Airline Pricing Analysis
Gourav Halder
5 October 2018
Read the data using read.csv
air = read.csv(paste("AirlinePricingData.csv", sep=""))
# View(air)
# library(psych)
# describe(air)Q1a. Write R code to generate the correlation matrix for the given continuous variables {“Price”, “AdvancedBookingDays”, “FlyingMinutes”, “Capacity”, “SeatPitch”, “SeatWidth”}
var1 = air[, c(17:18, 8, 11:13)]
library(psych)
matrix = cor(var1)
round(matrix, 2)## Price AdvancedBookingDays FlyingMinutes Capacity
## Price 1.00 -0.01 -0.02 -0.03
## AdvancedBookingDays -0.01 1.00 0.01 -0.01
## FlyingMinutes -0.02 0.01 1.00 -0.32
## Capacity -0.03 -0.01 -0.32 1.00
## SeatPitch 0.07 -0.01 -0.03 0.51
## SeatWidth -0.06 0.05 -0.18 0.45
## SeatPitch SeatWidth
## Price 0.07 -0.06
## AdvancedBookingDays -0.01 0.05
## FlyingMinutes -0.03 -0.18
## Capacity 0.51 0.45
## SeatPitch 1.00 0.32
## SeatWidth 0.32 1.00Q1b. Write R code to generate the correlation matrix, along with their significance values, for the given continuous variables {“Price”, “AdvancedBookingDays”, “FlyingMinutes”, “Capacity”, “SeatPitch”, “SeatWidth”}
## Call:corr.test(x = var1, use = "complete")
## Correlation matrix
## Price AdvancedBookingDays FlyingMinutes Capacity
## Price 1.00 -0.01 -0.02 -0.03
## AdvancedBookingDays -0.01 1.00 0.01 -0.01
## FlyingMinutes -0.02 0.01 1.00 -0.32
## Capacity -0.03 -0.01 -0.32 1.00
## SeatPitch 0.07 -0.01 -0.03 0.51
## SeatWidth -0.06 0.05 -0.18 0.45
## SeatPitch SeatWidth
## Price 0.07 -0.06
## AdvancedBookingDays -0.01 0.05
## FlyingMinutes -0.03 -0.18
## Capacity 0.51 0.45
## SeatPitch 1.00 0.32
## SeatWidth 0.32 1.00
## Sample Size
## [1] 305
## Probability values (Entries above the diagonal are adjusted for multiple tests.)
## Price AdvancedBookingDays FlyingMinutes Capacity
## Price 0.00 1.00 1.00 1
## AdvancedBookingDays 0.87 0.00 1.00 1
## FlyingMinutes 0.75 0.93 0.00 0
## Capacity 0.65 0.88 0.00 0
## SeatPitch 0.19 0.81 0.55 0
## SeatWidth 0.30 0.34 0.00 0
## SeatPitch SeatWidth
## Price 1 1.00
## AdvancedBookingDays 1 1.00
## FlyingMinutes 1 0.01
## Capacity 0 0.00
## SeatPitch 0 0.00
## SeatWidth 0 0.00
##
## To see confidence intervals of the correlations, print with the short=FALSE optionQ1c. Write R code to visualize the correlation matrix in Q1b.
library(psych)
corr.test(var1, use="complete")Q1d. Write R code to generate the corrgram.
library(corrgram)
corrgram(var1, order=TRUE, lower.panel=panel.conf,
upper.panel=panel.pie, text.panel=panel.txt,
main="Corrgram of air intercorrelations")
Q1e. Write R code to generate the following corrgram. (Hint: This is a repeat of the previous question, where you had flexibility to create the corrgram of YOUR choice. Here, you will need to use package PerformanceAnalytics.)
library("PerformanceAnalytics")## Loading required package: xts## Loading required package: zoo##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric##
## Attaching package: 'PerformanceAnalytics'## The following object is masked from 'package:graphics':
##
## legendchart.Correlation(var1, histogram = TRUE)
Q2a. Test whether the ticket prices of Mumbai to Delhi flights are more than INR 5000.
bom_to_del <- subset(air,air$DepartureCityCode == 'BOM' & air$ArrivalCityCode == 'DEL')
t.test(bom_to_del$Price, mu = 5000)##
## One Sample t-test
##
## data: bom_to_del$Price
## t = 6.0784, df = 129, p-value = 1.277e-08
## alternative hypothesis: true mean is not equal to 5000
## 95 percent confidence interval:
## 5844.506 6659.601
## sample estimates:
## mean of x
## 6252.054Since, P-value is less than 0.05 hence, we reject null hypotheis and accept alternate hypothesis of mean flight price more than INR 5000.
Q2b. Test whether the ticket prices of morning flights are greater than the afternoon flights
t.test(air$Price ~ air$Departure, data=air, alternative = "greater")##
## Welch Two Sample t-test
##
## data: air$Price by air$Departure
## t = 1.736, df = 296.58, p-value = 0.0418
## alternative hypothesis: true difference in means is greater than 0
## 95 percent confidence interval:
## 22.71262 Inf
## sample estimates:
## mean in group AM mean in group PM
## 5598.893 5140.610Since, P-value is less than 0.05 hence, we reject null hypotheis and accept alternate hypothesis of mean morning flight price more than afternoon flight price
Q2c. Test whether the ticket prices around Diwali is more compared to non-Diwali ticket prices.
t.test(air$Price ~ air$IsDiwali, data=air, alternative = "greater")##
## Welch Two Sample t-test
##
## data: air$Price by air$IsDiwali
## t = -2.9799, df = 244.52, p-value = 0.9984
## alternative hypothesis: true difference in means is greater than 0
## 95 percent confidence interval:
## -1295.591 Inf
## sample estimates:
## mean in group 0 mean in group 1
## 5063.810 5897.479Since, P-value is more than 0.05 hence, we accept null hypotheis of mean flight price around Diwali NOT more than flight price of Non-Diwali
Q2d. Test whether the ticket prices on Air India flights are greater than IndiGo flights
subset_data = subset(air, air$Airline == "IndiGo" | air$Airline == "Air India")
t.test(subset_data$Price ~ subset_data$Airline, data=subset_data, alternative = "greater")##
## Welch Two Sample t-test
##
## data: subset_data$Price by subset_data$Airline
## t = 2.7205, df = 87.71, p-value = 0.00393
## alternative hypothesis: true difference in means is greater than 0
## 95 percent confidence interval:
## 566.0833 Inf
## sample estimates:
## mean in group Air India mean in group IndiGo
## 6335.000 4879.525Since, P-value is less than 0.05 hence, we reject null hypotheis and accept alternate hypothesis of mean flight price of Air India more than IndiGo
Q3a. Run a simple linear regression of airline ticket Price on the Advanced Booking Days. Write R code to output the summary of the model.
Y = airline ticket price (Dependent Variable) X = advance booking days (Independent Variable) Y = b0 + b1*X + e
reg <- lm(Price ~ AdvancedBookingDays, data = air)
summary(reg)##
## Call:
## lm(formula = Price ~ AdvancedBookingDays, data = air)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2786.5 -1320.8 -688.9 351.2 12594.0
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5422.959 224.497 24.16 <2e-16 ***
## AdvancedBookingDays -0.983 6.154 -0.16 0.873
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2392 on 303 degrees of freedom
## Multiple R-squared: 8.422e-05, Adjusted R-squared: -0.003216
## F-statistic: 0.02552 on 1 and 303 DF, p-value: 0.8732Therefore, the regression model is: Airline ticket price = 5422.959 - Advance booking days*0.983