Setting Working Directory

setwd("E:/Internship/Tasks/Week 3/Week 3, Day 3 (Wed)")

Reading File

airline <-read.csv(paste("SixAirlinesDataV2.csv",sep=""))

Viewing Data

View(airline)

Airline vs Aircraft

table(airline$Airline,airline$Aircraft)
##            
##             AirBus Boeing
##   AirFrance     36     38
##   British       47    128
##   Delta         12     34
##   Jet            7     54
##   Singapore     16     24
##   Virgin        33     29

Summarizing data

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

Summary Using Describe

library("psych", lib.loc="~/R/win-library/3.4")
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

Boxplots

boxplot(airline$PriceEconomy,airline$PricePremium,horizontal=TRUE,main="Boxplot of PriceEconomy and PricePremium",xlab="Price", Ylab="Airline 1= Premium Airline 2 = Economy")

boxplot(airline$PriceRelative,ylim=c(0,1),main="Boxplot for PriceRelative")

boxplot(airline$PitchPremium,airline$PitchEconomy,main="Boxplot for Pitch of Premium & Economy ",ylim=c(30,45))

boxplot(airline$WidthPremium,airline$WidthEconomy,main="Boxplot for Width of Premium & Economy ",ylim=c(15,25))

boxplot(airline$SeatsTotal,airline$SeatsPremium,airline$SeatsEconomy,ylim=c(10,350),main="Number of Seats total then premium and then Economy")

table(airline$TravelMonth)
## 
## Aug Jul Oct Sep 
## 127  75 127 129
plot(airline$PriceEconomy~airline$PitchEconomy)

plot(airline$PriceEconomy~airline$WidthEconomy)

plot(airline$PricePremium~airline$PitchPremium)

plot(airline$PricePremium~airline$WidthPremium)

plot(airline$PricePremium~airline$PitchDifference)

plot(airline$PricePremium~airline$WidthDifference)

plot(airline$PriceRelative~airline$PitchDifference)

plot(airline$PriceRelative~airline$WidthDifference)

plot(airline$PriceRelative~airline$PriceEconomy)

plot(airline$PriceRelative~airline$PricePremium)

cor.test(airline[,"PriceEconomy"],airline[,"PitchEconomy"])
## 
##  Pearson's product-moment correlation
## 
## data:  airline[, "PriceEconomy"] and airline[, "PitchEconomy"]
## t = 8.469, df = 456, p-value = 3.428e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.2867196 0.4452479
## sample estimates:
##       cor 
## 0.3686612

Correlation value is satisfactory in above variables

cor.test(airline[,"PriceEconomy"],airline[,"WidthEconomy"])
## 
##  Pearson's product-moment correlation
## 
## data:  airline[, "PriceEconomy"] and airline[, "WidthEconomy"]
## t = 1.4552, df = 456, p-value = 0.1463
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.02378438  0.15862920
## sample estimates:
##        cor 
## 0.06799061

Above variables are not Correlated much

cor.test(airline[,"PricePremium"],airline[,"PitchPremium"])
## 
##  Pearson's product-moment correlation
## 
## data:  airline[, "PricePremium"] and airline[, "PitchPremium"]
## t = 1.8981, df = 456, p-value = 0.05831
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.003112919  0.178716114
## sample estimates:
##        cor 
## 0.08853915

Not good correlation in above variables

cor.test(airline[,"PricePremium"],airline[,"WidthPremium"])
## 
##  Pearson's product-moment correlation
## 
## data:  airline[, "PricePremium"] and airline[, "WidthPremium"]
## t = 1.3699, df = 456, p-value = 0.1714
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.02776966  0.15473916
## sample estimates:
##        cor 
## 0.06402004

Above variables are not significantly correlated

cor.test(airline[,"PricePremium"],airline[,"PitchDifference"])
## 
##  Pearson's product-moment correlation
## 
## data:  airline[, "PricePremium"] and airline[, "PitchDifference"]
## t = -0.38585, df = 456, p-value = 0.6998
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.1095118  0.0736825
## sample estimates:
##         cor 
## -0.01806629

Insignificant Correlation in above variables

cor.test(airline[,"PricePremium"],airline[,"WidthDifference"])
## 
##  Pearson's product-moment correlation
## 
## data:  airline[, "PricePremium"] and airline[, "WidthDifference"]
## t = -0.24585, df = 456, p-value = 0.8059
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.10303032  0.08019923
## sample estimates:
##         cor 
## -0.01151218

Insignificant Correlation in above variables

cor.test(airline[,"PricePremium"],airline[,"PercentPremiumSeats"])
## 
##  Pearson's product-moment correlation
## 
## data:  airline[, "PricePremium"] and airline[, "PercentPremiumSeats"]
## t = 2.5024, df = 456, p-value = 0.01268
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.0250311 0.2058228
## sample estimates:
##      cor 
## 0.116391

Above variables are not very well correlated

cor.test(airline[,"PriceEconomy"],airline[,"PricePremium"])
## 
##  Pearson's product-moment correlation
## 
## data:  airline[, "PriceEconomy"] and airline[, "PricePremium"]
## t = 44.452, df = 456, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.8826622 0.9172579
## sample estimates:
##       cor 
## 0.9013887

Strong correlation in above variables but its very aubvious

cor.test(airline[,"PriceRelative"],airline[,"PriceEconomy"])
## 
##  Pearson's product-moment correlation
## 
## data:  airline[, "PriceRelative"] and airline[, "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

Significant Correlation in above variables but dont make much sense

cor.test(airline[,"PriceRelative"],airline[,"PricePremium"])
## 
##  Pearson's product-moment correlation
## 
## data:  airline[, "PriceRelative"] and airline[, "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

Above variables are Weekly Correlated

cor.test(airline[,"PriceRelative"],airline[,"PercentPremiumSeats"])
## 
##  Pearson's product-moment correlation
## 
## data:  airline[, "PriceRelative"] and airline[, "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

Above variables are Weekly Correlated

cor.test(airline[,"PriceRelative"],airline[,"PitchDifference"])
## 
##  Pearson's product-moment correlation
## 
## data:  airline[, "PriceRelative"] and airline[, "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

Strong Correlation Found in above variables

cor.test(airline[,"PriceRelative"],airline[,"WidthDifference"])
## 
##  Pearson's product-moment correlation
## 
## data:  airline[, "PriceRelative"] and airline[, "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

Strong Correlation found in above variables

PriceRelative has shown good correlation with “PitchDifference” and “WidthDifference” which can be thought in practical aspect too.

Hypothesis 1: PricePremium depends on PitchPremium,WidthPremium,PitchDiffernce,WidthDifference and PercentPremiumSeats

Lets Check

fit <-lm(PricePremium ~ PitchPremium + WidthPremium + PitchDifference + WidthDifference + PercentPremiumSeats, data=airline)
summary(fit)
## 
## Call:
## lm(formula = PricePremium ~ PitchPremium + WidthPremium + PitchDifference + 
##     WidthDifference + PercentPremiumSeats, data = airline)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2201.6 -1022.2  -152.9   864.2  6221.4 
## 
## Coefficients:
##                      Estimate Std. Error t value Pr(>|t|)    
## (Intercept)         -44382.86    4808.47  -9.230  < 2e-16 ***
## PitchPremium          1347.23     153.29   8.789  < 2e-16 ***
## WidthPremium            47.34     119.95   0.395    0.693    
## PitchDifference      -1070.29     122.10  -8.766  < 2e-16 ***
## WidthDifference        191.48     117.13   1.635    0.103    
## PercentPremiumSeats     73.96      13.00   5.687 2.32e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1172 on 452 degrees of freedom
## Multiple R-squared:  0.181,  Adjusted R-squared:  0.172 
## F-statistic: 19.98 on 5 and 452 DF,  p-value: < 2.2e-16
residuals(fit)
##            1            2            3            4            5 
##  1488.085677  1488.085677  1488.085677  1488.085677   762.085677 
##            6            7            8            9           10 
##   762.085677   762.085677   760.085677   760.085677   752.085677 
##           11           12           13           14           15 
##   752.085677   752.085677   752.085677   419.085677   419.085677 
##           16           17           18           19           20 
##   419.085677   267.085677   267.085677   267.085677   -41.914323 
##           21           22           23           24           25 
##   -41.914323   -41.914323   -45.914323   -45.914323   -45.914323 
##           26           27           28           29           30 
##  -152.914323  -152.914323  -152.914323  -416.914323  -416.914323 
##           31           32           33           34           35 
##  -416.914323  -472.914323  -472.914323  -472.914323  -472.914323 
##           36           37           38           39           40 
##  -688.914323  -688.914323  -688.914323  -724.914323  -724.914323 
##           41           42           43           44           45 
##  -724.914323  -724.914323  -919.914323  -919.914323  -919.914323 
##           46           47           48           49           50 
## -1023.914323 -1023.914323 -1023.914323 -1463.914323 -1463.914323 
##           51           52           53           54           55 
## -1463.914323   848.839620   784.839620   784.839620   784.839620 
##           56           57           58           59           60 
##    46.839620    46.839620    46.839620  -889.160380  -889.160380 
##           61           62           63           64           65 
## -1330.160380   715.945063   715.945063   715.945063   715.945063 
##           66           67           68           69           70 
##   443.945063   443.945063   443.945063   443.945063    -3.054937 
##           71           72           73           74           75 
##    -3.054937    -3.054937 -1818.054937  -400.784063  -369.784063 
##           76           77           78           79           80 
##  -330.784063  -336.784063  -342.784063  -167.784063  -209.784063 
##           81           82           83           84           85 
##    22.215937  1185.896929  1185.896929  1185.896929  1185.896929 
##           86           87           88           89           90 
##   752.896929   752.896929   752.896929   751.896929 -1287.242722 
##           91           92           93           94           95 
## -1287.242722 -1287.242722 -1287.242722 -1195.242722 -1195.242722 
##           96           97           98           99          100 
## -1195.242722 -1195.242722  -807.584307  2016.147587  2016.147587 
##          101          102          103          104          105 
##  2016.147587  2016.147587  1989.147587  1989.147587  1989.147587 
##          106          107          108          109          110 
##  1989.147587  1045.147587  1045.147587  1045.147587    87.147587 
##          111          112          113          114          115 
##    87.147587    87.147587 -1060.852413 -1104.852413 -1104.852413 
##          116          117          118          119          120 
## -1139.852413 -1150.852413 -1150.852413 -1198.852413 -1223.852413 
##          121          122          123          124          125 
## -1227.852413 -1227.852413 -1240.852413 -1261.852413 -1268.852413 
##          126          127          128          129          130 
## -1270.852413 -1283.852413 -1299.852413 -1308.852413 -1309.852413 
##          131          132          133          134          135 
## -1309.852413 -1312.852413 -1335.852413 -1345.852413 -1348.852413 
##          136          137          138          139          140 
## -1371.852413 -1371.852413 -1374.852413 -1381.852413 -1390.852413 
##          141          142          143          144          145 
## -1390.852413 -1405.852413 -1405.852413 -1405.852413 -1415.852413 
##          146          147          148          149          150 
## -1421.852413 -1447.852413 -1447.852413 -1449.852413 -1422.486614 
##          151          152          153          154          155 
## -1460.852413 -1146.900164 -1016.900164  -956.900164  -726.900164 
##          156          157          158          159          160 
##  -380.349100  -380.349100  -380.349100  -380.349100   964.650900 
##          161          162          163          164          165 
##   964.650900   964.650900   964.650900  1513.348981  1513.348981 
##          166          167          168          169          170 
##  1513.348981  1513.348981  1019.650900  1019.650900  1019.650900 
##          171          172          173          174          175 
##  1019.650900  1509.650900  -289.349100  1698.348981  1698.348981 
##          176          177          178          179          180 
##  1698.348981  1698.348981  -534.349100  1540.650900   531.650900 
##          181          182          183          184          185 
##   531.650900   531.650900   531.650900  -289.349100   662.612520 
##          186          187          188          189          190 
##   662.612520   839.612520   839.612520   839.612520   662.612520 
##          191          192          193          194          195 
##  1056.612520  1056.612520  1056.612520  1056.612520  1071.612520 
##          196          197          198          199          200 
##  1071.612520  1071.612520  1071.612520  1583.612520  1583.612520 
##          201          202          203          204          205 
##  1583.612520  1614.612520  1614.612520   573.612520   573.612520 
##          206          207          208          209          210 
##   573.612520   573.612520   483.612520 -1331.387480 -1331.387480 
##          211          212          213          214          215 
## -1331.387480  -794.613276  -794.613276  -794.613276   453.386724 
##          216          217          218          219          220 
##   453.386724   453.386724   453.386724   453.386724   453.386724 
##          221          222          223          224          225 
##   453.386724   453.386724   401.386724   401.386724   401.386724 
##          226          227          228          229          230 
##   657.386724   657.386724   381.386724   381.386724   381.386724 
##          231          232          233          234          235 
##   516.386724   869.386724   869.386724   869.386724   869.386724 
##          236          237          238          239          240 
##   869.386724   869.386724   869.386724   869.386724  2144.093171 
##          241          242          243          244          245 
##  2144.093171  2144.093171  1862.093171  1862.093171  1862.093171 
##          246          247          248          249          250 
##  1835.093171  1835.093171  1835.093171  1835.093171  1734.093171 
##          251          252          253          254          255 
##  1734.093171  1734.093171  1660.093171  1660.093171  1660.093171 
##          256          257          258          259          260 
##  1660.093171  1107.093171  1107.093171  1107.093171  1058.093171 
##          261          262          263          264          265 
##   927.093171   927.093171   927.093171   913.093171   913.093171 
##          266          267          268          269          270 
##   913.093171   684.093171   501.093171   501.093171   501.093171 
##          271          272          273          274          275 
##   419.093171   419.093171   419.093171   419.093171   238.093171 
##          276          277          278          279          280 
##   185.093171  -165.906829  -165.906829  -452.906829  -527.906829 
##          281          282          283          284          285 
##  -684.696294  -684.696294  -604.696294  -604.696294  -604.696294 
##          286          287          288          289          290 
##   468.998981   468.998981   468.998981  -554.696294  -554.696294 
##          291          292          293          294          295 
##  -632.696294   478.998981  -649.696294  -649.696294 -2201.593284 
##          296          297          298          299          300 
##  -870.635568  -697.635568 -2120.593284 -2120.593284  -341.696294 
##          301          302          303          304          305 
## -2004.593284  -743.635568  -743.635568  -703.696294 -1722.593284 
##          306          307          308          309          310 
##  -620.635568  -647.696294 -1564.613276 -1564.613276 -1564.613276 
##          311          312          313          314          315 
## -1616.613276 -1616.613276 -1477.613276 -1474.613276  -834.468479 
##          316          317          318          319          320 
## -1053.468479 -1053.468479 -1097.468479  -558.468479  -558.468479 
##          321          322          323          324          325 
##  -558.468479 -1149.468479 -1605.468479 -1605.468479  -921.468479 
##          326          327          328          329          330 
##  -921.468479  -921.468479 -1098.468479 -1098.468479 -1098.468479 
##          331          332          333          334          335 
## -1886.468479 -1886.468479 -1886.468479 -1886.468479  -941.468479 
##          336          337          338          339          340 
##  -941.468479  -941.468479  -941.468479  1391.178915  1391.178915 
##          341          342          343          344          345 
##  1391.178915   200.178915   482.178915   645.178915   645.178915 
##          346          347          348          349          350 
##   645.178915   586.178915   586.178915   586.178915   943.178915 
##          351          352          353          354          355 
##   943.178915   943.178915   943.178915   756.012774   756.012774 
##          356          357          358          359          360 
##   756.012774   756.012774  1008.178915  1008.178915  1008.178915 
##          361          362          363          364          365 
##  1133.012774  1133.012774   662.178915   662.178915   662.178915 
##          366          367          368          369          370 
##   662.178915  6221.423745  6221.423745  6221.423745  1277.423745 
##          371          372          373          374          375 
##  1277.423745  1277.423745   -40.576255  -339.576255  -339.576255 
##          376          377          378          379          380 
##  -366.576255  -395.576255  -395.576255  -925.891511  -925.891511 
##          381          382          383          384          385 
##  -925.891511 -1010.891511 -1010.891511  -888.891511  -874.891511 
##          386          387          388          389          390 
## -1090.891511 -1141.891511 -1141.891511 -1141.891511 -1180.891511 
##          391          392          393          394          395 
## -1180.891511 -1180.891511  -788.891511  -925.891511 -1090.891511 
##          396          397          398          399          400 
## -1090.891511  -788.891511 -1141.891511 -1180.891511 -1141.891511 
##          401          402          403          404          405 
## -1141.891511 -1141.891511 -1141.891511  -925.891511  -712.891511 
##          406          407          408          409          410 
##  -702.188592  -702.188592  -702.188592  -702.188592 -1246.300891 
##          411          412          413          414          415 
## -1246.300891 -1246.300891 -1246.300891 -1246.300891 -1246.300891 
##          416          417          418          419          420 
## -1246.300891 -1246.300891 -1140.300891 -1140.300891 -1140.300891 
##          421          422          423          424          425 
## -1140.300891 -1140.300891 -1140.300891 -1140.300891 -1140.300891 
##          426          427          428          429          430 
##  1149.648555  1149.648555   641.648555   641.648555  1056.648555 
##          431          432          433          434          435 
##  1056.648555  1056.648555   948.648555   948.648555   948.648555 
##          436          437          438          439          440 
##   948.648555  1562.648555  1562.648555  1149.648555  -366.869428 
##          441          442          443          444          445 
##  -514.869428  -514.869428  -481.869428  -481.869428  -481.869428 
##          446          447          448          449          450 
##  -481.869428  -366.869428  -428.869428  -607.869428  -607.869428 
##          451          452          453          454          455 
##  -607.869428  -428.869428  -460.869428  -447.869428  -361.869428 
##          456          457          458 
##  -361.869428  -215.869428  -342.869428
plot(fit)

## The above model is not suiting very appropropiately because residuals are quite significant but main significatnt variable from this model by p-values are PitchEconomy,PitchDiffernce and PercentPremiumSeats

Assuming Hypothesis 2

Hypothesis 2: “PricePremium” depends on PitchPremium,PitchDiffernce and PercentPremiumSeats only

Lets try to build a model with these variables

fit <-lm(PricePremium ~ PitchPremium  + PitchDifference + PercentPremiumSeats, data=airline)
summary(fit)
## 
## Call:
## lm(formula = PricePremium ~ PitchPremium + PitchDifference + 
##     PercentPremiumSeats, data = airline)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2075.3 -1005.8  -106.7   852.6  5981.5 
## 
## Coefficients:
##                      Estimate Std. Error t value Pr(>|t|)    
## (Intercept)         -41543.46    4746.87  -8.752  < 2e-16 ***
## PitchPremium          1280.67     141.20   9.070  < 2e-16 ***
## PitchDifference       -905.53     104.13  -8.696  < 2e-16 ***
## PercentPremiumSeats     61.42      11.95   5.142 4.06e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1181 on 454 degrees of freedom
## Multiple R-squared:  0.1649, Adjusted R-squared:  0.1594 
## F-statistic: 29.88 on 3 and 454 DF,  p-value: < 2.2e-16
residuals(fit)
##            1            2            3            4            5 
##  1425.304500  1425.304500  1425.304500  1425.304500   699.304500 
##            6            7            8            9           10 
##   699.304500   699.304500   697.304500   697.304500   689.304500 
##           11           12           13           14           15 
##   689.304500   689.304500   689.304500   356.304500   356.304500 
##           16           17           18           19           20 
##   356.304500   204.304500   204.304500   204.304500  -104.695500 
##           21           22           23           24           25 
##  -104.695500  -104.695500  -108.695500  -108.695500  -108.695500 
##           26           27           28           29           30 
##  -215.695500  -215.695500  -215.695500  -479.695500  -479.695500 
##           31           32           33           34           35 
##  -479.695500  -535.695500  -535.695500  -535.695500  -535.695500 
##           36           37           38           39           40 
##  -751.695500  -751.695500  -751.695500  -787.695500  -787.695500 
##           41           42           43           44           45 
##  -787.695500  -787.695500  -982.695500  -982.695500  -982.695500 
##           46           47           48           49           50 
## -1086.695500 -1086.695500 -1086.695500 -1526.695500 -1526.695500 
##           51           52           53           54           55 
## -1526.695500   771.007628   707.007628   707.007628   707.007628 
##           56           57           58           59           60 
##   -30.992372   -30.992372   -30.992372  -966.992372  -966.992372 
##           61           62           63           64           65 
## -1407.992372  1079.509328  1079.509328  1079.509328  1079.509328 
##           66           67           68           69           70 
##   807.509328   807.509328   807.509328   807.509328   360.509328 
##           71           72           73           74           75 
##   360.509328   360.509328 -1454.490672  -363.262633  -332.262633 
##           76           77           78           79           80 
##  -293.262633  -299.262633  -305.262633  -130.262633  -172.262633 
##           81           82           83           84           85 
##    59.737367  1048.363369  1048.363369  1048.363369  1048.363369 
##           86           87           88           89           90 
##   615.363369   615.363369   615.363369   614.363369 -1140.146805 
##           91           92           93           94           95 
## -1140.146805 -1140.146805 -1140.146805 -1048.146805 -1048.146805 
##           96           97           98           99          100 
## -1048.146805 -1048.146805  -702.185671  1836.346320  1836.346320 
##          101          102          103          104          105 
##  1836.346320  1836.346320  1809.346320  1809.346320  1809.346320 
##          106          107          108          109          110 
##  1809.346320   865.346320   865.346320   865.346320   -92.653680 
##          111          112          113          114          115 
##   -92.653680   -92.653680 -1240.653680 -1284.653680 -1284.653680 
##          116          117          118          119          120 
## -1319.653680 -1330.653680 -1330.653680 -1378.653680 -1403.653680 
##          121          122          123          124          125 
## -1407.653680 -1407.653680 -1420.653680 -1441.653680 -1448.653680 
##          126          127          128          129          130 
## -1450.653680 -1463.653680 -1479.653680 -1488.653680 -1489.653680 
##          131          132          133          134          135 
## -1489.653680 -1492.653680 -1515.653680 -1525.653680 -1528.653680 
##          136          137          138          139          140 
## -1551.653680 -1551.653680 -1554.653680 -1561.653680 -1570.653680 
##          141          142          143          144          145 
## -1570.653680 -1585.653680 -1585.653680 -1585.653680 -1595.653680 
##          146          147          148          149          150 
## -1601.653680 -1627.653680 -1627.653680 -1629.653680 -1606.928549 
##          151          152          153          154          155 
## -1640.653680 -1116.943489  -986.943489  -926.943489  -696.943489 
##          156          157          158          159          160 
##   -86.771127   -86.771127   -86.771127   -86.771127  1258.228873 
##          161          162          163          164          165 
##  1258.228873  1258.228873  1258.228873  1806.299836  1806.299836 
##          166          167          168          169          170 
##  1806.299836  1806.299836  1313.228873  1313.228873  1313.228873 
##          171          172          173          174          175 
##  1313.228873  1803.228873     4.228873  1991.299836  1991.299836 
##          176          177          178          179          180 
##  1991.299836  1991.299836  -240.771127  1834.228873   825.228873 
##          181          182          183          184          185 
##   825.228873   825.228873   825.228873     4.228873   943.648146 
##          186          187          188          189          190 
##   943.648146  1120.648146  1120.648146  1120.648146   943.648146 
##          191          192          193          194          195 
##  1337.648146  1337.648146  1337.648146  1337.648146  1352.648146 
##          196          197          198          199          200 
##  1352.648146  1352.648146  1352.648146  1864.648146  1864.648146 
##          201          202          203          204          205 
##  1864.648146  1895.648146  1895.648146   854.648146   854.648146 
##          206          207          208          209          210 
##   854.648146   854.648146   764.648146 -1050.351854 -1050.351854 
##          211          212          213          214          215 
## -1050.351854  -845.523726  -845.523726  -845.523726   402.476274 
##          216          217          218          219          220 
##   402.476274   402.476274   402.476274   402.476274   402.476274 
##          221          222          223          224          225 
##   402.476274   402.476274   350.476274   350.476274   350.476274 
##          226          227          228          229          230 
##   606.476274   606.476274   330.476274   330.476274   330.476274 
##          231          232          233          234          235 
##   465.476274   818.476274   818.476274   818.476274   818.476274 
##          236          237          238          239          240 
##   818.476274   818.476274   818.476274   818.476274  1933.437732 
##          241          242          243          244          245 
##  1933.437732  1933.437732  1651.437732  1651.437732  1651.437732 
##          246          247          248          249          250 
##  1624.437732  1624.437732  1624.437732  1624.437732  1523.437732 
##          251          252          253          254          255 
##  1523.437732  1523.437732  1449.437732  1449.437732  1449.437732 
##          256          257          258          259          260 
##  1449.437732   896.437732   896.437732   896.437732   847.437732 
##          261          262          263          264          265 
##   716.437732   716.437732   716.437732   702.437732   702.437732 
##          266          267          268          269          270 
##   702.437732   473.437732   290.437732   290.437732   290.437732 
##          271          272          273          274          275 
##   208.437732   208.437732   208.437732   208.437732    27.437732 
##          276          277          278          279          280 
##   -25.562268  -376.562268  -376.562268  -663.562268  -738.562268 
##          281          282          283          284          285 
##  -628.965349  -628.965349  -548.965349  -548.965349  -548.965349 
##          286          287          288          289          290 
##   367.869676   367.869676   367.869676  -498.965349  -498.965349 
##          291          292          293          294          295 
##  -576.965349   377.869676  -593.965349  -593.965349 -2075.288277 
##          296          297          298          299          300 
##  -808.131756  -635.131756 -1994.288277 -1994.288277  -285.965349 
##          301          302          303          304          305 
## -1878.288277  -681.131756  -681.131756  -647.965349 -1596.288277 
##          306          307          308          309          310 
##  -558.131756  -591.965349 -1615.523726 -1615.523726 -1615.523726 
##          311          312          313          314          315 
## -1667.523726 -1667.523726 -1528.523726 -1525.523726  -829.131410 
##          316          317          318          319          320 
## -1048.131410 -1048.131410 -1092.131410  -553.131410  -553.131410 
##          321          322          323          324          325 
##  -553.131410 -1144.131410 -1600.131410 -1600.131410  -916.131410 
##          326          327          328          329          330 
##  -916.131410  -916.131410 -1093.131410 -1093.131410 -1093.131410 
##          331          332          333          334          335 
## -1881.131410 -1881.131410 -1881.131410 -1881.131410  -936.131410 
##          336          337          338          339          340 
##  -936.131410  -936.131410  -936.131410  1528.988514  1528.988514 
##          341          342          343          344          345 
##  1528.988514   337.988514   619.988514   782.988514   782.988514 
##          346          347          348          349          350 
##   782.988514   723.988514   723.988514   723.988514  1080.988514 
##          351          352          353          354          355 
##  1080.988514  1080.988514  1080.988514   891.815598   891.815598 
##          356          357          358          359          360 
##   891.815598   891.815598  1145.988514  1145.988514  1145.988514 
##          361          362          363          364          365 
##  1268.815598  1268.815598   799.988514   799.988514   799.988514 
##          366          367          368          369          370 
##   799.988514  5981.544639  5981.544639  5981.544639  1037.544639 
##          371          372          373          374          375 
##  1037.544639  1037.544639  -280.455361  -579.455361  -579.455361 
##          376          377          378          379          380 
##  -606.455361  -635.455361  -635.455361  -847.025958  -847.025958 
##          381          382          383          384          385 
##  -847.025958  -932.025958  -932.025958  -810.025958  -796.025958 
##          386          387          388          389          390 
## -1012.025958 -1063.025958 -1063.025958 -1063.025958 -1102.025958 
##          391          392          393          394          395 
## -1102.025958 -1102.025958  -710.025958  -847.025958 -1012.025958 
##          396          397          398          399          400 
## -1012.025958  -710.025958 -1063.025958 -1102.025958 -1063.025958 
##          401          402          403          404          405 
## -1063.025958 -1063.025958 -1063.025958  -847.025958  -634.025958 
##          406          407          408          409          410 
##  -592.975543  -592.975543  -592.975543  -592.975543 -1284.234917 
##          411          412          413          414          415 
## -1284.234917 -1284.234917 -1284.234917 -1284.234917 -1284.234917 
##          416          417          418          419          420 
## -1284.234917 -1284.234917 -1178.234917 -1178.234917 -1178.234917 
##          421          422          423          424          425 
## -1178.234917 -1178.234917 -1178.234917 -1178.234917 -1178.234917 
##          426          427          428          429          430 
##  1053.585658  1053.585658   545.585658   545.585658   960.585658 
##          431          432          433          434          435 
##   960.585658   960.585658   852.585658   852.585658   852.585658 
##          436          437          438          439          440 
##   852.585658  1466.585658  1466.585658  1053.585658  -372.288442 
##          441          442          443          444          445 
##  -520.288442  -520.288442  -487.288442  -487.288442  -487.288442 
##          446          447          448          449          450 
##  -487.288442  -372.288442  -434.288442  -613.288442  -613.288442 
##          451          452          453          454          455 
##  -613.288442  -434.288442  -466.288442  -453.288442  -367.288442 
##          456          457          458 
##  -367.288442  -221.288442  -348.288442
plot(fit)

The value of residuals have decreased in magnitudes but still residuals are quite significant, so model is still not that correct.

PricePremium highly depends on PitchPremium,PitchDifference and PercentPremiumSeats

Best hyspothesis which can be founded “PricePremium” = -41543.46 + 1280.67(PitchPremium) -905.53(PitchDifference) + 61.42(PercentPremiumSeats)

Hypothesis 3: “PriceRelative”" depends on PitchPremium,WidthPremium,PitchDiffernce,WidthDifference and PercentPremiumSeats

Trying to model PriceRelative as a function of PitchPremium, WidthPremium, PitchDifference and PercentPremiumSeats

fit <-lm(PriceRelative ~ PitchPremium + WidthPremium + PitchDifference+WidthDifference+PercentPremiumSeats, data=airline)
summary(fit)
## 
## Call:
## lm(formula = PriceRelative ~ PitchPremium + WidthPremium + PitchDifference + 
##     WidthDifference + PercentPremiumSeats, data = airline)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.90154 -0.26666 -0.08043  0.17473  1.33169 
## 
## Coefficients:
##                      Estimate Std. Error t value Pr(>|t|)    
## (Intercept)          3.370057   1.553415   2.169 0.030569 *  
## PitchPremium        -0.189787   0.049522  -3.832 0.000145 ***
## WidthPremium         0.169372   0.038752   4.371 1.54e-05 ***
## PitchDifference      0.187854   0.039445   4.762 2.58e-06 ***
## WidthDifference     -0.032875   0.037840  -0.869 0.385415    
## PercentPremiumSeats -0.012929   0.004201  -3.077 0.002215 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3787 on 452 degrees of freedom
## Multiple R-squared:  0.3015, Adjusted R-squared:  0.2937 
## F-statistic: 39.01 on 5 and 452 DF,  p-value: < 2.2e-16
residuals(fit)
##             1             2             3             4             5 
##  0.0408900964  0.0408900964  0.0408900964  0.0408900964  0.3308900964 
##             6             7             8             9            10 
##  0.3308900964  0.3308900964  0.6908900964  0.6908900964  0.4108900964 
##            11            12            13            14            15 
##  0.4108900964  0.2208900964 -0.0791099036  0.1808900964  0.1808900964 
##            16            17            18            19            20 
##  0.1808900964  0.0408900964  0.0408900964  0.0408900964  0.0008900964 
##            21            22            23            24            25 
##  0.0008900964  0.0008900964 -0.0091099036 -0.0091099036 -0.0091099036 
##            26            27            28            29            30 
##  0.0108900964 -0.0091099036 -0.0091099036  0.0008900964  0.0008900964 
##            31            32            33            34            35 
##  0.0008900964  0.0808900964  0.0808900964  0.0808900964  0.0808900964 
##            36            37            38            39            40 
##  0.3108900964  0.3108900964  0.3108900964 -0.0991099036 -0.0991099036 
##            41            42            43            44            45 
## -0.0991099036 -0.0991099036 -0.1691099036 -0.1691099036 -0.1691099036 
##            46            47            48            49            50 
## -0.2591099036 -0.2591099036 -0.2591099036  0.1808900964  0.1808900964 
##            51            52            53            54            55 
##  0.1808900964  0.6753751600  0.0053751600  0.0053751600  0.0053751600 
##            56            57            58            59            60 
## -0.0146248400 -0.0146248400 -0.0146248400 -0.1446248400 -0.1446248400 
##            61            62            63            64            65 
##  0.2553751600  0.0650160504  0.0650160504  0.0650160504  0.0650160504 
##            66            67            68            69            70 
## -0.2749839496 -0.2749839496 -0.2749839496 -0.2749839496 -0.4049839496 
##            71            72            73            74            75 
## -0.4049839496 -0.4049839496 -0.5649839496 -0.1756818489 -0.1856818489 
##            76            77            78            79            80 
## -0.1956818489 -0.1956818489 -0.1956818489 -0.2256818489 -0.2256818489 
##            81            82            83            84            85 
## -0.2356818489  0.6538325789  0.6538325789  0.6538325789  0.6538325789 
##            86            87            88            89            90 
## -0.0161674211 -0.0161674211 -0.0161674211 -0.0161674211 -0.3843218602 
##            91            92            93            94            95 
## -0.3843218602 -0.3843218602 -0.3843218602 -0.5343218602 -0.5343218602 
##            96            97            98            99           100 
## -0.5343218602 -0.6043218602  0.1304743341  0.0302614659  0.0302614659 
##           101           102           103           104           105 
##  0.0302614659  0.0302614659  0.4502614659  0.4502614659  0.4502614659 
##           106           107           108           109           110 
##  0.4502614659  0.0102614659  0.0102614659  0.0102614659  0.8102614659 
##           111           112           113           114           115 
##  0.8102614659 -0.0997385341 -0.3997385341 -0.3597385341 -0.3597385341 
##           116           117           118           119           120 
## -0.4197385341 -0.3497385341 -0.3497385341 -0.3797385341 -0.3697385341 
##           121           122           123           124           125 
## -0.4097385341 -0.4097385341 -0.3497385341 -0.3197385341 -0.2897385341 
##           126           127           128           129           130 
## -0.2997385341 -0.3097385341 -0.3897385341 -0.2897385341 -0.2797385341 
##           131           132           133           134           135 
## -0.3197385341 -0.3297385341 -0.2997385341 -0.2797385341 -0.2797385341 
##           136           137           138           139           140 
## -0.2097385341 -0.2597385341 -0.1997385341 -0.2697385341 -0.2297385341 
##           141           142           143           144           145 
## -0.2297385341 -0.1597385341 -0.1597385341 -0.1597385341 -0.2097385341 
##           146           147           148           149           150 
## -0.1697385341 -0.1697385341 -0.1697385341 -0.0597385341 -0.1545223062 
##           151           152           153           154           155 
## -0.1297385341 -0.0223059919 -0.0523059919 -0.0623059919 -0.0923059919 
##           156           157           158           159           160 
##  1.0828715961  1.0828715961  1.0828715961  1.0828715961  0.9928715961 
##           161           162           163           164           165 
##  0.9928715961  0.9928715961  0.6428715961  0.2322251405  0.2322251405 
##           166           167           168           169           170 
##  0.2322251405  0.2322251405  0.1728715961  0.1728715961  0.1728715961 
##           171           172           173           174           175 
##  0.1728715961  0.1028715961 -0.1771284039 -0.2277748595 -0.2277748595 
##           176           177           178           179           180 
## -0.2277748595 -0.2277748595 -0.2371284039 -0.2471284039 -0.3371284039 
##           181           182           183           184           185 
## -0.3371284039 -0.3371284039 -0.3371284039 -0.4771284039 -0.2900575175 
##           186           187           188           189           190 
## -0.2900575175 -0.3700575175 -0.3700575175 -0.3700575175 -0.4500575175 
##           191           192           193           194           195 
##  0.3299424825  0.3299424825  0.3299424825  0.3299424825  0.2799424825 
##           196           197           198           199           200 
##  0.2799424825  0.2799424825  0.2799424825  0.0899424825  0.0899424825 
##           201           202           203           204           205 
##  0.0899424825 -0.2600575175 -0.2600575175 -0.3400575175 -0.3400575175 
##           206           207           208           209           210 
## -0.3400575175 -0.3400575175 -0.4900575175 -0.6500575175 -0.6500575175 
##           211           212           213           214           215 
## -0.6500575175  1.2511380384  0.8611380384  0.3211380384 -0.2288619616 
##           216           217           218           219           220 
## -0.2288619616 -0.2288619616 -0.2288619616 -0.2288619616 -0.2288619616 
##           221           222           223           224           225 
## -0.2288619616 -0.2288619616 -0.2288619616 -0.2288619616 -0.2288619616 
##           226           227           228           229           230 
## -0.2388619616 -0.2388619616 -0.2388619616 -0.2388619616 -0.2388619616 
##           231           232           233           234           235 
## -0.2688619616 -0.2788619616 -0.2788619616 -0.2788619616 -0.2788619616 
##           236           237           238           239           240 
## -0.2788619616 -0.2788619616 -0.2788619616 -0.2788619616  0.6384558462 
##           241           242           243           244           245 
##  0.6384558462 -0.2315441538 -0.0415441538 -0.0415441538 -0.0415441538 
##           246           247           248           249           250 
## -0.1315441538 -0.1315441538 -0.1315441538 -0.1315441538  0.4884558462 
##           251           252           253           254           255 
##  0.4884558462  0.4884558462 -0.1615441538 -0.1615441538 -0.1615441538 
##           256           257           258           259           260 
## -0.1615441538 -0.1315441538 -0.1315441538 -0.1315441538  0.6384558462 
##           261           262           263           264           265 
## -0.0715441538 -0.0715441538 -0.0715441538 -0.0915441538 -0.0915441538 
##           266           267           268           269           270 
## -0.0915441538  0.3084558462 -0.4215441538 -0.4215441538 -0.4215441538 
##           271           272           273           274           275 
##  0.6184558462  0.6184558462  0.4184558462 -0.2915441538  0.3084558462 
##           276           277           278           279           280 
## -0.3215441538 -0.3215441538 -0.3215441538 -0.2815441538  0.0784558462 
##           281           282           283           284           285 
##  0.1292750440  0.1292750440  0.1092750440  0.1092750440  0.1092750440 
##           286           287           288           289           290 
## -0.0804334520 -0.0804334520 -0.0804334520  0.0992750440  0.0992750440 
##           291           292           293           294           295 
##  0.0992750440 -0.0904334520  0.0892750440  0.0892750440  0.2731992791 
##           296           297           298           299           300 
##  0.0862567654  0.0762567654  0.2631992791  0.2631992791  0.0592750440 
##           301           302           303           304           305 
##  0.2531992791  0.0462567654  0.0462567654  0.0392750440  0.2231992791 
##           306           307           308           309           310 
##  0.0362567654  0.0292750440  1.1911380384  0.6511380384  0.5111380384 
##           311           312           313           314           315 
##  0.1111380384  0.1111380384  0.0911380384  0.0711380384  0.6409453647 
##           316           317           318           319           320 
##  0.3609453647  0.3609453647  0.3009453647  0.1309453647  0.1309453647 
##           321           322           323           324           325 
##  0.1309453647  0.0809453647  0.0109453647  0.0109453647 -0.3390546353 
##           326           327           328           329           330 
## -0.3390546353 -0.3390546353 -0.3390546353 -0.3390546353 -0.3390546353 
##           331           332           333           334           335 
## -0.3690546353 -0.3690546353 -0.3690546353 -0.3690546353 -0.3790546353 
##           336           337           338           339           340 
## -0.3790546353 -0.3790546353 -0.3790546353  0.0811689922  0.0811689922 
##           341           342           343           344           345 
##  0.0811689922 -0.1988310078 -0.2088310078 -0.2088310078 -0.2088310078 
##           346           347           348           349           350 
## -0.2088310078 -0.2388310078 -0.2388310078 -0.2388310078 -0.2488310078 
##           351           352           353           354           355 
## -0.2488310078 -0.2488310078 -0.2488310078 -0.2508996660 -0.2508996660 
##           356           357           358           359           360 
## -0.2508996660 -0.2508996660 -0.2488310078 -0.2488310078 -0.2488310078 
##           361           362           363           364           365 
## -0.2508996660 -0.2508996660 -0.2488310078 -0.2488310078 -0.2488310078 
##           366           367           368           369           370 
## -0.2488310078  0.8683310114  0.8683310114  0.8683310114 -0.3816689886 
##           371           372           373           374           375 
## -0.3816689886 -0.3816689886  0.2483310114 -0.0416689886 -0.0416689886 
##           376           377           378           379           380 
## -0.4816689886 -0.0016689886 -0.1516689886  0.9553437614  0.9553437614 
##           381           382           383           384           385 
##  0.9553437614  0.9353437614  0.7353437614  0.7053437614  0.5953437614 
##           386           387           388           389           390 
##  0.3553437614  0.3253437614  0.3253437614  0.3253437614  0.1753437614 
##           391           392           393           394           395 
##  0.1753437614  0.1753437614  0.1553437614  0.1253437614  0.1053437614 
##           396           397           398           399           400 
##  0.1053437614 -0.0246562386 -0.1246562386 -0.1446562386 -0.1946562386 
##           401           402           403           404           405 
## -0.1946562386 -0.1946562386 -0.1946562386 -0.4346562386 -0.7646562386 
##           406           407           408           409           410 
##  1.3316906131  1.3316906131  1.1316906131  0.2516906131  0.4763399226 
##           411           412           413           414           415 
##  0.4763399226  0.4763399226  0.4763399226  0.4763399226  0.4763399226 
##           416           417           418           419           420 
##  0.4763399226  0.4763399226  0.0963399226  0.0963399226  0.0963399226 
##           421           422           423           424           425 
##  0.0963399226  0.0963399226  0.0963399226  0.0963399226  0.0963399226 
##           426           427           428           429           430 
##  0.8045932292  0.8045932292 -0.2754067708 -0.2754067708 -0.2854067708 
##           431           432           433           434           435 
## -0.2854067708 -0.2854067708 -0.3154067708 -0.3154067708 -0.3154067708 
##           436           437           438           439           440 
## -0.3154067708 -0.3254067708 -0.3254067708 -0.3354067708  0.6884601175 
##           441           442           443           444           445 
##  0.6584601175  0.6584601175  0.2784601175  0.2784601175  0.2784601175 
##           446           447           448           449           450 
##  0.2784601175  0.1984601175  0.0484601175 -0.2515398825 -0.2515398825 
##           451           452           453           454           455 
## -0.2515398825 -0.3715398825 -0.4215398825 -0.4415398825 -0.5715398825 
##           456           457           458 
## -0.5715398825 -0.6415398825 -0.9015398825
plot(fit)

## Residuals are significant in this too but main significatnt variable from this model by p-values are PitchEconomy and WidthDiffernce

PitchPremium,WidthPremium and PrecentPremiumSeats are very significant from above correaltion.

A model of price relative with only above significant variables.

fit <-lm(PriceRelative ~ PitchPremium + WidthPremium + PitchDifference, data=airline)
summary(fit)
## 
## Call:
## lm(formula = PriceRelative ~ PitchPremium + WidthPremium + PitchDifference, 
##     data = airline)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.79298 -0.27258 -0.09128  0.15439  1.33742 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      1.70237    1.46917   1.159  0.24717    
## PitchPremium    -0.13686    0.04421  -3.096  0.00208 ** 
## WidthPremium     0.15466    0.02529   6.115 2.09e-09 ***
## PitchDifference  0.14370    0.03355   4.283 2.25e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3818 on 454 degrees of freedom
## Multiple R-squared:  0.2866, Adjusted R-squared:  0.2819 
## F-statistic:  60.8 on 3 and 454 DF,  p-value: < 2.2e-16
residuals(fit)
##             1             2             3             4             5 
## -0.0662804656 -0.0662804656 -0.0662804656 -0.0662804656  0.2237195344 
##             6             7             8             9            10 
##  0.2237195344  0.2237195344  0.5837195344  0.5837195344  0.3037195344 
##            11            12            13            14            15 
##  0.3037195344  0.1137195344 -0.1862804656  0.0737195344  0.0737195344 
##            16            17            18            19            20 
##  0.0737195344 -0.0662804656 -0.0662804656 -0.0662804656 -0.1062804656 
##            21            22            23            24            25 
## -0.1062804656 -0.1062804656 -0.1162804656 -0.1162804656 -0.1162804656 
##            26            27            28            29            30 
## -0.0962804656 -0.1162804656 -0.1162804656 -0.1062804656 -0.1062804656 
##            31            32            33            34            35 
## -0.1062804656 -0.0262804656 -0.0262804656 -0.0262804656 -0.0262804656 
##            36            37            38            39            40 
##  0.2037195344  0.2037195344  0.2037195344 -0.2062804656 -0.2062804656 
##            41            42            43            44            45 
## -0.2062804656 -0.2062804656 -0.2762804656 -0.2762804656 -0.2762804656 
##            46            47            48            49            50 
## -0.3662804656 -0.3662804656 -0.3662804656  0.0737195344  0.0737195344 
##            51            52            53            54            55 
##  0.0737195344  0.5837195344 -0.0862804656 -0.0862804656 -0.0862804656 
##            56            57            58            59            60 
## -0.1062804656 -0.1062804656 -0.1062804656 -0.2362804656 -0.2362804656 
##            61            62            63            64            65 
##  0.1637195344 -0.0256079909 -0.0256079909 -0.0256079909 -0.0256079909 
##            66            67            68            69            70 
## -0.3656079909 -0.3656079909 -0.3656079909 -0.3656079909 -0.4956079909 
##            71            72            73            74            75 
## -0.4956079909 -0.4956079909 -0.6556079909 -0.1742579619 -0.1842579619 
##            76            77            78            79            80 
## -0.1942579619 -0.1942579619 -0.1942579619 -0.2242579619 -0.2242579619 
##            81            82            83            84            85 
## -0.2342579619  0.6237195344  0.6237195344  0.6237195344  0.6237195344 
##            86            87            88            89            90 
## -0.0462804656 -0.0462804656 -0.0462804656 -0.0462804656 -0.4329845566 
##            91            92            93            94            95 
## -0.4329845566 -0.4329845566 -0.4329845566 -0.5829845566 -0.5829845566 
##            96            97            98            99           100 
## -0.5829845566 -0.6529845566  0.1241029959  0.0437195344  0.0437195344 
##           101           102           103           104           105 
##  0.0437195344  0.0437195344  0.4637195344  0.4637195344  0.4637195344 
##           106           107           108           109           110 
##  0.4637195344  0.0237195344  0.0237195344  0.0237195344  0.8237195344 
##           111           112           113           114           115 
##  0.8237195344 -0.0862804656 -0.3862804656 -0.3462804656 -0.3462804656 
##           116           117           118           119           120 
## -0.4062804656 -0.3362804656 -0.3362804656 -0.3662804656 -0.3562804656 
##           121           122           123           124           125 
## -0.3962804656 -0.3962804656 -0.3362804656 -0.3062804656 -0.2762804656 
##           126           127           128           129           130 
## -0.2862804656 -0.2962804656 -0.3762804656 -0.2762804656 -0.2662804656 
##           131           132           133           134           135 
## -0.3062804656 -0.3162804656 -0.2862804656 -0.2662804656 -0.2662804656 
##           136           137           138           139           140 
## -0.1962804656 -0.2462804656 -0.1862804656 -0.2562804656 -0.2162804656 
##           141           142           143           144           145 
## -0.2162804656 -0.1462804656 -0.1462804656 -0.1462804656 -0.1962804656 
##           146           147           148           149           150 
## -0.1562804656 -0.1562804656 -0.1562804656 -0.0462804656 -0.1362804656 
##           151           152           153           154           155 
## -0.1162804656  0.0025995480 -0.0274004520 -0.0374004520 -0.0674004520 
##           156           157           158           159           160 
##  1.0643920091  1.0643920091  1.0643920091  1.0643920091  0.9743920091 
##           161           162           163           164           165 
##  0.9743920091  0.9743920091  0.6243920091  0.2143920091  0.2143920091 
##           166           167           168           169           170 
##  0.2143920091  0.2143920091  0.1543920091  0.1543920091  0.1543920091 
##           171           172           173           174           175 
##  0.1543920091  0.0843920091 -0.1956079909 -0.2456079909 -0.2456079909 
##           176           177           178           179           180 
## -0.2456079909 -0.2456079909 -0.2556079909 -0.2656079909 -0.3556079909 
##           181           182           183           184           185 
## -0.3556079909 -0.3556079909 -0.3556079909 -0.4956079909 -0.2956079909 
##           186           187           188           189           190 
## -0.2956079909 -0.3756079909 -0.3756079909 -0.3756079909 -0.4556079909 
##           191           192           193           194           195 
##  0.3243920091  0.3243920091  0.3243920091  0.3243920091  0.2743920091 
##           196           197           198           199           200 
##  0.2743920091  0.2743920091  0.2743920091  0.0843920091  0.0843920091 
##           201           202           203           204           205 
##  0.0843920091 -0.2656079909 -0.2656079909 -0.3456079909 -0.3456079909 
##           206           207           208           209           210 
## -0.3456079909 -0.3456079909 -0.4956079909 -0.6556079909 -0.6556079909 
##           211           212           213           214           215 
## -0.6556079909  1.2574167295  0.8674167295  0.3274167295 -0.2225832705 
##           216           217           218           219           220 
## -0.2225832705 -0.2225832705 -0.2225832705 -0.2225832705 -0.2225832705 
##           221           222           223           224           225 
## -0.2225832705 -0.2225832705 -0.2225832705 -0.2225832705 -0.2225832705 
##           226           227           228           229           230 
## -0.2325832705 -0.2325832705 -0.2325832705 -0.2325832705 -0.2325832705 
##           231           232           233           234           235 
## -0.2625832705 -0.2725832705 -0.2725832705 -0.2725832705 -0.2725832705 
##           236           237           238           239           240 
## -0.2725832705 -0.2725832705 -0.2725832705 -0.2725832705  0.6837195344 
##           241           242           243           244           245 
##  0.6837195344 -0.1862804656  0.0037195344  0.0037195344  0.0037195344 
##           246           247           248           249           250 
## -0.0862804656 -0.0862804656 -0.0862804656 -0.0862804656  0.5337195344 
##           251           252           253           254           255 
##  0.5337195344  0.5337195344 -0.1162804656 -0.1162804656 -0.1162804656 
##           256           257           258           259           260 
## -0.1162804656 -0.0862804656 -0.0862804656 -0.0862804656  0.6837195344 
##           261           262           263           264           265 
## -0.0262804656 -0.0262804656 -0.0262804656 -0.0462804656 -0.0462804656 
##           266           267           268           269           270 
## -0.0462804656  0.3537195344 -0.3762804656 -0.3762804656 -0.3762804656 
##           271           272           273           274           275 
##  0.6637195344  0.6637195344  0.4637195344 -0.2462804656  0.3537195344 
##           276           277           278           279           280 
## -0.2762804656 -0.2762804656 -0.2762804656 -0.2362804656  0.1237195344 
##           281           282           283           284           285 
##  0.1741029959  0.1741029959  0.1541029959  0.1541029959  0.1541029959 
##           286           287           288           289           290 
##  0.0004058007  0.0004058007  0.0004058007  0.1441029959  0.1441029959 
##           291           292           293           294           295 
##  0.1441029959 -0.0095941993  0.1341029959  0.1341029959  0.2609605058 
##           296           297           298           299           300 
##  0.1241029959  0.1141029959  0.2509605058  0.2509605058  0.1041029959 
##           301           302           303           304           305 
##  0.2409605058  0.0841029959  0.0841029959  0.0841029959  0.2109605058 
##           306           307           308           309           310 
##  0.0741029959  0.0741029959  1.1974167295  0.6574167295  0.5174167295 
##           311           312           313           314           315 
##  0.1174167295  0.1174167295  0.0974167295  0.0774167295  0.6527529669 
##           316           317           318           319           320 
##  0.3727529669  0.3727529669  0.3127529669  0.1427529669  0.1427529669 
##           321           322           323           324           325 
##  0.1427529669  0.0927529669  0.0227529669  0.0227529669 -0.3272470331 
##           326           327           328           329           330 
## -0.3272470331 -0.3272470331 -0.3272470331 -0.3272470331 -0.3272470331 
##           331           332           333           334           335 
## -0.3572470331 -0.3572470331 -0.3572470331 -0.3572470331 -0.3672470331 
##           336           337           338           339           340 
## -0.3672470331 -0.3672470331 -0.3672470331  0.0574167295  0.0574167295 
##           341           342           343           344           345 
##  0.0574167295 -0.2225832705 -0.2325832705 -0.2325832705 -0.2325832705 
##           346           347           348           349           350 
## -0.2325832705 -0.2625832705 -0.2625832705 -0.2625832705 -0.2725832705 
##           351           352           353           354           355 
## -0.2725832705 -0.2725832705 -0.2725832705 -0.2725832705 -0.2725832705 
##           356           357           358           359           360 
## -0.2725832705 -0.2725832705 -0.2725832705 -0.2725832705 -0.2725832705 
##           361           362           363           364           365 
## -0.2725832705 -0.2725832705 -0.2725832705 -0.2725832705 -0.2725832705 
##           366           367           368           369           370 
## -0.2725832705  0.9437195344  0.9437195344  0.9437195344 -0.3062804656 
##           371           372           373           374           375 
## -0.3062804656 -0.3062804656  0.3237195344  0.0337195344  0.0337195344 
##           376           377           378           379           380 
## -0.4062804656  0.0737195344 -0.0762804656  0.9770154434  0.9770154434 
##           381           382           383           384           385 
##  0.9770154434  0.9570154434  0.7570154434  0.7270154434  0.6170154434 
##           386           387           388           389           390 
##  0.3770154434  0.3470154434  0.3470154434  0.3470154434  0.1970154434 
##           391           392           393           394           395 
##  0.1970154434  0.1970154434  0.1770154434  0.1470154434  0.1270154434 
##           396           397           398           399           400 
##  0.1270154434 -0.0029845566 -0.1029845566 -0.1229845566 -0.1729845566 
##           401           402           403           404           405 
## -0.1729845566 -0.1729845566 -0.1729845566 -0.4129845566 -0.7429845566 
##           406           407           408           409           410 
##  1.3374167295  1.3374167295  1.1374167295  0.2574167295  0.5327529669 
##           411           412           413           414           415 
##  0.5327529669  0.5327529669  0.5327529669  0.5327529669  0.5327529669 
##           416           417           418           419           420 
##  0.5327529669  0.5327529669  0.1527529669  0.1527529669  0.1527529669 
##           421           422           423           424           425 
##  0.1527529669  0.1527529669  0.1527529669  0.1527529669  0.1527529669 
##           426           427           428           429           430 
##  0.8574167295  0.8574167295 -0.2225832705 -0.2225832705 -0.2325832705 
##           431           432           433           434           435 
## -0.2325832705 -0.2325832705 -0.2625832705 -0.2625832705 -0.2625832705 
##           436           437           438           439           440 
## -0.2625832705 -0.2725832705 -0.2725832705 -0.2825832705  0.7970154434 
##           441           442           443           444           445 
##  0.7670154434  0.7670154434  0.3870154434  0.3870154434  0.3870154434 
##           446           447           448           449           450 
##  0.3870154434  0.3070154434  0.1570154434 -0.1429845566 -0.1429845566 
##           451           452           453           454           455 
## -0.1429845566 -0.2629845566 -0.3129845566 -0.3329845566 -0.4629845566 
##           456           457           458 
## -0.4629845566 -0.5329845566 -0.7929845566
plot(fit)

## The value of residuals have decreased in magnitudes but still residuals are quite significant so model cant be relied much but this is the best we could find

So PriceRelative higly depends on PitchPremium, WidthPremium and PitchDifference

PriceRelative = 1.70237 -0.13686(PitchPremium) + 0.15466(WidthPremium) + 0.14370(PitchDiffernce)