Airline
Nimit
18 January 2018
Mini Project:
Research Question: What factors explain the difference in price between an economy ticket and a premium-economy airline ticket?*
airline<- read.csv("SixAirlinesDataV2.csv")
View(airline)#summary statistics
summary(airline)## 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. :24.69#number of instances
nrow(airline)## [1] 458#number of column
ncol(airline)## [1] 18library(psych)
describe(airline)## 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 0.23#Data Types
str(airline)## '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 ...Visualization of single variable
#Fligth Duration
boxplot(airline$FlightDuration, horizontal = TRUE, main="Flight Duration", xlab="Flight hours",col="seashell4")
#Visuzlize Seats
boxplot(airline$SeatsEconomy, airline$SeatsPremium ,col=c("skyblue","darkgoldenrod1"), horizontal = TRUE, main="Seats Economy vs Seats Premium", xlab="Seats ", names=c("Economy","Premium"))
#Visualize Pitch
boxplot(airline$PitchEconomy,airline$PitchPremium, col=c("skyblue","darkgoldenrod1"), horizontal = TRUE, main="Pitch Economy vs Pitch Premium" ,xlab="Inch", names=c("Economy","Premium"))
#Vizualize Width
boxplot(airline$WidthEconomy,airline$WidthPremium, col=c("skyblue","darkgoldenrod1"), horizontal = TRUE, main="Width Economy vs Width Premium", xlab="Inch", names=c("Economy","Premium"))
#Vizualize Price
boxplot(airline$PriceEconomy, airline$PricePremium, col=c("skyblue","darkgoldenrod1"), horizontal = TRUE, main="Price Economy vs Price Premium", xlab="Ticke price",
names=c("Economy","Premium"))
#Relative Price distribution
boxplot(airline$PriceRelative, horizontal = TRUE, main="Relative Price", xlab="times", col="seashell4")
Scatter plot matrix resembles relationship between PricePrimium and other relevant factor.
library(car)##
## Attaching package: 'car'## The following object is masked from 'package:psych':
##
## logitscatterplotMatrix(airline[,c("FlightDuration","PricePremium","SeatsPremium", "PriceEconomy")], spread=FALSE, smoother.args=list(lty=20),pch = 20, main="Scatter Plot Matrix")
Subsetting two data frames
Subsetting of Airline dataset in two: One having relative price increases by more than 50 %, and other having relative price increases by less than 50%.[moreRelativePrice]
This is being done in order to visualize clearly on what factor explains the difference between economic class and premium class ticket prices.[lessRelativePrice]
moreRelativePrice<- airline[which(airline$PriceRelative > 0.5 ),]
#airline having premium price greater by 50 % or more
lessRelativePrice<- airline[which(airline$PriceRelative < 0.5 ),]
#airline having premium price greater by 50% or less
View(moreRelativePrice)
View(lessRelativePrice)Comparing two subsets
# Comparing two subsets
par(mfrow=c(1,2))
hist(moreRelativePrice$FlightDuration, xlab="hours of flight", main=" relativer price > 50 % ", ylim=c(0,40), col = "dodgerblue3")
hist(lessRelativePrice$FlightDuration, xlab="hours of flight", main="relative price < 50", col="dodgerblue4")
par(mfrow=c(1,1))
#Visuzlize Seats Economy between two sets
boxplot(moreRelativePrice$SeatsEconomy, lessRelativePrice$SeatsEconomy ,col=c("dodgerblue3","dodgerblue4"), horizontal = TRUE, main="Seats Economy", xlab="Seats ", names=c("RltPrc > 0.5","RltPrc < 0.5"))
#Visualize Seats Premium between two sets
boxplot(moreRelativePrice$SeatsPremium,lessRelativePrice$SeatsPremium, col=c("dodgerblue3","dodgerblue4"), horizontal = TRUE, main="Seats Premium" ,xlab="Inch", names=c("RltPrc > 0.5","RltPrc < 0.5"))
#Vizualize Pitch Economy between two sets
boxplot(moreRelativePrice$PitchEconomy, lessRelativePrice$PitchEconomy, col=c("dodgerblue3","dodgerblue4"), horizontal = TRUE, main="Pitch Economy", xlab="Inch", names=c("RltPrc > 0.5","RltPrc < 0.5"))
#Vizualize Pitch Premium between two sets
boxplot(moreRelativePrice$PricePremium, lessRelativePrice$PitchPremium, col=c("dodgerblue3","dodgerblue4"), horizontal = TRUE, main="Pitch Premium", xlab="Ticket price",
names=c("RltPrc > 0.5","RltPrc < 0.5"))
#Vizualize Width Economy between two sets
boxplot(moreRelativePrice$WidthEconomy, lessRelativePrice$WidthEconomy, col=c("dodgerblue3","dodgerblue4"), horizontal = TRUE, main="Width Economy", xlab="Inch", names=c("RltPrc > 0.5","RltPrc < 0.5"))
#Vizualize Width Premium between two sets
boxplot(moreRelativePrice$WidthPremium, lessRelativePrice$WidthPremium, col=c("dodgerblue3","dodgerblue4"), horizontal = TRUE, main="Width Premium", xlab="Inch",names=c("RltPrc > 0.5","RltPrc < 0.5"))
#Vizualize Price Economy between two sets
boxplot(moreRelativePrice$PriceEconomy, lessRelativePrice$PriceEconomy, col=c("dodgerblue3","dodgerblue4"), horizontal = TRUE, main="Price Economy", xlab="Ticket price", names=c("RltPrc > 0.5","RltPrc < 0.5"))
#Vizualize Price Premium between two sets
boxplot(moreRelativePrice$PricePremium, lessRelativePrice$PricePremium, col=c("dodgerblue3","dodgerblue4"), horizontal = TRUE, main="Price Premium", xlab="Ticket price",names=c("RltPrc > 0.5","RltPrc < 0.5"))
Corelation bewteen different variable
#airline dataframe
library(corrgram)## Warning: replacing previous import by 'magrittr::%>%' when loading
## 'dendextend'corrgram(airline, lower.panel=panel.shade,
upper.panel=panel.pie,
main="Corrgram of airplane intercorrelations")
Noted down Relative price correlated
Positively with- PitchDifference,WidthDifference, %ofPremiumSeat, widthPremium, PitchPremium, FlightDuration Negatively with- PriceEconomy, PitchEconomy
Price Premium is correlated:
Positively with- PriceEconomy, flightDuration, PitchEconomy,SeatsPremium, SeatsEconomy,WidthEconomy,PitchPremium, widthPremium,
Draw model from here that have link with PricePremium
Model E: \(PricePremium = \beta_0 WidthPremium+ \beta_1 PitchPremium + \beta_2 SeatsPreemium + \beta_3 PitchEconomy + \beta_4 FlightDuration + \beta_5 PriceEconomy + \epsilon\)
#fitting
ModelE<- lm(PricePremium ~ WidthPremium + PitchPremium + SeatsPremium + PitchEconomy + FlightDuration + PriceEconomy , data=airline)moreRelativePrice subset corrgram
library(corrgram)
corrgram(moreRelativePrice, lower.panel=panel.shade,
upper.panel=panel.pie,
main="Corrgram of airplane having relative price greater by more than 50%")
lessRelativePrice subset corrgram
library(corrgram)
corrgram(lessRelativePrice, lower.panel=panel.shade,
upper.panel=panel.pie,
main="Corrgram of airplane where relative price is greater by less than 50%")
Describe Both subset to findout link between variable
library(psych)
describe(moreRelativePrice)[,1:8] # premium price greater by 50% or more ## vars n mean sd median trimmed mad
## Airline* 1 159 3.87 1.66 4.00 3.91 2.97
## Aircraft* 2 159 1.72 0.45 2.00 1.77 0.00
## FlightDuration 3 159 8.48 3.54 8.91 8.57 3.84
## TravelMonth* 4 159 2.51 1.14 3.00 2.51 1.48
## IsInternational* 5 159 2.00 0.00 2.00 2.00 0.00
## SeatsEconomy 6 159 207.41 79.44 198.00 199.26 75.61
## SeatsPremium 7 159 32.14 14.77 36.00 31.57 11.86
## PitchEconomy 8 159 30.97 0.69 31.00 30.97 0.00
## PitchPremium 9 159 38.50 0.87 38.00 38.39 0.00
## WidthEconomy 10 159 17.87 0.64 18.00 17.84 0.00
## WidthPremium 11 159 20.12 0.92 20.00 20.15 1.48
## PriceEconomy 12 159 983.81 708.60 794.00 932.48 929.59
## PricePremium 13 159 1902.48 1397.84 1619.00 1808.81 1810.25
## PriceRelative 14 159 1.00 0.37 0.98 0.97 0.36
## SeatsTotal 15 159 239.55 89.39 233.00 230.71 97.85
## PitchDifference 16 159 7.53 1.49 7.00 7.42 0.00
## WidthDifference 17 159 2.25 1.30 2.00 2.19 1.48
## PercentPremiumSeats 18 159 13.58 5.25 12.90 13.32 3.14
## min
## Airline* 1.00
## Aircraft* 1.00
## FlightDuration 2.50
## TravelMonth* 1.00
## IsInternational* 2.00
## SeatsEconomy 122.00
## SeatsPremium 8.00
## PitchEconomy 30.00
## PitchPremium 38.00
## WidthEconomy 17.00
## WidthPremium 19.00
## PriceEconomy 108.00
## PricePremium 228.00
## PriceRelative 0.51
## SeatsTotal 140.00
## PitchDifference 6.00
## WidthDifference 1.00
## PercentPremiumSeats 4.71describe(lessRelativePrice)[,1:8] # premium price greater by less than 50%## vars n mean sd median trimmed mad min
## Airline* 1 297 2.54 1.45 2.00 2.32 1.48 1.00
## Aircraft* 2 297 1.64 0.48 2.00 1.68 0.00 1.00
## FlightDuration 3 297 7.09 3.44 7.58 7.06 4.57 1.25
## TravelMonth* 4 297 2.59 1.19 3.00 2.61 1.48 1.00
## IsInternational* 5 297 1.87 0.34 2.00 1.95 0.00 1.00
## SeatsEconomy 6 297 199.86 74.81 185.00 193.95 85.99 78.00
## SeatsPremium 7 297 34.51 12.33 36.00 34.14 11.86 8.00
## PitchEconomy 8 297 31.35 0.59 31.00 31.35 0.00 30.00
## PitchPremium 9 297 37.58 1.40 38.00 37.85 0.00 34.00
## WidthEconomy 10 297 17.82 0.51 18.00 17.83 0.00 17.00
## WidthPremium 11 297 19.11 1.02 19.00 19.14 0.00 17.00
## PriceEconomy 12 297 1515.41 1066.39 1566.00 1465.93 1546.35 65.00
## PricePremium 13 297 1820.49 1228.70 1866.00 1803.03 1853.25 86.00
## PriceRelative 14 297 0.21 0.15 0.16 0.20 0.18 0.02
## SeatsTotal 15 297 234.37 83.22 227.00 228.42 90.44 98.00
## PitchDifference 16 297 6.23 1.72 7.00 6.46 0.00 2.00
## WidthDifference 17 297 1.29 0.97 1.00 1.19 0.00 0.00
## PercentPremiumSeats 18 297 15.23 4.53 13.21 14.79 1.91 4.71By looking at descriptive statistics of both subsets (keepin in mind research question)
Independent variables: Airline, flight duration, international, preimum seats, pitchpremium, width premium
Model C: dependent variable PricePremium
Independent variables: Airline, flight duration, international, % preimum seats, pitchDiff, widthDiff
MOdel D: dependent variable PricePremium
#fitting
#ModelC
ModelC<- lm(data=airline, PricePremium ~ WidthPremium+PitchPremium+SeatsPremium+IsInternational+FlightDuration+Airline)
#ModelD
ModelD<- lm(data=airline, PricePremium ~
WidthDifference + PitchDifference + PercentPremiumSeats + IsInternational + FlightDuration + Airline)Summary Of Models
summary(ModelA)##
## Call:
## lm(formula = PriceRelative ~ WidthPremium + PitchPremium + SeatsPremium +
## IsInternational + FlightDuration + Airline, data = airline)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.83411 -0.19613 -0.07034 0.10600 1.49599
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -5.049968 2.605255 -1.938 0.053206 .
## WidthPremium 0.088042 0.105365 0.836 0.403832
## PitchPremium 0.102672 0.107413 0.956 0.339659
## SeatsPremium -0.002909 0.002238 -1.300 0.194273
## IsInternationalInternational -0.538517 0.319354 -1.686 0.092441 .
## FlightDuration 0.032995 0.006485 5.088 5.34e-07 ***
## AirlineBritish 0.318163 0.061071 5.210 2.89e-07 ***
## AirlineDelta 0.047813 0.262269 0.182 0.855424
## AirlineJet 0.524994 0.134652 3.899 0.000111 ***
## AirlineSingapore 0.200817 0.128960 1.557 0.120129
## AirlineVirgin 0.417242 0.224194 1.861 0.063389 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3596 on 447 degrees of freedom
## Multiple R-squared: 0.3771, Adjusted R-squared: 0.3632
## F-statistic: 27.06 on 10 and 447 DF, p-value: < 2.2e-16summary(ModelB)##
## Call:
## lm(formula = PriceRelative ~ WidthDifference + PitchDifference +
## PercentPremiumSeats + IsInternational + FlightDuration +
## Airline, data = airline)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.88196 -0.21539 -0.05383 0.09694 1.45141
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.050485 0.256814 -0.197 0.844243
## WidthDifference 0.067328 0.074380 0.905 0.365853
## PitchDifference 0.058924 0.061407 0.960 0.337794
## PercentPremiumSeats -0.012408 0.004371 -2.839 0.004735 **
## IsInternationalInternational -0.371244 0.232699 -1.595 0.111333
## FlightDuration 0.035629 0.006111 5.830 1.06e-08 ***
## AirlineBritish 0.320360 0.105061 3.049 0.002430 **
## AirlineDelta 0.056939 0.169423 0.336 0.736970
## AirlineJet 0.531661 0.136657 3.890 0.000115 ***
## AirlineSingapore 0.303967 0.077303 3.932 9.75e-05 ***
## AirlineVirgin 0.433824 0.099631 4.354 1.66e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3564 on 447 degrees of freedom
## Multiple R-squared: 0.3881, Adjusted R-squared: 0.3744
## F-statistic: 28.35 on 10 and 447 DF, p-value: < 2.2e-16summary(ModelC)##
## Call:
## lm(formula = PricePremium ~ WidthPremium + PitchPremium + SeatsPremium +
## IsInternational + FlightDuration + Airline, data = airline)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2085.9 -402.1 31.7 402.3 4301.1
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -6601.360 5511.018 -1.198 0.232
## WidthPremium 168.890 222.885 0.758 0.449
## PitchPremium 122.550 227.215 0.539 0.590
## SeatsPremium -3.310 4.734 -0.699 0.485
## IsInternationalInternational 215.730 675.544 0.319 0.750
## FlightDuration 186.173 13.718 13.571 < 2e-16 ***
## AirlineBritish -862.600 129.186 -6.677 7.24e-11 ***
## AirlineDelta -675.414 554.789 -1.217 0.224
## AirlineJet -2232.487 284.835 -7.838 3.38e-14 ***
## AirlineSingapore -2257.155 272.795 -8.274 1.50e-15 ***
## AirlineVirgin -677.676 474.247 -1.429 0.154
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 760.6 on 447 degrees of freedom
## Multiple R-squared: 0.659, Adjusted R-squared: 0.6513
## F-statistic: 86.37 on 10 and 447 DF, p-value: < 2.2e-16summary(ModelD)##
## Call:
## lm(formula = PricePremium ~ WidthDifference + PitchDifference +
## PercentPremiumSeats + IsInternational + FlightDuration +
## Airline, data = airline)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2182.8 -356.3 50.4 346.8 4426.9
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 466.848 545.713 0.855 0.392742
## WidthDifference 280.053 158.053 1.772 0.077094 .
## PitchDifference -32.619 130.486 -0.250 0.802719
## PercentPremiumSeats 12.369 9.288 1.332 0.183605
## IsInternationalInternational 535.579 494.470 1.083 0.279331
## FlightDuration 190.689 12.985 14.685 < 2e-16 ***
## AirlineBritish -835.041 223.247 -3.740 0.000208 ***
## AirlineDelta -811.169 360.014 -2.253 0.024733 *
## AirlineJet -2147.692 290.389 -7.396 6.99e-13 ***
## AirlineSingapore -1991.787 164.263 -12.126 < 2e-16 ***
## AirlineVirgin -851.408 211.710 -4.022 6.79e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 757.3 on 447 degrees of freedom
## Multiple R-squared: 0.6619, Adjusted R-squared: 0.6544
## F-statistic: 87.53 on 10 and 447 DF, p-value: < 2.2e-16summary(ModelE)##
## Call:
## lm(formula = PricePremium ~ WidthPremium + PitchPremium + SeatsPremium +
## PitchEconomy + FlightDuration + PriceEconomy, data = airline)
##
## Residuals:
## Min 1Q Median 3Q Max
## -818.4 -226.2 -58.5 110.7 3218.9
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 12828.5902 2048.2019 6.263 8.80e-10 ***
## WidthPremium 138.4292 31.0832 4.454 1.07e-05 ***
## PitchPremium -151.7004 26.6887 -5.684 2.36e-08 ***
## SeatsPremium 8.0837 1.6563 4.881 1.47e-06 ***
## PitchEconomy -327.9169 47.2049 -6.947 1.31e-11 ***
## FlightDuration 74.2077 7.7840 9.533 < 2e-16 ***
## PriceEconomy 1.1109 0.0281 39.530 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 458.7 on 451 degrees of freedom
## Multiple R-squared: 0.8749, Adjusted R-squared: 0.8732
## F-statistic: 525.6 on 6 and 451 DF, p-value: < 2.2e-16INFERENCE
\(ModelE: PricePremium = \beta_0 WidthPremium + \beta_1 PitchPremium + \beta_2 SeatsPremium + \beta_3 PitchEconomy +\beta_4 FlightDuration + \beta_5 PriceEconomy\)
is best as it has maximum Adjusted R-squared value 87%
Hypothesis
\(H0: \beta_0 = \beta_1 = \beta_2 = \beta_3 = \beta_4 = \beta_5 = 0\)
- Among all models, Model E have more Adjusted R-squared i.e., 87%.
- In model E, the beta coefficient of WidthPremium, PitchPremium, SeatsPremium, PitchEconomy, FlightDuration, PriceEconomy are significantly different from zero as [p.value < 0.001 ] and we can reject the null hypothesis.
- F-statistic have a p-value < 0.05 infers that overall model is signified and there is the relationship between all the independent variable considered together and PricePremium.
- Independent variable PricePremium is best choice than RelativePrice considering the research question.
- If flight duration increases by 1 hour keeping all other variable constant Price premium goes up by approx. 74 times.
- On the increase of WidthPremium by one inch keeping all other variables constant Price premium goes up by approx. 138 times.