AirlinesProject
Deepank Varshney
December 22, 2017
SYNOPSIS- Amalysing the factors on which the difference between cost of premium and economy seats in airlines exist.
Reading data into R
setwd("~/winter internship")
airl <- read.csv(paste("SixAirlinesDataV2.csv",sep=""))
View(airl)Summary Statistcis
library(psych)
describe(airl)## 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 0.23hist(airl$PriceRelative,
main="Distribution of Relative price of premium seats wrt to economy seats",
xlab = "Relative price of premium seats wrt to economy seats",ylab = "count",breaks = 15,col="darkred")
This suggest that the difference between price of premium seats and economy seats for most of the flights is not very high,though is quite significant
hist(airl$PercentPremiumSeats,
main="Distribution ofPercentage of premium seats ",
xlab = "Percentage of premium seats",ylab = "count",breaks = 15,col="green")
This gives us a fair idea that approx 10-16% of total seats are permium seats and rest are economy seats in general
aggregate(airl$PriceEconomy,by=list(airl$Aircraft),mean)## Group.1 x
## 1 AirBus 1369.954
## 2 Boeing 1305.987The mean price of economy seats is higher of Airbus manufacterer than Boeing
aggregate(airl$PricePremium,by=list(airl$Aircraft),mean)## Group.1 x
## 1 AirBus 1869.503
## 2 Boeing 1833.332The mean price of premium seats is higher of Airbus manufacterer than Boeing
aggregate(airl$PriceRelative,by=list(airl$Aircraft),mean)## Group.1 x
## 1 AirBus 0.4147682
## 2 Boeing 0.5228339Though,The mean price of premium seats is higher of Airbus manufacterer than Boeing,the relative price(or difference in price of premium and economy) of Boeing is higher than Airbus
t.test(airl$PriceRelative~ airl$Aircraft)##
## Welch Two Sample t-test
##
## data: airl$PriceRelative by airl$Aircraft
## t = -2.6145, df = 363.72, p-value = 0.009306
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.18934647 -0.02678486
## sample estimates:
## mean in group AirBus mean in group Boeing
## 0.4147682 0.5228339Since o-value is less than 0.05, therefore,The relatice price bw economy and premium depends on the manufacturer,where boeing manufacter has hifger price difference
boxplot(airl$PriceRelative ~ airl$WidthDifference, horizontal=TRUE,
xlab="Price of economy seats",ylab="width" ,las=1,
main="Relative price at different widths")
library(lattice)
barchart(WidthDifference ~ PriceRelative,data = airl,col="orange")
Therefore,width is directly related to relative price
boxplot(airl$PriceRelative ~ airl$PitchDifference, horizontal=TRUE,
xlab="Price of premium seats",ylab="pitch/leg space", las=1,
main="Relative price at different leg spaces provided")
library(lattice)
barchart(PitchDifference ~ PriceRelative,data = airl,col="pink")
Therefore,leg space is directly related to relative price
aggregate(airl$PriceRelative,by=list(airl$IsInternational),mean)## Group.1 x
## 1 Domestic 0.0847500
## 2 International 0.5257177boxplot(airl$PriceRelative ~ airl$IsInternational, horizontal=TRUE,
xlab="Relative Price of seats", las=1,
main="Relative price of premium and economy seats in domestic and international flights")
t.test(airl$PriceRelative~ airl$IsInternational)##
## Welch Two Sample t-test
##
## data: airl$PriceRelative by airl$IsInternational
## t = -19.451, df = 446.12, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.4855215 -0.3964139
## sample estimates:
## mean in group Domestic mean in group International
## 0.0847500 0.5257177It can be clearly seen that the relative price of premium and economy seats is higher in international flights than domestic flights
boxplot(airl$PriceRelative ~ airl$Airline, horizontal=TRUE,
xlab="Relative Price of seats", las=1,
main="Relative price of premium and economy seats in different airlines")
aggregate(airl$PriceRelative,by=list(airl$Airline),mean)## Group.1 x
## 1 AirFrance 0.2047297
## 2 British 0.4375429
## 3 Delta 0.1250000
## 4 Jet 0.9396721
## 5 Singapore 0.5297500
## 6 Virgin 0.7606452It can be seen that Virgin airline, jet airline and singapore airline have higher relative prices than the rest
boxplot(airl$PriceRelative ~ airl$TravelMonth, horizontal=TRUE,
xlab="Relative Price of seats", las=1,
main="Relative price of premium and economy seats in different months")
aggregate(airl$PriceRelative,by=list(airl$TravelMonth),mean)## Group.1 x
## 1 Aug 0.4766142
## 2 Jul 0.4986667
## 3 Oct 0.5207874
## 4 Sep 0.4579070It can be seen that the relative price is nearly same irrespective of the month and thus, doesn’t depend on it
library(car)##
## Attaching package: 'car'## The following object is masked from 'package:psych':
##
## logitscatterplot(airl$FlightDuration, airl$PriceRelative, main = "scatterplot- Relative Price vs Flight Duration", pch=16)
library(car)
scatterplot(airl$PercentPremiumSeats, airl$PriceRelative, main = "scatterplot- Relative Price vs Percent Premium Flight", pch=16)
attach(airl)
cor(airl[,c(16,17,18,14,3)])## PitchDifference WidthDifference PercentPremiumSeats
## PitchDifference 1.00000000 0.7608911 -0.09264869
## WidthDifference 0.76089108 1.0000000 -0.27559416
## PercentPremiumSeats -0.09264869 -0.2755942 1.00000000
## PriceRelative 0.46873025 0.4858024 -0.16156556
## FlightDuration -0.03749288 -0.1185607 0.06051625
## PriceRelative FlightDuration
## PitchDifference 0.4687302 -0.03749288
## WidthDifference 0.4858024 -0.11856070
## PercentPremiumSeats -0.1615656 0.06051625
## PriceRelative 1.0000000 0.12107501
## FlightDuration 0.1210750 1.00000000library(corrgram)
corrgram(airl,order=TRUE,lower.panel = panel.shade,upper.panel = panel.pie,text.panel = panel.txt)
Tests
cor.test(airl$PriceRelative,airl$PitchDifference)##
## Pearson's product-moment correlation
##
## data: airl$PriceRelative and airl$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
## 0.4687302Variables are correlated
cor.test(airl$PriceRelative,airl$WidthDifference)##
## Pearson's product-moment correlation
##
## data: airl$PriceRelative and airl$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
## 0.4858024Variables are correlated
cor.test(airl$PriceRelative,airl$PercentPremiumSeats)##
## Pearson's product-moment correlation
##
## data: airl$PriceRelative and airl$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
## -0.1615656Variables are negatively correlated
cor.test(airl$PriceRelative,airl$PriceEconomy)##
## Pearson's product-moment correlation
##
## data: airl$PriceRelative and airl$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
## -0.2885671Variables are negatively correlated
cor.test(airl$PriceRelative,airl$PricePremium)##
## Pearson's product-moment correlation
##
## data: airl$PriceRelative and airl$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
## 0.03184654Variables are not correlated
cor.test(airl$PriceRelative,airl$FlightDuration)##
## Pearson's product-moment correlation
##
## data: airl$PriceRelative and airl$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
## 0.121075Variables are weakly correlated
Regression
model1 <- lm(PriceRelative ~ WidthDifference + PitchDifference + FlightDuration + PercentPremiumSeats + PriceEconomy , data = airl)
summary(model1)##
## Call:
## lm(formula = PriceRelative ~ WidthDifference + PitchDifference +
## FlightDuration + PercentPremiumSeats + PriceEconomy, data = airl)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.78376 -0.19987 -0.03123 0.11576 1.00628
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -8.085e-02 8.938e-02 -0.904 0.36622
## WidthDifference 1.418e-01 2.163e-02 6.559 1.48e-10 ***
## PitchDifference 3.778e-02 1.408e-02 2.683 0.00756 **
## FlightDuration 5.793e-02 5.426e-03 10.676 < 2e-16 ***
## PercentPremiumSeats -3.699e-03 3.424e-03 -1.080 0.28060
## PriceEconomy -2.269e-04 1.937e-05 -11.714 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3341 on 452 degrees of freedom
## Multiple R-squared: 0.4563, Adjusted R-squared: 0.4503
## F-statistic: 75.87 on 5 and 452 DF, p-value: < 2.2e-16Since p value is less than 0.05 for the f statistic,therefore we reject the null hypothesis.Also R square is 45% which is a decent value.
Statistically significant factors(p<0.05) are 1. width difference 2. Pitch Difference 3.Flight Duration 4. PriceEconomy
Statistically Insignificant factors(p<0.05) from the model are 1.Percent Premium seats
Other factors affecting the difference in pricing of premium and economy seats are- 1.IsInternational 2.Aircraft 3.Airline
model1$coefficients## (Intercept) WidthDifference PitchDifference
## -0.0808471384 0.1418456387 0.0377823295
## FlightDuration PercentPremiumSeats PriceEconomy
## 0.0579340072 -0.0036987340 -0.0002269145confint(model1)## 2.5 % 97.5 %
## (Intercept) -0.2565086589 0.0948143820
## WidthDifference 0.0993460728 0.1843452046
## PitchDifference 0.0101105418 0.0654541172
## FlightDuration 0.0472700550 0.0685979594
## PercentPremiumSeats -0.0104274603 0.0030299922
## PriceEconomy -0.0002649847 -0.0001888443library(coefplot)## Loading required package: ggplot2##
## Attaching package: 'ggplot2'## The following objects are masked from 'package:psych':
##
## %+%, alphacoefplot(model1,predictors=c("WidthDifference","PitchDifference","FlightDuration","PercentPremiumSeats","PriceEconomy"))## Warning: Ignoring unknown aesthetics: xmin, xmax
This shows that B coefficient of width difference in the model is the highest and Price Economy the lowest.However even an increase of 100 units in price changes the relative price by 2%.
airl$PriceRelative## [1] 0.38 0.38 0.38 0.38 0.67 0.67 0.67 1.03 1.03 0.75 0.75 0.56 0.26 0.52
## [15] 0.52 0.52 0.38 0.38 0.38 0.34 0.34 0.34 0.33 0.33 0.33 0.35 0.33 0.33
## [29] 0.34 0.34 0.34 0.42 0.42 0.42 0.42 0.65 0.65 0.65 0.24 0.24 0.24 0.24
## [43] 0.17 0.17 0.17 0.08 0.08 0.08 0.52 0.52 0.52 1.03 0.36 0.36 0.36 0.34
## [57] 0.34 0.34 0.21 0.21 0.61 0.73 0.73 0.73 0.73 0.39 0.39 0.39 0.39 0.26
## [71] 0.26 0.26 0.10 0.09 0.08 0.07 0.07 0.07 0.04 0.04 0.03 1.07 1.07 1.07
## [85] 1.07 0.40 0.40 0.40 0.40 0.48 0.48 0.48 0.48 0.33 0.33 0.33 0.26 0.09
## [99] 0.49 0.49 0.49 0.49 0.91 0.91 0.91 0.91 0.47 0.47 0.47 1.27 1.27 0.36
## [113] 0.06 0.10 0.10 0.04 0.11 0.11 0.08 0.09 0.05 0.05 0.11 0.14 0.17 0.16
## [127] 0.15 0.07 0.17 0.18 0.14 0.13 0.16 0.18 0.18 0.25 0.20 0.26 0.19 0.23
## [141] 0.23 0.30 0.30 0.30 0.25 0.29 0.29 0.29 0.40 0.31 0.33 0.13 0.10 0.09
## [155] 0.06 1.82 1.82 1.82 1.82 1.73 1.73 1.73 1.38 0.97 0.97 0.97 0.97 0.91
## [169] 0.91 0.91 0.91 0.84 0.56 0.51 0.51 0.51 0.51 0.50 0.49 0.40 0.40 0.40
## [183] 0.40 0.26 0.46 0.46 0.38 0.38 0.38 0.30 1.08 1.08 1.08 1.08 1.03 1.03
## [197] 1.03 1.03 0.84 0.84 0.84 0.49 0.49 0.41 0.41 0.41 0.41 0.26 0.10 0.10
## [211] 0.10 1.56 1.17 0.63 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08
## [225] 0.08 0.07 0.07 0.07 0.07 0.07 0.04 0.03 0.03 0.03 0.03 0.03 0.03 0.03
## [239] 0.03 1.13 1.13 0.26 0.45 0.45 0.45 0.36 0.36 0.36 0.36 0.98 0.98 0.98
## [253] 0.33 0.33 0.33 0.33 0.36 0.36 0.36 1.13 0.42 0.42 0.42 0.40 0.40 0.40
## [267] 0.80 0.07 0.07 0.07 1.11 1.11 0.91 0.20 0.80 0.17 0.17 0.17 0.21 0.57
## [281] 0.14 0.14 0.12 0.12 0.12 0.11 0.11 0.11 0.11 0.11 0.11 0.10 0.10 0.10
## [295] 0.09 0.09 0.08 0.08 0.08 0.07 0.07 0.05 0.05 0.05 0.04 0.04 0.04 1.50
## [309] 0.96 0.82 0.42 0.42 0.40 0.38 1.11 0.83 0.83 0.77 0.60 0.60 0.60 0.55
## [323] 0.48 0.48 0.13 0.13 0.13 0.13 0.13 0.13 0.10 0.10 0.10 0.10 0.09 0.09
## [337] 0.09 0.09 0.36 0.36 0.36 0.08 0.07 0.07 0.07 0.07 0.04 0.04 0.04 0.03
## [351] 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03
## [365] 0.03 0.03 1.39 1.39 1.39 0.14 0.14 0.14 0.77 0.48 0.48 0.04 0.52 0.37
## [379] 1.89 1.89 1.89 1.87 1.67 1.64 1.53 1.29 1.26 1.26 1.26 1.11 1.11 1.11
## [393] 1.09 1.06 1.04 1.04 0.91 0.81 0.79 0.74 0.74 0.74 0.74 0.50 0.17 1.64
## [407] 1.64 1.44 0.56 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.61 0.61 0.61
## [421] 0.61 0.61 0.61 0.61 0.61 1.16 1.16 0.08 0.08 0.07 0.07 0.07 0.04 0.04
## [435] 0.04 0.04 0.03 0.03 0.02 1.71 1.68 1.68 1.30 1.30 1.30 1.30 1.22 1.07
## [449] 0.77 0.77 0.77 0.65 0.60 0.58 0.45 0.45 0.38 0.12fitted(model1)## 1 2 3 4 5
## 0.329587112 0.329587112 0.329587112 0.329587112 0.300036872
## 6 7 8 9 10
## 0.300036872 0.300036872 0.275798315 0.275798315 0.513504931
## 11 12 13 14 15
## 0.513504931 0.466760545 0.360791476 0.507928500 0.507928500
## 16 17 18 19 20
## 0.507928500 0.353432589 0.353432589 0.353432589 0.254429326
## 21 22 23 24 25
## 0.254429326 0.254429326 0.245357719 0.245357719 0.245357719
## 26 27 28 29 30
## 0.391173474 0.385727526 0.385727526 0.210912983 0.210912983
## 31 32 33 34 35
## 0.210912983 0.174212507 0.174212507 0.174212507 0.174212507
## 36 37 38 39 40
## 0.802962535 0.802962535 0.802962535 0.178296968 0.178296968
## 41 42 43 44 45
## 0.178296968 0.178296968 0.291843406 0.291843406 0.291843406
## 46 47 48 49 50
## 0.457283644 0.457283644 0.457283644 0.857312177 0.857312177
## 51 52 53 54 55
## 0.857312177 0.280236796 0.391272692 0.391272692 0.391272692
## 56 57 58 59 60
## 0.220052022 0.220052022 0.220052022 0.727229388 0.701159085
## 61 62 63 64 65
## 0.847267156 0.585048240 0.585048240 0.585048240 0.585048240
## 66 67 68 69 70
## 0.578900902 0.578900902 0.578900902 0.578900902 0.507696017
## 71 72 73 74 75
## 0.507696017 0.507696017 0.859426891 0.040500253 0.049108085
## 76 77 78 79 80
## 0.024616238 0.023081025 0.042981394 -0.030330367 0.011063746
## 81 82 83 84 85
## -0.041580417 0.324222256 0.324222256 0.324222256 0.324222256
## 86 87 88 89 90
## 0.281445253 0.281445253 0.281445253 0.281672168 0.900070079
## 91 92 93 94 95
## 0.900070079 0.900070079 0.900070079 0.875109484 0.875109484
## 96 97 98 99 100
## 0.875109484 0.869436622 0.076708390 0.374241615 0.374241615
## 101 102 103 104 105
## 0.374241615 0.374241615 0.457631340 0.457631340 0.457631340
## 106 107 108 109 110
## 0.457631340 0.627523383 0.627523383 0.627523383 0.752054250
## 111 112 113 114 115
## 0.752054250 0.643362207 0.401333077 0.384846370 0.384846370
## 116 117 118 119 120
## 0.319332727 0.376166215 0.376166215 0.402999530 0.355373106
## 121 122 123 124 125
## 0.339528117 0.339528117 0.345654808 0.400446066 0.320675835
## 126 127 128 129 130
## 0.422060348 0.477628779 0.355865961 0.483301642 0.329071671
## 131 132 133 134 135
## 0.361311908 0.429094697 0.463734563 0.393813113 0.491243649
## 136 137 138 139 140
## 0.309311731 0.471676570 0.309992475 0.376969009 0.346090258
## 141 142 143 144 145
## 0.346090258 0.316346081 0.316346081 0.316346081 0.452466890
## 146 147 148 149 150
## 0.410604786 0.328242065 0.328242065 0.325422660 0.392860068
## 151 152 153 154 155
## 0.330965039 0.162101938 0.144165747 0.120122756 0.078360544
## 156 157 158 159 160
## 1.075119760 1.075119760 1.075119760 1.075119760 1.007024764
## 161 162 163 164 165
## 1.007024764 1.007024764 0.970491530 0.723787331 0.723787331
## 166 167 168 169 170
## 0.723787331 0.723787331 0.822511494 0.822511494 0.822511494
## 171 172 173 174 175
## 0.822511494 0.724885829 1.033722623 0.621780672 0.621780672
## 176 177 178 179 180
## 0.621780672 0.621780672 1.061179277 0.672442961 0.586443443
## 181 182 183 184 185
## 0.586443443 0.586443443 0.586443443 0.974724854 0.636446140
## 186 187 188 189 190
## 0.636446140 0.654080825 0.654080825 0.654080825 0.589474840
## 191 192 193 194 195
## 0.632238436 0.632238436 0.632238436 0.632238436 0.603589805
## 196 197 198 199 200
## 0.603589805 0.603589805 0.603589805 0.728584563 0.728584563
## 201 202 203 204 205
## 0.728584563 0.676141695 0.676141695 0.585642913 0.585642913
## 206 207 208 209 210
## 0.585642913 0.585642913 0.532033687 0.883764561 0.883764561
## 211 212 213 214 215
## 0.883764561 0.648875238 0.623233900 0.567186020 0.120682938
## 216 217 218 219 220
## 0.120682938 0.120682938 0.120682938 0.120682938 0.120682938
## 221 222 223 224 225
## 0.120682938 0.120682938 0.074548485 0.074548485 0.074548485
## 226 227 228 229 230
## -0.011827886 -0.011827886 0.165630387 0.165630387 0.165630387
## 231 232 233 234 235
## 0.071254604 0.055108110 0.055108110 0.059163490 0.059163490
## 236 237 238 239 240
## 0.053949430 0.053949430 0.059163490 0.059163490 0.506218321
## 241 242 243 244 245
## 0.506218321 0.251166428 0.409015892 0.409015892 0.409015892
## 246 247 248 249 250
## 0.317276598 0.317276598 0.317276598 0.317276598 0.420394478
## 251 252 253 254 255
## 0.420394478 0.420394478 0.421196196 0.421196196 0.421196196
## 256 257 258 259 260
## 0.421196196 0.406889445 0.406889445 0.406889445 0.535270617
## 261 262 263 264 265
## 0.414364217 0.414364217 0.414364217 0.327458233 0.327458233
## 266 267 268 269 270
## 0.327458233 0.535270617 0.294010345 0.294010345 0.294010345
## 271 272 273 274 275
## 0.746818497 0.746818497 0.726169278 0.601820134 0.591772326
## 276 277 278 279 280
## 0.619462060 0.687536409 0.687536409 0.516159636 0.798724511
## 281 282 283 284 285
## 0.131089521 0.129351501 0.134347837 0.135506517 0.136085857
## 286 287 288 289 290
## 0.162509619 0.162509619 0.162509619 0.107359930 0.100987189
## 291 292 293 294 295
## 0.127980069 0.160240474 0.120854261 0.128965022 0.020285898
## 296 297 298 299 300
## 0.021789536 0.002762016 0.039891246 0.039891246 0.074669324
## 301 302 303 304 305
## 0.032663279 -0.015139366 -0.013980685 -0.027046211 -0.052182851
## 306 307 308 309 310
## -0.043629189 -0.039753423 0.715588100 0.694485052 0.686996873
## 311 312 313 314 315
## 0.631258932 0.631258932 0.641840889 0.604256107 0.864524132
## 316 317 318 319 320
## 0.864524132 0.864524132 0.864524132 0.682092118 0.682092118
## 321 322 323 324 325
## 0.682092118 0.667480401 0.728066571 0.728066571 0.769102966
## 326 327 328 329 330
## 0.769102966 0.769102966 0.515512334 0.515512334 0.515512334
## 331 332 333 334 335
## 0.332966587 0.332966587 0.332966587 0.332966587 0.652776150
## 336 337 338 339 340
## 0.652776150 0.652776150 0.652776150 0.204571444 0.204571444
## 341 342 343 344 345
## 0.204571444 0.232956403 0.130831474 0.204396962 0.204396962
## 346 347 348 349 350
## 0.204396962 0.134214545 0.086129319 0.086129319 0.159804643
## 351 352 353 354 355
## 0.159804643 0.159804643 0.159804643 0.104167912 0.104167912
## 356 357 358 359 360
## 0.104167912 0.108802633 0.139614226 0.139614226 0.139614226
## 361 362 363 364 365
## 0.250130262 0.250130262 0.357288797 0.357288797 0.357288797
## 366 367 368 369 370
## 0.357288797 0.383717743 0.383717743 0.383717743 0.567142707
## 371 372 373 374 375
## 0.567142707 0.567142707 0.655303685 0.672095357 0.672095357
## 376 377 378 379 380
## 0.660536124 0.722483781 0.709322741 0.972472984 0.972472984
## 381 382 383 384 385
## 0.972472984 0.978826590 0.976557445 1.018385495 1.015208692
## 386 387 388 389 390
## 1.026911816 0.940141289 0.940141289 0.940141289 0.951679875
## 391 392 393 394 395
## 0.951679875 0.951679875 0.995694046 0.957269713 1.023054269
## 396 397 398 399 400
## 1.027688990 0.989567355 0.933560768 0.947368499 1.037991600
## 401 402 403 404 405
## 1.037991600 1.037991600 1.037991600 0.937301237 0.875580494
## 406 407 408 409 410
## 0.645834172 0.645834172 0.634034619 0.544630307 0.909261329
## 411 412 413 414 415
## 0.909261329 0.909261329 0.909261329 0.493874497 0.493874497
## 416 417 418 419 420
## 0.493874497 0.493874497 0.828466363 0.828466363 0.828466363
## 421 422 423 424 425
## 0.828466363 0.471592878 0.471592878 0.471592878 0.471592878
## 426 427 428 429 430
## 0.662551976 0.662551976 0.103612486 0.103612486 0.192514433
## 431 432 433 434 435
## 0.192514433 0.192514433 0.066020463 0.071234524 0.071234524
## 436 437 438 439 440
## 0.071234524 0.105711045 0.105711045 0.277251163 1.129234341
## 441 442 443 444 445
## 0.996425791 0.996425791 1.132411144 1.132411144 1.132411144
## 446 447 448 449 450
## 1.132411144 1.119250103 0.976911145 0.957378119 0.957378119
## 451 452 453 454 455
## 0.957378119 0.963523189 0.932644439 0.929467636 0.910179904
## 456 457 458
## 0.910179904 0.920631377 0.880681020