Airline Industry Case Analysis
Sai Harshini
December 20, 2017
R Markdown
- Reading the data into R
plane.df <- read.csv(paste("SixAirlinesDataV2.csv", sep=""))
View(plane.df)str(plane.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 ...- Summarizing the data to understand the mean, median, standard deviation of each variable
summary(plane.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(plane.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 0.23mean(plane.df$SeatsEconomy)## [1] 202.3122sd(plane.df$SeatsEconomy)## [1] 76.37353mean(plane.df$SeatsPremium)## [1] 33.64847sd(plane.df$SeatsPremium)## [1] 13.26142mean(plane.df$PitchEconomy)## [1] 31.21834sd(plane.df$PitchEconomy)## [1] 0.6551695mean(plane.df$PitchPremium)## [1] 37.90611sd(plane.df$PitchPremium)## [1] 1.313924mean(plane.df$WidthEconomy)## [1] 17.83843sd(plane.df$WidthEconomy)## [1] 0.5575102mean(plane.df$WidthPremium)## [1] 19.47162sd(plane.df$WidthPremium)## [1] 1.097173- To draw Box Plots / Bar Plots to visualize the distribution of each variable independently
hist(plane.df$SeatsEconomy,
col="blue",
xlab="SeatsEconomy",
main="Seats Economy")
hist(plane.df$SeatsPremium,
col="blue",
xlab="SeatsPremium",
main="Seats Premium")
hist(plane.df$PitchEconomy,
col="blue",
xlab="PitchEconomy",
main="Pitch Economy")
hist(plane.df$PitchPremium,
col="blue",
xlab="PitchPremium",
main="Pitch Premium")
hist(plane.df$WidthEconomy,
col="blue",
xlab="WidthEconomy",
main="Width Economy")
hist(plane.df$WidthPremium,
col="blue",
xlab="WidthPremium",
main="Width Premium")
par(mfrow=c(2, 1))
boxplot(plane.df$PriceEconomy, xlab="Prices", ylab="Economy Class",
main="Economy Class prices", horizontal=TRUE)
boxplot(plane.df$PricePremium, xlab="Prices", ylab="Premium Class",
main="Premium Class prices", horizontal=TRUE)
par(mfrow=c(1, 1))boxplot(plane.df$PriceRelative, xlab="Prices", ylab="Price Relative",
main="Relative prices", horizontal=TRUE)
hist(plane.df$SeatsTotal,
col="blue",
xlab="SeatsEconomy",
main="Seats Economy")
hist(plane.df$PitchDifference,
col="blue",
xlab="PitchDifference",
main="Pitch Difference")
hist(plane.df$WidthDifference,
col="blue",
xlab="WidthDifference",
main="Width Difference")
boxplot(plane.df$PercentPremiumSeats, xlab="Percentages", ylab="PercentagePremium",
main="Percentage of Premium Seats", horizontal=TRUE)
- To draw Scatter Plots to understand how are the variables correlated pair-wise
library(car)##
## Attaching package: 'car'## The following object is masked from 'package:psych':
##
## logitscatterplot(PriceRelative ~ PitchDifference, data=plane.df,main="Scatterplot of Relative Price vs. PitchDifference",
xlab="PitchDifference",
ylab="PriceRelative")
scatterplot(PriceRelative ~ WidthDifference, data=plane.df,main="Scatterplot of Relative Price vs. WidthDifference",
xlab="WidthDifference",
ylab="PriceRelative")
scatterplot(PriceRelative ~ PercentPremiumSeats , data=plane.df,main="Scatterplot of Relative Price vs. PercentPremiumSeats",
xlab="PercentPremiumSeats",
ylab="PriceRelative")
5 ) To draw a Corrgram; To Create a Variance-Covariance Matrix
library(corrgram)
corrgram(plane.df, order=FALSE,
lower.panel=panel.shade,
upper.panel=panel.pie,
diag.panel=panel.minmax,
text.panel=panel.txt,
main="Corrgram of plane.df intercorrelations")
cor(plane.df[ , 6:18])## 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 1.00000000round(2)## [1] 2T-tests
Null Hyhothesis 1 :- There is no significant difference between the prices of Economy Tickets and Premium tickets.
t.test(plane.df$PriceEconomy, plane.df$PitchPremium, paired = TRUE)##
## Paired t-test
##
## data: plane.df$PriceEconomy and plane.df$PitchPremium
## t = 27.919, df = 457, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 1198.427 1379.914
## sample estimates:
## mean of the differences
## 1289.17p value is less than 0.05. So we reject the null hypothesis and conclude in the favour of alternative hypothesis that there is a significant difference between the prices of Economy Tickets and Premium tickets.
Null Hyhothesis 2 :- There is no significant difference between the number of seats in Economy Class and Premium Class.
t.test(plane.df$SeatsEconomy, plane.df$SeatsPremium, paired = TRUE)##
## Paired t-test
##
## data: plane.df$SeatsEconomy and plane.df$SeatsPremium
## t = 52.414, df = 457, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 162.3400 174.9875
## sample estimates:
## mean of the differences
## 168.6638p value is less than 0.05. So we reject the null hypothesis and conclude in the favour of alternative hypothesis that there is a significant difference between the number of seats in Economy Class and Premium Class.
Formulating a Regression model.
To formulate a regression model of the form : y = b0 + b1x1 + b2x2 + …
Where y is PriceRelative and {x1,x2,x3,x4} are {PitchDifference, WidthDifference, PercentagePremiumSeats, SeatsTotal, FlightDuration}
lm = lm(PriceRelative~PitchDifference + WidthDifference + PercentPremiumSeats + SeatsTotal + FlightDuration, data= plane.df)
summary(lm)##
## Call:
## lm(formula = PriceRelative ~ PitchDifference + WidthDifference +
## PercentPremiumSeats + SeatsTotal + FlightDuration, data = plane.df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.8123 -0.2911 -0.0399 0.1527 1.1376
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.1292204 0.1138769 -1.135 0.257086
## PitchDifference 0.0629233 0.0163568 3.847 0.000137 ***
## WidthDifference 0.1113448 0.0255474 4.358 1.62e-05 ***
## PercentPremiumSeats -0.0072378 0.0041047 -1.763 0.078527 .
## SeatsTotal -0.0002205 0.0002285 -0.965 0.335167
## FlightDuration 0.0226697 0.0051823 4.374 1.51e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.381 on 452 degrees of freedom
## Multiple R-squared: 0.2927, Adjusted R-squared: 0.2849
## F-statistic: 37.41 on 5 and 452 DF, p-value: < 2.2e-16Beta coefficients
lm$coefficients## (Intercept) PitchDifference WidthDifference
## -0.1292204370 0.0629233100 0.1113448211
## PercentPremiumSeats SeatsTotal FlightDuration
## -0.0072377674 -0.0002204818 0.0226696594Since p value is less than 0.05 , we reject the null hyphotesis and conclude all the x variables as a whole hae a significant impact on y. Also t values for PitchDifference, WidthDifference and FlightDuration is leaa than 0.05, hence these variables have significant effect on PriceRelative
Hence , from the above analysis we can conclude that the factors that explain the difference in price between an economy ticket and a premium-economy airline ticket are Difference between the Pitches, Difference between the widths and flight durations.