465 -0.09264869
## WidthDifference PercentPremiumSeats
## FlightDuration -0.11856070 0.06051625
## SeatsEconomy -0.08067015 -0.33093522
## SeatsPremium -0.21616867 0.48502977
## PitchEconomy -0.63557430 -0.10280880
## PitchPremium 0.70328180 -0.17548741
## WidthEconomy -0.39320512 0.22714172
## WidthPremium 0.88414965 -0.18331206
## PriceEconomy -0.08449975 0.06532232
## PricePremium -0.01151218 0.11639097
## PriceRelative 0.48580244 -0.16156556
## SeatsTotal -0.10584398 -0.22091465
## PitchDifference 0.76089108 -0.09264869
## WidthDifference 1.00000000 -0.27559416
## PercentPremiumSeats -0.27559416 1.00000000Impelmentin regression for price of economy class:
fit1<-lm(air.df$PriceEconomy~ air.df$FlightDuration+air.df$SeatsEconomy+air.df$SeatsPremium+air.df$PitchDifference+air.df$WidthDifference+air.df$PricePremium)Getting summary stats of regression analysis:
summary(fit1)##
## Call:
## lm(formula = air.df$PriceEconomy ~ air.df$FlightDuration + air.df$SeatsEconomy +
## air.df$SeatsPremium + air.df$PitchDifference + air.df$WidthDifference +
## air.df$PricePremium)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2365.36 -217.56 14.31 160.67 912.01
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 469.97042 101.91927 4.611 5.22e-06 ***
## air.df$FlightDuration -14.65160 7.29161 -2.009 0.04509 *
## air.df$SeatsEconomy 0.60660 0.32494 1.867 0.06258 .
## air.df$SeatsPremium -10.16913 1.98929 -5.112 4.72e-07 ***
## air.df$PitchDifference -4.56145 17.67483 -0.258 0.79647
## air.df$WidthDifference -82.47864 27.17490 -3.035 0.00254 **
## air.df$PricePremium 0.73312 0.02011 36.461 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 408.6 on 451 degrees of freedom
## Multiple R-squared: 0.8313, Adjusted R-squared: 0.829
## F-statistic: 370.3 on 6 and 451 DF, p-value: < 2.2e-16Getting variable whose p-vlaue is significant:
which(summary(fit1)$coefficients[,4]<0.05)## (Intercept) air.df$FlightDuration air.df$SeatsPremium
## 1 2 4
## air.df$WidthDifference air.df$PricePremium
## 6 7Getting variable whose p-vlaue is not significant:
which(summary(fit1)$coefficients[,4]>0.05)## air.df$SeatsEconomy air.df$PitchDifference
## 3 5Getting confidence interval:
confint(fit1)## 2.5 % 97.5 %
## (Intercept) 269.67479442 670.2660411
## air.df$FlightDuration -28.98135553 -0.3218542
## air.df$SeatsEconomy -0.03198731 1.2451917
## air.df$SeatsPremium -14.07856714 -6.2597021
## air.df$PitchDifference -39.29670094 30.1737960
## air.df$WidthDifference -135.88377697 -29.0735063
## air.df$PricePremium 0.69360554 0.7726346Getting coefficients:
coefficients(fit1)## (Intercept) air.df$FlightDuration air.df$SeatsEconomy
## 469.9704178 -14.6516049 0.6066022
## air.df$SeatsPremium air.df$PitchDifference air.df$WidthDifference
## -10.1691346 -4.5614525 -82.4786416
## air.df$PricePremium
## 0.7331200Impelmentin regression for price of premium class:
fit2<-lm(air.df$PricePremium~ air.df$FlightDuration+air.df$SeatsEconomy+air.df$SeatsPremium+air.df$PitchDifference+air.df$WidthDifference+air.df$PriceEconomy)Getting summary stats of regression analysis:
summary(fit2)##
## Call:
## lm(formula = air.df$PricePremium ~ air.df$FlightDuration + air.df$SeatsEconomy +
## air.df$SeatsPremium + air.df$PitchDifference + air.df$WidthDifference +
## air.df$PriceEconomy)
##
## Residuals:
## Min 1Q Median 3Q Max
## -890.7 -256.1 -24.4 154.8 3545.4
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -473.51759 120.89029 -3.917 0.000104 ***
## air.df$FlightDuration 74.60808 7.88567 9.461 < 2e-16 ***
## air.df$SeatsEconomy -0.82139 0.38253 -2.147 0.032305 *
## air.df$SeatsPremium 15.21609 2.30282 6.608 1.10e-10 ***
## air.df$PitchDifference -28.15622 20.79226 -1.354 0.176361
## air.df$WidthDifference 149.55172 31.58030 4.736 2.93e-06 ***
## air.df$PriceEconomy 1.01851 0.02793 36.461 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 481.6 on 451 degrees of freedom
## Multiple R-squared: 0.862, Adjusted R-squared: 0.8602
## F-statistic: 469.6 on 6 and 451 DF, p-value: < 2.2e-16Getting variable whose p-vlaue is significant:
which(summary(fit2)$coefficients[,4]<0.05)## (Intercept) air.df$FlightDuration air.df$SeatsEconomy
## 1 2 3
## air.df$SeatsPremium air.df$WidthDifference air.df$PriceEconomy
## 4 6 7Getting variable whose p-vlaue is not significant:
which(summary(fit2)$coefficients[,4]>0.05)## air.df$PitchDifference
## 5Getting confidence interval:
confint(fit2)## 2.5 % 97.5 %
## (Intercept) -711.0957670 -235.93941844
## air.df$FlightDuration 59.1108533 90.10530535
## air.df$SeatsEconomy -1.5731505 -0.06962792
## air.df$SeatsPremium 10.6905016 19.74167400
## air.df$PitchDifference -69.0179491 12.70551341
## air.df$WidthDifference 87.4889300 211.61451794
## air.df$PriceEconomy 0.9636146 1.07340835Getting coefficients:
coefficients(fit2)## (Intercept) air.df$FlightDuration air.df$SeatsEconomy
## -473.5175927 74.6080793 -0.8213892
## air.df$SeatsPremium air.df$PitchDifference air.df$WidthDifference
## 15.2160878 -28.1562179 149.5517240
## air.df$PriceEconomy
## 1.0185115Summary:
Price of premium class: 1)Flight duration postively correlated.( 74.6080793) 2)Seats in economy negatively correlated.( -0.8213892) 3)Seats in premium postively correlated.( 15.2160878) 4)width difference postively correlated.( 149.5517240) 5)price of economy class postively correlated.( 1.0185115)
Insights for premium class: 1)More Duration means more distance and that means more cost. 2)If more seats are available in economy more peolpe try to fit in there so price of premium class need to be decreased. 3)More seats in premium class means more cost towards that particular compartment and more cost towards luxary. 4)More width of seats mean less number of seats in particular in same area so more cost. 5)With increase in price of economy class complany has to increase the price of premium class to mantain the standard of premium class.
Price of Economy class: 1)Flight duration is negatively correlated.( -14.6516049) 2)width difference negatively correlated.( -82.4786416) 3)price of premium class seat positively correlated.( 0.7331200)
Insight for economy class: 1)With less duration company has to spent his fixed class and can’t optimize small variable cost but with more duration it can optimize (increase)variable cost so company can provide economy service in less cost for more duration. 2)Less width difference means less comfort so less cost. 3)Increase in price of premium class will lead to increase in price of economy class because again then everyone try to fit in economy class.
Limitation: 1)Not applied subset sellection method. 2)No consideration of Factor variables.