getwd()
## [1] "C:/Users/TANAY/Downloads"
airlines <- read.csv("SixAirlinesDataV2.csv")

summary(airlines)
##       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
aggregate(airlines$PricePremium~airlines$Airline, FUN=mean)
##   airlines$Airline airlines$PricePremium
## 1        AirFrance             3065.2162
## 2          British             1937.0286
## 3            Delta              684.6739
## 4              Jet              483.3607
## 5        Singapore             1239.9250
## 6           Virgin             2721.6935
aggregate(airlines$PriceEconomy~airlines$Airline, FUN=mean)
##   airlines$Airline airlines$PriceEconomy
## 1        AirFrance             2769.7838
## 2          British             1293.4800
## 3            Delta              560.9348
## 4              Jet              276.1639
## 5        Singapore              860.2500
## 6           Virgin             1603.5323
library (car)
par(mfrow=c(2,2))
with(airlines,plot(Airline,PriceEconomy))
with(airlines,plot(Airline,PricePremium))
par(mfrow=c(1,1))

par(mfrow=c(2,2))
with(airlines,plot(IsInternational,PriceEconomy))
with(airlines,plot(IsInternational,PricePremium))
par(mfrow=c(1,1))

plot(airlines$Airline, airlines$SeatsEconomy, main="Airline and The Total Number of seats in Economy Class",col = c("blue","green","black","red","grey","yellow"))

plot(airlines$Airline, airlines$SeatsPremium, main="Airline and The Total Number of seats in Premium Class",col = c("blue","green","black","red","grey","yellow"))

plot(airlines$IsInternational,main = " Number of domestic and international flights",col="black")

library(car)

scatterplot(airlines$PriceRelative ~ airlines$PitchDifference,
              xlab="PitchDifference", ylab="PriceRelative",
              main="Scatter Plot of Relative price VS Pitch difference")

scatterplot(airlines$PriceRelative ~ airlines$WidthDifference,
              xlab="WidthDifference", ylab="PriceRelative",
              main="Scatter Plot of Relative price VS Width difference")

cor(airlines$PriceRelative,airlines$PitchDifference)
## [1] 0.4687302
cor(airlines$PriceRelative,airlines$WidthDifference)
## [1] 0.4858024
library("corrgram")
corrgram(airlines,upper.panel=panel.pie, main="Corrgram of airline variables")

cor.test(airlines$PriceRelative,airlines$PitchDifference)
## 
##  Pearson's product-moment correlation
## 
## data:  airlines$PriceRelative and airlines$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 
## 0.4687302
cor.test(airlines$PriceRelative,airlines$WidthDifference)
## 
##  Pearson's product-moment correlation
## 
## data:  airlines$PriceRelative and airlines$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 
## 0.4858024

p value<0.05 –> Relative price is correlated to the pitch difference and width difference between premium and economy seats.

fit1 <- lm(PricePremium ~ PriceEconomy + PitchDifference + WidthDifference + PercentPremiumSeats + SeatsTotal + IsInternational + TravelMonth + FlightDuration + Aircraft,data=airlines)
summary(fit1)
## 
## Call:
## lm(formula = PricePremium ~ PriceEconomy + PitchDifference + 
##     WidthDifference + PercentPremiumSeats + SeatsTotal + IsInternational + 
##     TravelMonth + FlightDuration + Aircraft, data = airlines)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -977.2 -246.3  -47.9  135.2 3419.7 
## 
## Coefficients:
##                                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                  -1.211e+03  1.755e+02  -6.898 1.82e-11 ***
## PriceEconomy                  1.064e+00  3.114e-02  34.175  < 2e-16 ***
## PitchDifference               8.510e+01  3.913e+01   2.175 0.030163 *  
## WidthDifference               1.240e+02  3.438e+01   3.607 0.000345 ***
## PercentPremiumSeats           3.177e+01  5.250e+00   6.052 3.04e-09 ***
## SeatsTotal                    1.925e+00  3.360e-01   5.729 1.87e-08 ***
## IsInternationalInternational -7.537e+02  2.135e+02  -3.530 0.000458 ***
## TravelMonthJul               -3.441e+01  7.074e+01  -0.486 0.626904    
## TravelMonthOct                2.692e+01  6.036e+01   0.446 0.655795    
## TravelMonthSep               -2.097e+00  6.015e+01  -0.035 0.972203    
## FlightDuration                8.455e+01  8.809e+00   9.598  < 2e-16 ***
## AircraftBoeing               -2.082e+00  5.651e+01  -0.037 0.970625    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 480.7 on 446 degrees of freedom
## Multiple R-squared:  0.8641, Adjusted R-squared:  0.8607 
## F-statistic: 257.7 on 11 and 446 DF,  p-value: < 2.2e-16
fit <- lm(PriceRelative ~ PitchDifference + WidthDifference  ,data=airlines)
summary(fit)
## 
## Call:
## lm(formula = PriceRelative ~ PitchDifference + WidthDifference, 
##     data = airlines)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.84163 -0.28484 -0.07241  0.17698  1.18778 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     -0.10514    0.08304  -1.266 0.206077    
## PitchDifference  0.06019    0.01590   3.785 0.000174 ***
## WidthDifference  0.11621    0.02356   4.933 1.14e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3886 on 455 degrees of freedom
## Multiple R-squared:  0.2593, Adjusted R-squared:  0.2561 
## F-statistic: 79.65 on 2 and 455 DF,  p-value: < 2.2e-16

Conclusion: What factors explain the difference in price between an economy ticket and a premium-economy airline ticket? Pitch difference, Width difference.

y=-0.10514 + 0.06019 x1 + 0.11621 x2 where y=Relative price x1=PitchDifference x2=WidthDifference