Airline
Aditya Satheesh
20 December 2017
Reading dataset into R
airline.df <- read.csv(paste("SixAirlinesDataV2.csv",sep = ""))
View(airline.df)Summary Statistics using describe command
library(psych)
describe(airline.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 0.23Summary Statistics using summary command
summary(airline.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. :24.69Plot of Premium Economy vs Economy seat price
plot(~PriceEconomy + PricePremium, data=airline.df, main="Premium Economy Price vs. Economy Price")
abline(0,1)
Economy Pricing
hist(airline.df$PriceEconomy, xlab="Economy Seat prices",col="lightblue", main="Economoy seat pricing")
boxplot(airline.df$PriceEconomy,col="blue")
Premium Economy Pricing
hist(airline.df$PricePremium, xlab="Economy Seat prices",col="lightblue", main="Economoy seat pricing")
boxplot(airline.df$PricePremium,col="blue")
Economy seats
hist(airline.df$SeatsEconomy, xlab="Seats Economy",col = "lightblue",main = "Economy class")
boxplot(airline.df$SeatsEconomy,col="blue")
Premium Economy Seats
hist(airline.df$SeatsPremium, xlab="Seats Economy",col = "lightblue",main = "Economy class")
boxplot(airline.df$SeatsPremium,col="blue")
Boxplot to show the variations in economy seats between different aircrafts
boxplot(airline.df$SeatsEconomy ~ airline.df$Aircraft, horizontal=TRUE, yaxt="n", ylab="Aircraft", xlab="SeatsEconomy", main="Aircraft Vs. SeatsEconomy", col=c("blue", "green"))
axis(side=2, at=c(1,2), labels = c("Boeing", "Airbus"))
Scatterplot Matrix for PriceEconomy and PricePremium
library(car)
scatterplotMatrix(formula = ~ PriceEconomy + PricePremium, data=airline.df, diagonal="histogram")
COrrelation
options(digits=2)
cor(airline.df$PitchDifference, airline.df$WidthDifference)## [1] 0.76The correlation between pitch difference and width difference was found to be 0.76
Corrgram
library(corrgram)
corrgram(airline.df, order=TRUE, lower.panel=panel.shade, upper.panel=panel.pie, text.panel=panel.txt, main="Corrgram of airlines intercorrelation")
Correlation Test
cor.test(airline.df$PitchEconomy, airline.df$PriceEconomy)##
## Pearson's product-moment correlation
##
## data: airline.df$PitchEconomy and airline.df$PriceEconomy
## t = 8, df = 500, p-value = 3e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.29 0.45
## sample estimates:
## cor
## 0.37Since p value is less than 0.05 the correlation is statistically significant
Hypothesis - Greater the duration of the flight, more expensive the price of the ticket
t.test(airline.df$PriceRelative,airline.df$FlightDuration)##
## Welch Two Sample t-test
##
## data: airline.df$PriceRelative and airline.df$FlightDuration
## t = -40, df = 500, p-value <2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -7.4 -6.8
## sample estimates:
## mean of x mean of y
## 0.49 7.58Since the p value is <2e-16 the null hypothesis cannot be rejected
Linear Regression
model.lm = lm(PriceRelative~PitchDifference + WidthDifference + FlightDuration, data= airline.df)
summary(model.lm)##
## Call:
## lm(formula = PriceRelative ~ PitchDifference + WidthDifference +
## FlightDuration, data = airline.df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.7482 -0.2837 -0.0603 0.1645 1.1572
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.25490 0.08885 -2.87 0.00431 **
## PitchDifference 0.05475 0.01567 3.49 0.00052 ***
## WidthDifference 0.12997 0.02336 5.56 4.5e-08 ***
## FlightDuration 0.02160 0.00509 4.24 2.7e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.38 on 454 degrees of freedom
## Multiple R-squared: 0.288, Adjusted R-squared: 0.283
## F-statistic: 61.1 on 3 and 454 DF, p-value: <2e-16Since p value is less than 2e-16 it is statistically significant
Beta Coefficients
model.lm$coefficients## (Intercept) PitchDifference WidthDifference FlightDuration
## -0.255 0.055 0.130 0.022The multiple R squared value(0.288) indicates that the model accounts for 28.8% of the variance in Relative Price.
The residual error of 0.38 can be thought oof as the average error in predicting relative price from the various factors in this model.