airplane<- read.csv(paste("airline.csv", sep=""))
library(psych)
summary(airplane)
##       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
describe(airplane)
##                     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
attach(airplane)
mean(FlightDuration)
## [1] 7.577838
median(FlightDuration)
## [1] 7.79
sd(FlightDuration)
## [1] 3.542064
mean(SeatsEconomy)
## [1] 202.3122
median(SeatsEconomy)
## [1] 185
sd(SeatsEconomy)
## [1] 76.37353
mean(SeatsPremium)
## [1] 33.64847
median(SeatsPremium)
## [1] 36
sd(SeatsPremium)
## [1] 13.26142
mean(PitchEconomy)
## [1] 31.21834
sd(PitchEconomy)
## [1] 0.6551695
median(PitchEconomy)
## [1] 31
mean(PitchPremium)
## [1] 37.90611
median(PitchPremium)
## [1] 38
sd(PitchPremium)
## [1] 1.313924
mean(WidthEconomy)
## [1] 17.83843
median(WidthEconomy)
## [1] 18
sd(WidthEconomy)
## [1] 0.5575102
mean(WidthPremium)
## [1] 19.47162
median(WidthPremium)
## [1] 19
sd(WidthPremium)
## [1] 1.097173
mean(PriceRelative)
## [1] 0.4872052
median(PriceRelative)
## [1] 0.365
sd(PriceRelative)
## [1] 0.4505873
mean(SeatsTotal)
## [1] 235.9607
median(SeatsTotal)
## [1] 227
sd(SeatsTotal)
## [1] 85.29315
mean(PitchDifference)
## [1] 6.687773
median(PitchDifference)
## [1] 7
sd(PitchDifference)
## [1] 1.761708
mean(WidthDifference)
## [1] 1.633188
mean(WidthDifference)
## [1] 1.633188
sd(WidthDifference)
## [1] 1.189281
mean(PercentPremiumSeats)
## [1] 14.64541
median(PercentPremiumSeats)
## [1] 13.21
sd(PercentPremiumSeats)
## [1] 4.842451
barplot(table(airplane$IsInternational))

library(lattice)
 histogram(~PitchDifference,
 main = "Pitch Difference Analysis", xlab="Difference in Pitch", ylab = "Frequency", col='blue' )

histogram(~WidthDifference,
 main = "Width Difference Analysis", xlab="Difference in Width", ylab = "Frequency", col='blue' )

histogram(~PitchDifference,
 main = "Pitch Difference Analysis", xlab="Difference in pitch", ylab = "Frequency", col='blue' ) 

plot(~PriceEconomy + PricePremium, main="Premium Economy Price vs Economy Price",pch = 25)
abline(lm(PriceEconomy~PricePremium))

plot(~TravelMonth + PriceRelative, main="Price Relative vs Travel Month",pch = 25,col = c("blue","green"))

library(car)
## 
## Attaching package: 'car'
## The following object is masked from 'package:psych':
## 
##     logit
scatterplotMatrix(formula=~PriceRelative+PitchDifference+WidthDifference+PercentPremiumSeats,cex=0.8)

library(car)
scatterplotMatrix(formula=~Airline+PriceEconomy+PricePremium+PercentPremiumSeats,cex=0.8)

plot(Airline,PriceRelative,main="Airline vs Relative Price",xlab="Airline",ylab="Relative Pricing", col = c("blue","green","red","blue","green","red"))

plot(Aircraft,PriceRelative,main="Flight Type vs Relative Price",xlab="Flight Type",ylab="Relative Pricing", col = c("blue","green"))

library(corrgram)
corrgram(airplane,order= T, text.panel=panel.txt,lower.panel = panel.shade,upper.panel = panel.pie, main="Corrgram of all variables")

cor(airplane[, c(6:18)])  # only numeric cols
##                     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
t.test(airplane$PricePremium, airplane$PriceEconomy)
## 
##  Welch Two Sample t-test
## 
## data:  airplane$PricePremium and airplane$PriceEconomy
## t = 6.8304, df = 856.56, p-value = 1.605e-11
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  369.2793 667.0831
## sample estimates:
## mean of x mean of y 
##  1845.258  1327.076
t.test(airplane$PriceRelative, airplane$PitchDifference)
## 
##  Welch Two Sample t-test
## 
## data:  airplane$PriceRelative and airplane$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
t.test(airplane$PriceRelative, airplane$PercentPremiumSeats)
## 
##  Welch Two Sample t-test
## 
## data:  airplane$PriceRelative and airplane$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
t.test(airplane$PriceRelative, airplane$WidthDifference)
## 
##  Welch Two Sample t-test
## 
## data:  airplane$PriceRelative and airplane$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

REGRESSION ANALYSIS

model <- lm(formula = PriceRelative ~ PitchDifference + WidthDifference + PercentPremiumSeats, data = airplane)
summary(model)
## 
## Call:
## lm(formula = PriceRelative ~ PitchDifference + WidthDifference + 
##     PercentPremiumSeats, data = airplane)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.88643 -0.29471 -0.05005  0.19013  1.17157 
## 
## Coefficients:
##                      Estimate Std. Error t value Pr(>|t|)    
## (Intercept)         -0.031508   0.097220  -0.324    0.746    
## PitchDifference      0.064596   0.016171   3.994 7.56e-05 ***
## WidthDifference      0.104782   0.024813   4.223 2.92e-05 ***
## PercentPremiumSeats -0.005764   0.003971  -1.451    0.147    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3882 on 454 degrees of freedom
## Multiple R-squared:  0.2627, Adjusted R-squared:  0.2579 
## F-statistic: 53.93 on 3 and 454 DF,  p-value: < 2.2e-16
model2<-lm(PricePremium~PriceEconomy+WidthDifference+PitchDifference+IsInternational+Aircraft+Airline+PercentPremiumSeats, data=airplane)
summary(model2)
## 
## Call:
## lm(formula = PricePremium ~ PriceEconomy + WidthDifference + 
##     PitchDifference + IsInternational + Aircraft + Airline + 
##     PercentPremiumSeats, data = airplane)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -764.25 -273.97  -48.45  113.47 2992.49 
## 
## Coefficients:
##                                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                  -907.41964  356.28049  -2.547 0.011203 *  
## PriceEconomy                    1.28330    0.03705  34.635  < 2e-16 ***
## WidthDifference              -111.26957  102.88310  -1.082 0.280053    
## PitchDifference                32.44698   79.48605   0.408 0.683316    
## IsInternationalInternational  545.24275  320.37657   1.702 0.089475 .  
## AircraftBoeing                106.07548   57.76813   1.836 0.066989 .  
## AirlineBritish                778.75194  151.98215   5.124 4.46e-07 ***
## AirlineDelta                  939.92534  231.05147   4.068 5.61e-05 ***
## AirlineJet                    684.79734  192.31458   3.561 0.000409 ***
## AirlineSingapore              572.45834  125.92648   4.546 7.05e-06 ***
## AirlineVirgin                1377.93939  141.56578   9.734  < 2e-16 ***
## PercentPremiumSeats           -18.71280    5.72975  -3.266 0.001175 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 457.5 on 446 degrees of freedom
## Multiple R-squared:  0.8769, Adjusted R-squared:  0.8739 
## F-statistic: 288.8 on 11 and 446 DF,  p-value: < 2.2e-16