Airline Ticket Pricing Analysis
Sameer Mathur
Delhi-Mumbai Airline Pricing Analysis
PART 1
READING AND PREPARING DATA
1a. Reading data
Number of Rows and Columns
# reading data into R
airline.df <- read.csv(paste("AirlinePricingData.csv"))
# rows and columns of the data frame
dim(airline.df)
[1] 305 25
Column Names
# data column names
colnames(airline.df)
[1] "FlightNumber" "Airline" "DepartureCityCode"
[4] "ArrivalCityCode" "DepartureTime" "ArrivalTime"
[7] "Departure" "FlyingMinutes" "Aircraft"
[10] "PlaneModel" "Capacity" "SeatPitch"
[13] "SeatWidth" "DataCollectionDate" "DateDeparture"
[16] "IsWeekend" "Price" "AdvancedBookingDays"
[19] "IsDiwali" "DayBeforeDiwali" "DayAfterDiwali"
[22] "MetroDeparture" "MetroArrival" "MarketShare"
[25] "LoadFactor"
1b. Data Types
# data types of the data columns
str(airline.df)
'data.frame': 305 obs. of 25 variables:
$ FlightNumber : Factor w/ 63 levels "6E 129","6E 155",..: 25 32 62 4 61 45 57 16 59 17 ...
$ Airline : Factor w/ 4 levels "Air India","IndiGo",..: 3 3 4 2 4 3 4 2 4 3 ...
$ DepartureCityCode : Factor w/ 2 levels "BOM","DEL": 2 1 2 2 1 1 2 2 1 1 ...
$ ArrivalCityCode : Factor w/ 2 levels "BOM","DEL": 1 2 1 1 2 2 1 1 2 2 ...
$ DepartureTime : int 225 300 350 455 555 605 635 640 645 700 ...
$ ArrivalTime : int 435 505 605 710 805 815 850 855 855 915 ...
$ Departure : Factor w/ 2 levels "AM","PM": 1 1 1 1 1 1 1 1 1 1 ...
$ FlyingMinutes : int 130 125 135 135 130 130 135 135 130 135 ...
$ Aircraft : Factor w/ 2 levels "Airbus","Boeing": 2 2 2 1 2 2 2 1 2 2 ...
$ PlaneModel : Factor w/ 9 levels "738","739","77W",..: 1 1 1 6 1 1 1 6 1 2 ...
$ Capacity : int 156 156 189 180 189 156 189 180 189 138 ...
$ SeatPitch : int 30 30 29 30 29 30 29 30 29 30 ...
$ SeatWidth : num 17 17 17 18 17 17 17 18 17 17 ...
$ DataCollectionDate : Factor w/ 7 levels "Sep 10 2018",..: 2 4 6 7 6 4 6 7 6 4 ...
$ DateDeparture : Factor w/ 20 levels "Nov 6 2018","Nov 8 2018",..: 1 1 1 1 1 1 1 1 1 1 ...
$ IsWeekend : Factor w/ 2 levels "No","Yes": 1 1 1 1 1 1 1 1 1 1 ...
$ Price : int 4051 11587 3977 4234 6837 6518 3189 4234 8623 6833 ...
$ AdvancedBookingDays: int 54 52 48 59 48 52 48 59 48 52 ...
$ IsDiwali : int 1 1 1 1 1 1 1 1 1 1 ...
$ DayBeforeDiwali : int 1 1 1 1 1 1 1 1 1 1 ...
$ DayAfterDiwali : int 0 0 0 0 0 0 0 0 0 0 ...
$ MetroDeparture : int 1 1 1 1 1 1 1 1 1 1 ...
$ MetroArrival : int 1 1 1 1 1 1 1 1 1 1 ...
$ MarketShare : num 15.4 15.4 13.2 39.6 13.2 15.4 13.2 39.6 13.2 15.4 ...
$ LoadFactor : num 83.3 83.3 94.1 87.2 94.1 ...
1c. Conversion of some data types of data columns into factor
# convert 'IsDiwali' into factor
airline.df$IsDiwali <- as.factor(airline.df$IsDiwali)
# convert 'DayBeforeDiwali' into factor
airline.df$DayBeforeDiwali <- as.factor(airline.df$DayBeforeDiwali)
# convert 'DayAfterDiwali' into factor
airline.df$DayAfterDiwali <- as.factor(airline.df$DayAfterDiwali)
# convert 'MetroDeparture' into factor
airline.df$MetroDeparture <- as.factor(airline.df$MetroDeparture)
# convert 'MetroArrival' into factor
airline.df$MetroArrival <- as.factor(airline.df$MetroArrival)
# verify
str(airline.df)
'data.frame': 305 obs. of 25 variables:
$ FlightNumber : Factor w/ 63 levels "6E 129","6E 155",..: 25 32 62 4 61 45 57 16 59 17 ...
$ Airline : Factor w/ 4 levels "Air India","IndiGo",..: 3 3 4 2 4 3 4 2 4 3 ...
$ DepartureCityCode : Factor w/ 2 levels "BOM","DEL": 2 1 2 2 1 1 2 2 1 1 ...
$ ArrivalCityCode : Factor w/ 2 levels "BOM","DEL": 1 2 1 1 2 2 1 1 2 2 ...
$ DepartureTime : int 225 300 350 455 555 605 635 640 645 700 ...
$ ArrivalTime : int 435 505 605 710 805 815 850 855 855 915 ...
$ Departure : Factor w/ 2 levels "AM","PM": 1 1 1 1 1 1 1 1 1 1 ...
$ FlyingMinutes : int 130 125 135 135 130 130 135 135 130 135 ...
$ Aircraft : Factor w/ 2 levels "Airbus","Boeing": 2 2 2 1 2 2 2 1 2 2 ...
$ PlaneModel : Factor w/ 9 levels "738","739","77W",..: 1 1 1 6 1 1 1 6 1 2 ...
$ Capacity : int 156 156 189 180 189 156 189 180 189 138 ...
$ SeatPitch : int 30 30 29 30 29 30 29 30 29 30 ...
$ SeatWidth : num 17 17 17 18 17 17 17 18 17 17 ...
$ DataCollectionDate : Factor w/ 7 levels "Sep 10 2018",..: 2 4 6 7 6 4 6 7 6 4 ...
$ DateDeparture : Factor w/ 20 levels "Nov 6 2018","Nov 8 2018",..: 1 1 1 1 1 1 1 1 1 1 ...
$ IsWeekend : Factor w/ 2 levels "No","Yes": 1 1 1 1 1 1 1 1 1 1 ...
$ Price : int 4051 11587 3977 4234 6837 6518 3189 4234 8623 6833 ...
$ AdvancedBookingDays: int 54 52 48 59 48 52 48 59 48 52 ...
$ IsDiwali : Factor w/ 2 levels "0","1": 2 2 2 2 2 2 2 2 2 2 ...
$ DayBeforeDiwali : Factor w/ 2 levels "0","1": 2 2 2 2 2 2 2 2 2 2 ...
$ DayAfterDiwali : Factor w/ 2 levels "0","1": 1 1 1 1 1 1 1 1 1 1 ...
$ MetroDeparture : Factor w/ 1 level "1": 1 1 1 1 1 1 1 1 1 1 ...
$ MetroArrival : Factor w/ 1 level "1": 1 1 1 1 1 1 1 1 1 1 ...
$ MarketShare : num 15.4 15.4 13.2 39.6 13.2 15.4 13.2 39.6 13.2 15.4 ...
$ LoadFactor : num 83.3 83.3 94.1 87.2 94.1 ...
PART 2
DATA SUMMARY
2a. Descriptive statistics of the data frame
# attaching data columns
attach(airline.df)
# descriptive statistics
library(psych)
describe(airline.df)[c(7, 10:12, 15:17, 22, 23), c(2:5, 8:9)]
n mean sd median min max
Departure* 305 1.45 0.50 1 1 2
PlaneModel* 305 3.82 2.71 3 1 9
Capacity 305 176.36 32.39 180 138 303
SeatPitch 305 30.26 0.93 30 29 33
DateDeparture* 305 8.14 6.69 7 1 20
IsWeekend* 305 1.13 0.34 1 1 2
Price 305 5394.54 2388.29 4681 2607 18015
MetroDeparture* 305 1.00 0.00 1 1 1
MetroArrival* 305 1.00 0.00 1 1 1
2b. Number of flights by airlines in Diwali
# flights by airline in Diwali
table(Airline, IsDiwali)
IsDiwali
Airline 0 1
Air India 25 16
IndiGo 48 32
Jet 87 57
Spice Jet 24 16
2c. Average ticket price and advanced booking days by airline
# average ticket price by airline
library(data.table)
dt <- data.table(airline.df)
dt[, list(AveragePrice = round(mean(Price), 2),
AveragePrice = round(sd(Price), 2)), by = Airline]
Airline AveragePrice AveragePrice
1: Jet 5496.15 1989.66
2: Spice Jet 5094.85 1787.42
3: IndiGo 4879.52 2956.46
4: Air India 6335.00 2693.64
PART 3
REGRESSION ANALYSIS
3a. Linear OLS Model
# linear OLS intearction model
fitOLSIntModel <- lm(Price ~
AdvancedBookingDays * Airline
+ Departure + IsWeekend
+ IsDiwali
+ DepartureCityCode
+ FlyingMinutes
+ SeatPitch
+ SeatWidth,
data = airline.df)
# summary of linear OLS interaction model
summary(fitOLSIntModel)
Call:
lm(formula = Price ~ AdvancedBookingDays * Airline + Departure +
IsWeekend + IsDiwali + DepartureCityCode + FlyingMinutes +
SeatPitch + SeatWidth, data = airline.df)
Residuals:
Min 1Q Median 3Q Max
-3405.0 -1327.7 -352.0 649.4 11141.5
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -5740.82 8645.69 -0.664 0.5072
AdvancedBookingDays -31.15 19.66 -1.584 0.1142
AirlineIndiGo 1806.95 923.82 1.956 0.0514
AirlineJet 1107.68 648.25 1.709 0.0886
AirlineSpice Jet 208.21 921.57 0.226 0.8214
DeparturePM -560.75 267.30 -2.098 0.0368
IsWeekendYes -444.72 405.74 -1.096 0.2740
IsDiwali1 4071.54 555.68 7.327 2.34e-12
DepartureCityCodeDEL -1421.50 342.21 -4.154 4.30e-05
FlyingMinutes 40.31 28.40 1.419 0.1569
SeatPitch -244.28 220.07 -1.110 0.2679
SeatWidth 796.64 492.66 1.617 0.1070
AdvancedBookingDays:AirlineIndiGo -80.68 18.33 -4.402 1.51e-05
AdvancedBookingDays:AirlineJet -44.87 17.68 -2.538 0.0117
AdvancedBookingDays:AirlineSpice Jet -46.78 22.34 -2.094 0.0372
(Intercept)
AdvancedBookingDays
AirlineIndiGo .
AirlineJet .
AirlineSpice Jet
DeparturePM *
IsWeekendYes
IsDiwali1 ***
DepartureCityCodeDEL ***
FlyingMinutes
SeatPitch
SeatWidth
AdvancedBookingDays:AirlineIndiGo ***
AdvancedBookingDays:AirlineJet *
AdvancedBookingDays:AirlineSpice Jet *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 2017 on 290 degrees of freedom
Multiple R-squared: 0.3197, Adjusted R-squared: 0.2868
F-statistic: 9.733 on 14 and 290 DF, p-value: < 2.2e-16
3b. Log-linear OLS Model
# linear OLS intearction model
fitLogOLSIntModel <- lm(log(Price) ~
AdvancedBookingDays * Airline
+ Departure + IsWeekend
+ IsDiwali
+ DepartureCityCode
+ FlyingMinutes
+ SeatPitch
+ SeatWidth,
data = airline.df)
# summary of linear OLS interaction model
summary(fitLogOLSIntModel)
Call:
lm(formula = log(Price) ~ AdvancedBookingDays * Airline + Departure +
IsWeekend + IsDiwali + DepartureCityCode + FlyingMinutes +
SeatPitch + SeatWidth, data = airline.df)
Residuals:
Min 1Q Median 3Q Max
-0.59755 -0.19913 -0.03802 0.15262 1.16078
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 6.380581 1.225651 5.206 3.66e-07
AdvancedBookingDays -0.008199 0.002787 -2.942 0.003525
AirlineIndiGo 0.165430 0.130964 1.263 0.207542
AirlineJet 0.146681 0.091899 1.596 0.111553
AirlineSpice Jet 0.025470 0.130646 0.195 0.845564
DeparturePM -0.052828 0.037893 -1.394 0.164347
IsWeekendYes -0.049339 0.057520 -0.858 0.391723
IsDiwali1 0.714659 0.078775 9.072 < 2e-16
DepartureCityCodeDEL -0.264292 0.048514 -5.448 1.09e-07
FlyingMinutes 0.008870 0.004026 2.203 0.028358
SeatPitch -0.028846 0.031198 -0.925 0.355924
SeatWidth 0.114373 0.069841 1.638 0.102587
AdvancedBookingDays:AirlineIndiGo -0.008971 0.002598 -3.453 0.000637
AdvancedBookingDays:AirlineJet -0.005310 0.002507 -2.118 0.035021
AdvancedBookingDays:AirlineSpice Jet -0.005399 0.003167 -1.705 0.089324
(Intercept) ***
AdvancedBookingDays **
AirlineIndiGo
AirlineJet
AirlineSpice Jet
DeparturePM
IsWeekendYes
IsDiwali1 ***
DepartureCityCodeDEL ***
FlyingMinutes *
SeatPitch
SeatWidth
AdvancedBookingDays:AirlineIndiGo ***
AdvancedBookingDays:AirlineJet *
AdvancedBookingDays:AirlineSpice Jet .
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.2859 on 290 degrees of freedom
Multiple R-squared: 0.3937, Adjusted R-squared: 0.3645
F-statistic: 13.45 on 14 and 290 DF, p-value: < 2.2e-16
PART 5
REGRESSION DIAGNOSTICS
5a. Hetroscedasticity Test
# Goldfeld-Quandt Test
library(lmtest)
gqtest(fitOLSIntModel, order.by = ~ Price, data = airline.df)
Goldfeld-Quandt test
data: fitOLSIntModel
GQ = 21.27, df1 = 138, df2 = 137, p-value < 2.2e-16
alternative hypothesis: variance increases from segment 1 to 2
5b. Breusch-Pagan Test
library(lmtest)
# BP-test for OLS model
bptest(fitOLSIntModel)
studentized Breusch-Pagan test
data: fitOLSIntModel
BP = 52.463, df = 14, p-value = 2.347e-06
5c. Normality plots of residuals
# distribution of studentized residuals
library(MASS)
sresid <- studres(fitOLSIntModel)
hist(sresid, freq=FALSE,
main="Distribution of Studentized Residuals")
xfit<-seq(min(sresid),max(sresid),length=40)
yfit<-dnorm(xfit)
lines(xfit, yfit)
5d. Residuals Plots for Log-Linear FGLS Model
# residual plots of OLS model
par(mfrow=c(2,2))
plot(fitOLSIntModel)
PART 6
FGLS REGRESSION MODEL
6a. Linear FGLS Model
# Step 1:Residuals of linear OLS Model
LogOLSModelRes <- resid(fitOLSIntModel)
# Step 2: Taking square of the residuals of linear OLS Model
LogOLSModelResSq <- LogOLSModelRes^2
# Step 3: Taking natural log of the squared residuals of linear OLS Model
lnOLSResSq <- log(LogOLSModelResSq)
# Step 4: Running auxiliary OLS Model
auxOLSModel <- lm(lnOLSResSq ~
AdvancedBookingDays * Airline
+ Departure + IsWeekend
+ IsDiwali
+ DepartureCityCode
+ FlyingMinutes
+ SeatPitch
+ SeatWidth,
data = airline.df)
# Step 5: Get fitted value of auxiliary OLS Model i.e. 'auxOLSModel'
fittedValue <- fitted(auxOLSModel)
# Step 6: Compute exponential values of fiited value for auxialiary OLS Model
expValue <- exp(fittedValue)
# Step 7: Fit Log-linear FGLS Model
fitFGLSIntModel <- lm(Price ~
AdvancedBookingDays * Airline
+ Departure + IsWeekend
+ IsDiwali
+ DepartureCityCode
+ FlyingMinutes
+ SeatPitch
+ SeatWidth,
weights = 1/expValue, data = airline.df)
# summary of linear FGLS model
summary(fitFGLSIntModel)
Call:
lm(formula = Price ~ AdvancedBookingDays * Airline + Departure +
IsWeekend + IsDiwali + DepartureCityCode + FlyingMinutes +
SeatPitch + SeatWidth, data = airline.df, weights = 1/expValue)
Weighted Residuals:
Min 1Q Median 3Q Max
-7.5444 -1.0129 -0.4436 0.8758 6.3196
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -6708.20 5272.58 -1.272 0.204292
AdvancedBookingDays -22.18 11.70 -1.896 0.058936
AirlineIndiGo 323.42 595.34 0.543 0.587367
AirlineJet 810.56 381.20 2.126 0.034318
AirlineSpice Jet 870.93 671.86 1.296 0.195905
DeparturePM -221.06 112.89 -1.958 0.051167
IsWeekendYes 607.47 307.89 1.973 0.049441
IsDiwali1 3199.38 321.04 9.966 < 2e-16
DepartureCityCodeDEL -1398.95 241.38 -5.796 1.77e-08
FlyingMinutes 53.79 15.29 3.517 0.000506
SeatPitch -110.40 120.42 -0.917 0.360036
SeatWidth 490.73 268.47 1.828 0.068597
AdvancedBookingDays:AirlineIndiGo -38.97 14.73 -2.646 0.008580
AdvancedBookingDays:AirlineJet -35.64 14.05 -2.537 0.011715
AdvancedBookingDays:AirlineSpice Jet -44.18 19.96 -2.214 0.027599
(Intercept)
AdvancedBookingDays .
AirlineIndiGo
AirlineJet *
AirlineSpice Jet
DeparturePM .
IsWeekendYes *
IsDiwali1 ***
DepartureCityCodeDEL ***
FlyingMinutes ***
SeatPitch
SeatWidth .
AdvancedBookingDays:AirlineIndiGo **
AdvancedBookingDays:AirlineJet *
AdvancedBookingDays:AirlineSpice Jet *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 1.665 on 290 degrees of freedom
Multiple R-squared: 0.4652, Adjusted R-squared: 0.4394
F-statistic: 18.02 on 14 and 290 DF, p-value: < 2.2e-16
6b. Log-linear FGLS Model
# Step 1:Residuals of linear OLS Model
LogOLSModelRes <- resid(fitLogOLSIntModel)
# Step 2: Taking square of the residuals of linear OLS Model
LogOLSModelResSq <- LogOLSModelRes^2
# Step 3: Taking natural log of the squared residuals of linear OLS Model
lnOLSResSq <- log(LogOLSModelResSq)
# Step 4: Running auxiliary OLS Model
auxOLSModel <- lm(lnOLSResSq ~
AdvancedBookingDays * Airline
+ Departure + IsWeekend
+ IsDiwali
+ DepartureCityCode
+ FlyingMinutes
+ SeatPitch
+ SeatWidth,
data = airline.df)
# Step 5: Get fitted value of auxiliary OLS Model i.e. 'auxOLSModel'
fittedValue <- fitted(auxOLSModel)
# Step 6: Compute exponential values of fiited value for auxialiary OLS Model
expValue <- exp(fittedValue)
# Step 7: Fit Log-linear FGLS Model
fitLogFGLSIntModel <- lm(log(Price) ~
AdvancedBookingDays * Airline
+ Departure + IsWeekend
+ IsDiwali
+ DepartureCityCode
+ FlyingMinutes
+ SeatPitch
+ SeatWidth,
weights = 1/expValue, data = airline.df)
# summary of linear FGLS model
summary(fitLogFGLSIntModel)
Call:
lm(formula = log(Price) ~ AdvancedBookingDays * Airline + Departure +
IsWeekend + IsDiwali + DepartureCityCode + FlyingMinutes +
SeatPitch + SeatWidth, data = airline.df, weights = 1/expValue)
Weighted Residuals:
Min 1Q Median 3Q Max
-7.4068 -1.1755 -0.3849 1.1028 5.6760
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 5.875369 0.912360 6.440 4.96e-10
AdvancedBookingDays -0.006190 0.002000 -3.096 0.002155
AirlineIndiGo 0.024338 0.111169 0.219 0.826857
AirlineJet 0.143865 0.067581 2.129 0.034115
AirlineSpice Jet 0.196338 0.132408 1.483 0.139206
DeparturePM -0.035454 0.024810 -1.429 0.154068
IsWeekendYes 0.113861 0.052979 2.149 0.032450
IsDiwali1 0.696111 0.056942 12.225 < 2e-16
DepartureCityCodeDEL -0.307427 0.041264 -7.450 1.08e-12
FlyingMinutes 0.010111 0.003001 3.370 0.000854
SeatPitch -0.015858 0.022113 -0.717 0.473877
SeatWidth 0.108791 0.049671 2.190 0.029304
AdvancedBookingDays:AirlineIndiGo -0.006156 0.002400 -2.565 0.010829
AdvancedBookingDays:AirlineJet -0.006296 0.002273 -2.770 0.005963
AdvancedBookingDays:AirlineSpice Jet -0.009210 0.003595 -2.562 0.010909
(Intercept) ***
AdvancedBookingDays **
AirlineIndiGo
AirlineJet *
AirlineSpice Jet
DeparturePM
IsWeekendYes *
IsDiwali1 ***
DepartureCityCodeDEL ***
FlyingMinutes ***
SeatPitch
SeatWidth *
AdvancedBookingDays:AirlineIndiGo *
AdvancedBookingDays:AirlineJet **
AdvancedBookingDays:AirlineSpice Jet *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 1.786 on 290 degrees of freedom
Multiple R-squared: 0.5193, Adjusted R-squared: 0.4961
F-statistic: 22.38 on 14 and 290 DF, p-value: < 2.2e-16
PART 7
MULTICOLLINEARITY TEST
7a. VIF
library(car)
vif(fitFGLSIntModel)
GVIF Df GVIF^(1/(2*Df))
AdvancedBookingDays 21.743703 1 4.663014
Airline 473.028934 3 2.791352
Departure 1.175864 1 1.084373
IsWeekend 1.387644 1 1.177983
IsDiwali 9.707042 1 3.115613
DepartureCityCode 3.518471 1 1.875759
FlyingMinutes 1.136829 1 1.066222
SeatPitch 3.348518 1 1.829895
SeatWidth 5.676174 1 2.382472
AdvancedBookingDays:Airline 1134.590363 3 3.229534
7b. Correlation Matrix
expVar <- airline.df[c("Price", "AdvancedBookingDays", "FlyingMinutes", "SeatPitch", "SeatWidth")]
#cor(expVar)
library(Hmisc)
rcorr(as.matrix(expVar))
Price AdvancedBookingDays FlyingMinutes SeatPitch
Price 1.00 -0.01 -0.02 0.07
AdvancedBookingDays -0.01 1.00 0.01 -0.01
FlyingMinutes -0.02 0.01 1.00 -0.03
SeatPitch 0.07 -0.01 -0.03 1.00
SeatWidth -0.06 0.05 -0.18 0.32
SeatWidth
Price -0.06
AdvancedBookingDays 0.05
FlyingMinutes -0.18
SeatPitch 0.32
SeatWidth 1.00
n= 305
P
Price AdvancedBookingDays FlyingMinutes SeatPitch
Price 0.8732 0.7513 0.1942
AdvancedBookingDays 0.8732 0.9292 0.8052
FlyingMinutes 0.7513 0.9292 0.5521
SeatPitch 0.1942 0.8052 0.5521
SeatWidth 0.2998 0.3411 0.0013 0.0000
SeatWidth
Price 0.2998
AdvancedBookingDays 0.3411
FlyingMinutes 0.0013
SeatPitch 0.0000
SeatWidth
7c. Farrar - Glauber Test
The mctest package in R provides the Farrar-Glauber test and other relevant tests for multicollinearity.
There are two functions viz. omcdiag() and imcdiag() under mctest package in R which will provide the overall and individual diagnostic checking for multicollinearity respectively.
library(mctest)
omcdiag(as.matrix(expVar), Price)
Call:
omcdiag(x = as.matrix(expVar), y = Price)
Overall Multicollinearity Diagnostics
MC Results detection
Determinant |X'X|: 0.8511 0
Farrar Chi-Square: 48.5237 1
Red Indicator: 0.1222 0
Sum of Lambda Inverse: 5.3489 0
Theil's Method: -3.6906 0
Condition Number: 151.2290 1
1 --> COLLINEARITY is detected by the test
0 --> COLLINEARITY is not detected by the test
imcdiag(expVar, Price)
Call:
imcdiag(x = expVar, y = Price)
All Individual Multicollinearity Diagnostics Result
VIF TOL Wi Fi Leamer CVIF Klein
Price 1.0145 0.9857 1.0912 1.4597 0.9928 0 0
AdvancedBookingDays 1.0044 0.9956 0.3296 0.4410 0.9978 0 0
FlyingMinutes 1.0367 0.9646 2.7531 3.6830 0.9821 0 0
SeatPitch 1.1269 0.8874 9.5161 12.7304 0.9420 0 0
SeatWidth 1.1664 0.8573 12.4809 16.6967 0.9259 0 0
1 --> COLLINEARITY is detected by the test
0 --> COLLINEARITY is not detected by the test
AdvancedBookingDays , SeatPitch , SeatWidth , coefficient(s) are non-significant may be due to multicollinearity
R-square of y on all x: 1
* use method argument to check which regressors may be the reason of collinearity
***