Airline Pricing Analysis
Dheepika C
16 February 2018
Summary
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. :24.69Creating Box Plots for price
boxplot(airline.df$PriceEconomy, horizontal = T)
boxplot(airline.df$PricePremium, horizontal = T)
Scatter Plots to understand how are the variables correlated pair-wise
attach(airline.df)
pairs(formula = ~ Aircraft + Airline+ PriceEconomy)
pairs(formula = ~ Aircraft + Airline+ PricePremium + PercentPremiumSeats )
Corrgram of airlines data
library(corrgram)
corrgram(airline.df, order=TRUE, lower.panel=panel.shade,
upper.panel=panel.pie, text.panel=panel.txt,
main="Corrgram of airlines data")
Variance-Covariance Matrix
round(cov(airline.df[,c(3,6:17)]),2)## FlightDuration SeatsEconomy SeatsPremium PitchEconomy
## FlightDuration 12.55 52.92 7.57 0.68
## SeatsEconomy 52.92 5832.92 633.07 7.21
## SeatsPremium 7.57 633.07 175.87 -0.30
## PitchEconomy 0.68 7.21 -0.30 0.43
## PitchPremium 0.45 11.96 0.09 -0.47
## WidthEconomy 0.90 15.91 3.37 0.11
## WidthPremium 0.40 8.58 -0.04 -0.39
## PriceEconomy 1983.54 9673.79 1489.38 238.70
## PricePremium 2959.98 17413.25 3717.36 190.85
## PriceRelative 0.19 0.14 -0.58 -0.12
## SeatsTotal 60.49 6465.99 808.94 6.91
## PitchDifference -0.23 4.75 0.38 -0.90
## WidthDifference -0.50 -7.33 -3.41 -0.50
## PitchPremium WidthEconomy WidthPremium PriceEconomy
## FlightDuration 0.45 0.90 0.40 1983.54
## SeatsEconomy 11.96 15.91 8.58 9673.79
## SeatsPremium 0.09 3.37 -0.04 1489.38
## PitchEconomy -0.47 0.11 -0.39 238.70
## PitchPremium 1.73 -0.02 1.08 65.43
## WidthEconomy -0.02 0.31 0.05 37.46
## WidthPremium 1.08 0.05 1.20 -61.85
## PriceEconomy 65.43 37.46 -61.85 976684.06
## PricePremium 149.85 108.12 90.48 1147494.77
## PriceRelative 0.25 -0.01 0.25 -128.50
## SeatsTotal 12.05 19.28 8.54 11163.18
## PitchDifference 2.20 -0.12 1.47 -173.28
## WidthDifference 1.10 -0.26 1.15 -99.32
## PricePremium PriceRelative SeatsTotal PitchDifference
## FlightDuration 2959.98 0.19 60.49 -0.23
## SeatsEconomy 17413.25 0.14 6465.99 4.75
## SeatsPremium 3717.36 -0.58 808.94 0.38
## PitchEconomy 190.85 -0.12 6.91 -0.90
## PitchPremium 149.85 0.25 12.05 2.20
## WidthEconomy 108.12 -0.01 19.28 -0.12
## WidthPremium 90.48 0.25 8.54 1.47
## PriceEconomy 1147494.77 -128.50 11163.18 -173.28
## PricePremium 1659293.12 18.48 21130.62 -41.00
## PriceRelative 18.48 0.20 -0.44 0.37
## SeatsTotal 21130.62 -0.44 7274.92 5.13
## PitchDifference -41.00 0.37 5.13 3.10
## WidthDifference -17.64 0.26 -10.74 1.59
## WidthDifference
## FlightDuration -0.50
## SeatsEconomy -7.33
## SeatsPremium -3.41
## PitchEconomy -0.50
## PitchPremium 1.10
## WidthEconomy -0.26
## WidthPremium 1.15
## PriceEconomy -99.32
## PricePremium -17.64
## PriceRelative 0.26
## SeatsTotal -10.74
## PitchDifference 1.59
## WidthDifference 1.41Hypothesis
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.
T-Tests
cor.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,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,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
## 0.4687302These 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.
Formulating a Regression Model using lm()
Dependent variable - PriceRelative Independent variables - PitchDifference, WidthDifference, PercentPremiumSeats and Flight Duration
fit <- lm(formula = airline.df$PriceRelative~ PitchDifference+WidthDifference+FlightDuration+PercentPremiumSeats, data = airline.df)
summary(fit)##
## Call:
## lm(formula = airline.df$PriceRelative ~ PitchDifference + WidthDifference +
## FlightDuration + PercentPremiumSeats, data = airline.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-16Since 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 = 0.059311 PitchDifference + 0.118140 WidthDifference + 0.021707 FlightDuration + -0.005999 PercentPremiumSeats + intercept
Inference
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.
The price increases with increase in width, pitch and flight duration.