Reading the given dataset into R.

setwd("C:/Users/Kalyan/Downloads")
airlines<-read.csv(paste("SixAirlinesDataV2.csv",sep=""))
View(airlines)

Summarizing the data.

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
library(psych)
describe(airlines)
##                     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
str(airlines)
## '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 each variable independently

Comparison of flight durations for each airlines

boxplot(airlines$FlightDuration~airlines$Airline,xlab="Airlines",ylab="Flight Duration",main="Flight duration for differnt airlines")

Comparison of number of seats in economy and premium economy classes for each airlines

par(mfrow=c(2,1))
boxplot(airlines$SeatsEconomy~airlines$Airline,xlab="Airlines",ylab="No. of seats in economy",main="Economy seats for differnt airlines")
boxplot(airlines$SeatsPremium~airlines$Airline,xlab="Airlines",ylab="No. of seats in premium economy",main="Premium economy seats for differnt airlines")

Maximum median of economy seats are present in British airlines.Next Virgin,Singapore,AirFrance airlines are all having the similar number of median count of seats in economy class.Delta airlines has the least median for economy seats. Maximum median of premium economy seats are also present in British airlines.Next Singapore,AirFrance airlines are both having the similar median for number of seats in economy class and Virgin airlines close to British airlines.Jet airlines has the least median count for premium economy seats.

Comparison of pitch of seats in economy and premium economy classes for each airlines

par(mfrow=c(2,1))
boxplot(airlines$PitchEconomy~airlines$Airline,xlab="Airlines",ylab="Pitch of seats in economy",main="Economy seat's pitch for differnt airlines")
boxplot(airlines$PitchPremium~airlines$Airline,xlab="Airlines",ylab="Pitch of seats in premium economy",main="Premium economy seat's pitch for differnt airlines")

Singapore,Delta and AirFrance have the maximum median for pitch of their economy class whereas Jet airines has the least median for the same. For premium economy seats AirFrance,British,Singapore and Virgin airlines have the same median for pitch of premium economy class.Jet airlines has the highest and Delta airlines the least.

Comparison of width of seats in economy and premium economy classes for each airlines

par(mfrow=c(2,1))
boxplot(airlines$WidthEconomy~airlines$Airline,xlab="Airlines",ylab="width of seats in economy",main="Economy seat's width for differnt airlines")
boxplot(airlines$WidthPremium~airlines$Airline,xlab="Airlines",ylab="width of seats in premium economy",main="Premium economy seat's width for differnt airlines")

Singapore airlines have the maximum median for width of their economy class whereas Delta and Jet airines are almost the same and has the least median for the same.British,Virgin and AirFrance are all similar in case of median for economy seat’s width. For premium economy seats AirFrance and British have the same median for width of premium economy class with Singapore airlines a bit more.Jet airlines has the highest with Virgin almost equal, and Delta airlines the least.

Comparison of price of seats in economy and premium economy classes for each airlines

par(mfrow=c(2,1))
boxplot(airlines$PriceEconomy~airlines$Airline,xlab="Airlines",ylab="Price of seats in economy",main="Economy seat's price for differnt airlines")
boxplot(airlines$PricePremium~airlines$Airline,xlab="Airlines",ylab="Price of seats in premium economy",main="Premium economy seat's price for differnt airlines")

Jet and Delta airlines have the least median for both premium economy and economy classes.AirFrance being the highest in both classes.

Comparison of relative price of seats in economy and premium economy classes for each airlines

boxplot(airlines$PriceRelative~airlines$Airline,xlab="Airlines",ylab="Relative Price of seats in economy and premium economy",main="Economy  and premium economy seat's relative price for differnt airlines")

So we can observe that Jet airlines has the highest median for the relative price between economy and premium economy.AirFrance and Delta airlines have the least median for the relative price.

Comparison of pitch difference of seats in economy and premium economy classes for each airlines

boxplot(airlines$PitchDifference~airlines$Airline,xlab="Airlines",ylab="Pitch difference of seats in economy and premium economy",main="Economy  and premium economy seat's pitch difference for differnt airlines")

Highest median for the difference in pitch between economy and premium economy is for Jet airways whereas the least being Delta airlines.

Comparison of width difference of seats in economy and premium economy classes for each airlines

boxplot(airlines$WidthDifference~airlines$Airline,xlab="Airlines",ylab="Width difference of seats in economy and premium economy",main="Economy  and premium economy seat's width difference for differnt airlines")

Again Jet airways has the highest median count in the difference in width between the economy and premium economy classes.Delta airlines has the least for the same.

The actual question is:What factors explain the difference in price between an economy ticket and a premium-economy airline ticket? So we need to check how the relative price data changes with either the pitch or width difference or th percentage of premium economy seats of the total seats. For this we’ll use scatterplots.

Visualization of relative price with respect to other property changes.

Scatterplots between relative price and pitch difference.

plot(airlines$PitchDifference,airlines$PriceRelative,main="Pitch difference vs Relative Price",xlab="Pitch difference",ylab="Relative Price")

Scatterplots between relative price and width difference.

plot(airlines$WidthDifference,airlines$PriceRelative,main="Width difference vs Relative Price",xlab="Width difference",ylab="Relative Price")

Scatterplots between percentage of premium seats and relative price.

plot(airlines$PercentPremiumSeats,airlines$PriceRelative,main="Percentage of premium seats vs Relative Price",xlab="Percentage of premium seats",ylab="Relative Price")

Now lets try looking at these factors and relations using a scatterplotmatrix.

Scatterplotmatrix

library(car)
## 
## Attaching package: 'car'
## The following object is masked from 'package:psych':
## 
##     logit
scatterplotMatrix(formula=~PriceRelative+PitchDifference+WidthDifference+PercentPremiumSeats,cex=0.8,data = airlines,main="Scatter plot Matrix",spread=FALSE)

So we could see here the relative price increasing with the pitch and width difference factors.

Lets check the correlation between all the variables using correlation matrix.

Correlations

cor(airlines[,6:18])
##                     SeatsEconomy SeatsPremium PitchEconomy PitchPremium
## SeatsEconomy         1.000000000  0.625056587   0.14412692  0.119221250
## SeatsPremium         0.625056587  1.000000000  -0.03421296  0.004883123
## PitchEconomy         0.144126924 -0.034212963   1.00000000 -0.550606241
## PitchPremium         0.119221250  0.004883123  -0.55060624  1.000000000
## WidthEconomy         0.373670252  0.455782883   0.29448586 -0.023740873
## WidthPremium         0.102431959 -0.002717527  -0.53929285  0.750259029
## PriceEconomy         0.128167220  0.113642176   0.36866123  0.050384550
## PricePremium         0.177000928  0.217612376   0.22614179  0.088539147
## PriceRelative        0.003956939 -0.097196009  -0.42302204  0.417539056
## SeatsTotal           0.992607966  0.715171053   0.12373524  0.107512784
## PitchDifference      0.035318044  0.016365566  -0.78254993  0.950591466
## WidthDifference     -0.080670148 -0.216168666  -0.63557430  0.703281797
## PercentPremiumSeats -0.330935223  0.485029771  -0.10280880 -0.175487414
##                     WidthEconomy WidthPremium PriceEconomy PricePremium
## SeatsEconomy          0.37367025  0.102431959   0.12816722   0.17700093
## SeatsPremium          0.45578288 -0.002717527   0.11364218   0.21761238
## PitchEconomy          0.29448586 -0.539292852   0.36866123   0.22614179
## PitchPremium         -0.02374087  0.750259029   0.05038455   0.08853915
## WidthEconomy          1.00000000  0.081918728   0.06799061   0.15054837
## WidthPremium          0.08191873  1.000000000  -0.05704522   0.06402004
## PriceEconomy          0.06799061 -0.057045224   1.00000000   0.90138870
## PricePremium          0.15054837  0.064020043   0.90138870   1.00000000
## PriceRelative        -0.04396116  0.504247591  -0.28856711   0.03184654
## SeatsTotal            0.40545860  0.091297500   0.13243313   0.19232533
## PitchDifference      -0.12722421  0.760121272  -0.09952511  -0.01806629
## WidthDifference      -0.39320512  0.884149655  -0.08449975  -0.01151218
## PercentPremiumSeats   0.22714172 -0.183312058   0.06532232   0.11639097
##                     PriceRelative  SeatsTotal PitchDifference
## SeatsEconomy          0.003956939  0.99260797      0.03531804
## SeatsPremium         -0.097196009  0.71517105      0.01636557
## PitchEconomy         -0.423022038  0.12373524     -0.78254993
## PitchPremium          0.417539056  0.10751278      0.95059147
## WidthEconomy         -0.043961160  0.40545860     -0.12722421
## WidthPremium          0.504247591  0.09129750      0.76012127
## PriceEconomy         -0.288567110  0.13243313     -0.09952511
## PricePremium          0.031846537  0.19232533     -0.01806629
## PriceRelative         1.000000000 -0.01156894      0.46873025
## SeatsTotal           -0.011568942  1.00000000      0.03416915
## PitchDifference       0.468730249  0.03416915      1.00000000
## WidthDifference       0.485802437 -0.10584398      0.76089108
## PercentPremiumSeats  -0.161565556 -0.22091465     -0.09264869
##                     WidthDifference PercentPremiumSeats
## SeatsEconomy            -0.08067015         -0.33093522
## SeatsPremium            -0.21616867          0.48502977
## PitchEconomy            -0.63557430         -0.10280880
## PitchPremium             0.70328180         -0.17548741
## WidthEconomy            -0.39320512          0.22714172
## WidthPremium             0.88414965         -0.18331206
## PriceEconomy            -0.08449975          0.06532232
## PricePremium            -0.01151218          0.11639097
## PriceRelative            0.48580244         -0.16156556
## SeatsTotal              -0.10584398         -0.22091465
## PitchDifference          0.76089108         -0.09264869
## WidthDifference          1.00000000         -0.27559416
## PercentPremiumSeats     -0.27559416          1.00000000

So we could see that there exists a good correlation between the prices of both classes.Also the relative price factor is in correlations with the pitch and width of the premium classes and even their differences as in pitch difference and width difference in between the economy and the premium economy class.

Corrgram plot

library(corrgram)
corrgram(airlines, order=FALSE,lower.panel=panel.shade,upper.panel=panel.pie,text.panel=panel.txt,main="Corrgram of airlines correlations")

So here lets observe from the correlations for the prices or the relative prices.We can see a strong positive correlation between prices of economy and premium economy.The premium economy price and the economy prices are strongly and positively correlated with the flight duration.Looking back to our question,we need to find out the reason for the difference between the prices of economy and premium economy classes.So,relative price is positively correlated with the pitch and width differences.Also there exists lesser correlation between relative price and percentage of premium seats.

Testing correlations between relative price and the pitch difference.

t.test(airlines$PriceRelative,airlines$PitchDifference)
## 
##  Welch Two Sample t-test
## 
## data:  airlines$PriceRelative and airlines$PitchDifference
## t = -72.974, df = 516.54, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -6.367495 -6.033640
## sample estimates:
## mean of x mean of y 
## 0.4872052 6.6877729
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

p value less than 0.05 in both the cases shows a significant relationship between both these variables.It rejects the null hypothesis and hence shows that the relative price and pitch difference are dependent upon each other.

Testing correlations between relative price and the width difference.

t.test(airlines$PriceRelative,airlines$WidthDifference)
## 
##  Welch Two Sample t-test
## 
## data:  airlines$PriceRelative and airlines$WidthDifference
## t = -19.284, df = 585.55, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -1.262697 -1.029268
## sample estimates:
## mean of x mean of y 
## 0.4872052 1.6331878
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 less than 0.05 in both the cases shows a significant relationship between both these variables.It rejects the null hypothesis and hence shows that the relative price and the difference in width are dependent upon each other.

Testing correlations between relative price and the percentage of premium seats.

t.test(airlines$PriceRelative,airlines$PercentPremiumSeats)
## 
##  Welch Two Sample t-test
## 
## data:  airlines$PriceRelative and airlines$PercentPremiumSeats
## t = -62.302, df = 464.91, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -14.60477 -13.71164
## sample estimates:
##  mean of x  mean of y 
##  0.4872052 14.6454148
cor.test(airlines$PriceRelative,airlines$PercentPremiumSeats)
## 
##  Pearson's product-moment correlation
## 
## data:  airlines$PriceRelative and airlines$PercentPremiumSeats
## t = -3.496, df = 456, p-value = 0.0005185
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.24949885 -0.07098966
## sample estimates:
##        cor 
## -0.1615656

p value less than 0.05 in both the cases shows a significant relationship between both these variables.It rejects the null hypothesis and hence shows that the relative price and the percentage of premium seats are dependent upon each other.

Now since we have seen the independent prices of each class to be in relation with the flight duration from the corrgram plot.Lets check the correlation between the relative price and the flight duration.We’ll do this using the above done tests.

Testing correlations between relative price and the flight duration.

t.test(airlines$PriceRelative,airlines$FlightDuration)
## 
##  Welch Two Sample t-test
## 
## data:  airlines$PriceRelative and airlines$FlightDuration
## t = -42.499, df = 471.79, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -7.418482 -6.762785
## sample estimates:
## mean of x mean of y 
## 0.4872052 7.5778384
cor.test(airlines$PriceRelative,airlines$FlightDuration)
## 
##  Pearson's product-moment correlation
## 
## data:  airlines$PriceRelative and airlines$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 
## 0.121075

p value less than 0.05 in both the cases shows a significant relationship between both these variables.It rejects the null hypothesis and hence shows that the relative price and flight duration are dependent upon each other.

Testing correlations between relative price and the economy price.

t.test(airlines$PriceRelative,airlines$PriceEconomy)
## 
##  Welch Two Sample t-test
## 
## data:  airlines$PriceRelative and airlines$PriceEconomy
## t = -28.727, df = 457, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -1417.339 -1235.840
## sample estimates:
##    mean of x    mean of y 
##    0.4872052 1327.0764192
cor.test(airlines$PriceRelative,airlines$PriceEconomy)
## 
##  Pearson's product-moment correlation
## 
## data:  airlines$PriceRelative and airlines$PriceEconomy
## t = -6.4359, df = 456, p-value = 3.112e-10
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.3704004 -0.2022889
## sample estimates:
##        cor 
## -0.2885671

p value less than 0.05 in both the cases shows a significant relationship between both these variables.It rejects the null hypothesis and hence shows that the relative price and economy seat prices are dependent upon each other.

Testing correlations between relative price and the premium economy price.

t.test(airlines$PriceRelative,airlines$PricePremium)
## 
##  Welch Two Sample t-test
## 
## data:  airlines$PriceRelative and airlines$PricePremium
## t = -30.649, df = 457, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -1963.055 -1726.486
## sample estimates:
##    mean of x    mean of y 
##    0.4872052 1845.2576419
cor.test(airlines$PriceRelative,airlines$PricePremium)
## 
##  Pearson's product-moment correlation
## 
## data:  airlines$PriceRelative and airlines$PricePremium
## t = 0.6804, df = 456, p-value = 0.4966
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.05995522  0.12311410
## sample estimates:
##        cor 
## 0.03184654

p value less than 0.05 in both the cases shows a significant relationship between both these variables.It rejects the null hypothesis and hence shows that the relative price and economy seat prices are dependent upon each other.

So hence we could see from the above done tests that relative price is dependent upon and correlated with the pitch difference,width difference,percent of premium economy seats and the flight duration.Also this difference will surely depend upon the independent prices i.e. the economy price and the premium economy price since they are the factors which actually give us the difference directly.

For this we could formulate a regression model as:Relative price=b0+b1(pitch difference)+b2(width difference)+b3(percent of premium seats)+b4(flight duration)+b5(economy price)+b6(premium economy price).

Regression Analysis

fit<-lm(formula = PriceRelative ~ PitchDifference + WidthDifference + PercentPremiumSeats+FlightDuration+PriceEconomy+PricePremium, data = airlines)
summary(fit)
## 
## Call:
## lm(formula = PriceRelative ~ PitchDifference + WidthDifference + 
##     PercentPremiumSeats + FlightDuration + PriceEconomy + PricePremium, 
##     data = airlines)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.71347 -0.14837 -0.00985  0.10434  0.93289 
## 
## Coefficients:
##                       Estimate Std. Error t value Pr(>|t|)    
## (Intercept)          1.868e-01  6.563e-02   2.846 0.004623 ** 
## PitchDifference      3.967e-02  1.013e-02   3.914 0.000105 ***
## WidthDifference      8.796e-02  1.578e-02   5.573 4.32e-08 ***
## PercentPremiumSeats -1.379e-02  2.513e-03  -5.488 6.79e-08 ***
## FlightDuration       2.196e-02  4.280e-03   5.130 4.32e-07 ***
## PriceEconomy        -7.049e-04  2.713e-05 -25.981  < 2e-16 ***
## PricePremium         4.674e-04  2.276e-05  20.536  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2404 on 451 degrees of freedom
## Multiple R-squared:  0.719,  Adjusted R-squared:  0.7153 
## F-statistic: 192.4 on 6 and 451 DF,  p-value: < 2.2e-16

This shows a significant p value(<0.05).Also the model fits properly and it is finally a good fit with an adjusted R-squared value of 0.7153 and multiple R-squared value of 0.719.