###Graphical plots with ggplot, and tidyverse
##descriptives
##modeling
#1 #loading data set and packages to be utilized in our investigations
library(ISLR)
WAGES <- as.data.frame(Wage)
head(WAGES)
## year age maritl race education region
## 231655 2006 18 1. Never Married 1. White 1. < HS Grad 2. Middle Atlantic
## 86582 2004 24 1. Never Married 1. White 4. College Grad 2. Middle Atlantic
## 161300 2003 45 2. Married 1. White 3. Some College 2. Middle Atlantic
## 155159 2003 43 2. Married 3. Asian 4. College Grad 2. Middle Atlantic
## 11443 2005 50 4. Divorced 1. White 2. HS Grad 2. Middle Atlantic
## 376662 2008 54 2. Married 1. White 4. College Grad 2. Middle Atlantic
## jobclass health health_ins logwage wage
## 231655 1. Industrial 1. <=Good 2. No 4.318063 75.04315
## 86582 2. Information 2. >=Very Good 2. No 4.255273 70.47602
## 161300 1. Industrial 1. <=Good 1. Yes 4.875061 130.98218
## 155159 2. Information 2. >=Very Good 1. Yes 5.041393 154.68529
## 11443 2. Information 1. <=Good 1. Yes 4.318063 75.04315
## 376662 2. Information 2. >=Very Good 1. Yes 4.845098 127.11574
str(WAGES)
## 'data.frame': 3000 obs. of 11 variables:
## $ year : int 2006 2004 2003 2003 2005 2008 2009 2008 2006 2004 ...
## $ age : int 18 24 45 43 50 54 44 30 41 52 ...
## $ maritl : Factor w/ 5 levels "1. Never Married",..: 1 1 2 2 4 2 2 1 1 2 ...
## $ race : Factor w/ 4 levels "1. White","2. Black",..: 1 1 1 3 1 1 4 3 2 1 ...
## $ education : Factor w/ 5 levels "1. < HS Grad",..: 1 4 3 4 2 4 3 3 3 2 ...
## $ region : Factor w/ 9 levels "1. New England",..: 2 2 2 2 2 2 2 2 2 2 ...
## $ jobclass : Factor w/ 2 levels "1. Industrial",..: 1 2 1 2 2 2 1 2 2 2 ...
## $ health : Factor w/ 2 levels "1. <=Good","2. >=Very Good": 1 2 1 2 1 2 2 1 2 2 ...
## $ health_ins: Factor w/ 2 levels "1. Yes","2. No": 2 2 1 1 1 1 1 1 1 1 ...
## $ logwage : num 4.32 4.26 4.88 5.04 4.32 ...
## $ wage : num 75 70.5 131 154.7 75 ...
summary(WAGES$year)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 2003 2004 2006 2006 2008 2009
##WE HAVE 3000 OBSERVATIONS WITH 11 VARIABLES ON WAGES PER INDIVIDUAL##
##WE WANT TO SEE THE UNDERLYING RELATIONSHIPS BETWEEN THIS 11 VARIABLES WITH RESPECT TO WAGES AS TO BUILD A MODEL THAT WILL HELP MANAGEMENT ASSIGN A PROPER WAGE TO A GIVEN INDIVIDUAL BASED ON THEIR EDU,RACE,AGE,..E.T.C ##
##OUR MAIN QUESTION IS WHAT ACTUALLY DRIVES WAGES? ##
##This wages info is from 2003 till 2009
##the packages we might utilize##
pacman::p_load(pacman,dplyr,GGally,ggplot2,ggvis,rio,
shiny,tidyr,stringr,httr,lubridate,
plotly,rmarkdown,ggthemes,psych,tidyverse)
names(WAGES)
## [1] "year" "age" "maritl" "race" "education"
## [6] "region" "jobclass" "health" "health_ins" "logwage"
## [11] "wage"
##We are trying to see what influences a persons wage
##The average wage is 111.7036##
mean(WAGES$wage) ##in thousands of dollars
## [1] 111.7036
##THE AVARAGE WAGE IS =$ 111703.6 WITH ,
##The average age in this study being 42 yrs
mean(WAGES$age)
## [1] 42.41467
str(WAGES)
## 'data.frame': 3000 obs. of 11 variables:
## $ year : int 2006 2004 2003 2003 2005 2008 2009 2008 2006 2004 ...
## $ age : int 18 24 45 43 50 54 44 30 41 52 ...
## $ maritl : Factor w/ 5 levels "1. Never Married",..: 1 1 2 2 4 2 2 1 1 2 ...
## $ race : Factor w/ 4 levels "1. White","2. Black",..: 1 1 1 3 1 1 4 3 2 1 ...
## $ education : Factor w/ 5 levels "1. < HS Grad",..: 1 4 3 4 2 4 3 3 3 2 ...
## $ region : Factor w/ 9 levels "1. New England",..: 2 2 2 2 2 2 2 2 2 2 ...
## $ jobclass : Factor w/ 2 levels "1. Industrial",..: 1 2 1 2 2 2 1 2 2 2 ...
## $ health : Factor w/ 2 levels "1. <=Good","2. >=Very Good": 1 2 1 2 1 2 2 1 2 2 ...
## $ health_ins: Factor w/ 2 levels "1. Yes","2. No": 2 2 1 1 1 1 1 1 1 1 ...
## $ logwage : num 4.32 4.26 4.88 5.04 4.32 ...
## $ wage : num 75 70.5 131 154.7 75 ...
#2. #DATA VISUALAZATION ##
##this is a plot of wages as a function of age##
ggplot(WAGES, aes(x=age ,
y=wage,
col=race))+geom_point()+
labs(x="Age",
y="Wage",
title = "Wage as a function of Age")+
geom_smooth(se=F)
## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'
#From our scatter plot we can see that most of our employees are white with a minor concentration of Asians and blacks but overall population is white
#there seems to be a cluster of outlier wages at >= $280 000 and the population is mainly white dominated with five or six Asians and their age group is from 30 yrs to 65yrs of age
#the highest earners according to our scatter plot are the Blacks with one or two whites included
#and their average wage is at around $320 000 with one Asian at around $300 000
##this is a plot of wages as a function of education and health insurance is the selector##
ggplot(WAGES, aes(x=education,
y=wage,col=health_ins))+geom_point()+
labs(x="Type of Education",
y="Wage per 1000",
title="Wage as a function of Education:Per Race Group")+
geom_smooth(method = lm)
## `geom_smooth()` using formula 'y ~ x'
#From the plot its apparent that most employees with qualifications less than high school
# earn considerably less than the other four categories of education with their max wage set at $150 000
# and most of them don't have health insurance.
# It is important to note that the number of employees with health insurance increase with qualification as well as the wages with respect to their qualifications
# Most employees with an advanced Degree have health insurance and they are the ones with a larger wage scale than the rest
###this is a scatter plot of wages as a function of age with education being the selector
ggplot(WAGES, aes(x=age,
y =wage,col=education))+
geom_point()+geom_smooth(method = lm)
## `geom_smooth()` using formula 'y ~ x'
labs(x="Age",
y="Wage",
title="Wage as a function of age per :Education group")
## $x
## [1] "Age"
##
## $y
## [1] "Wage"
##
## $title
## [1] "Wage as a function of age per :Education group"
##
## attr(,"class")
## [1] "labels"
#This plot shows us that there number of employees at around age group 20 yrs -30 yrs
# do not posses an advanced Degree.
#Most employees from across all age groups have graduated high school
#overall we can see that the majority of our employees have some formal education and their
#wages are in accordance with their levels of education and age with the average
#employee being 42 yrs old
###this is a scatter plot of wage as a function of age per marital class##
ggplot(WAGES, aes(x=age,
y=wage,col=maritl))+
geom_point()+
labs(x="Age",
y="Wage",title="Wage as a function of age per :Marital class")+
geom_smooth(method = lm, se=F)
## `geom_smooth()` using formula 'y ~ x'
# From our plot its evident that most 20yr old to about 25 yrs are single and have never been married with
# their average wage scale set at around $100 000 with slight variations due to education and other factors
#Most of our employees in the data in question are married and above 30 yrs of age
#there are a few divorce cases in our data set from the age of 30 yrs above above
##histogram of wages##
hist(WAGES$wage,col="blue",main="Hist of Wages",xlab="Wages")
rug(WAGES$wage,lwd=0.5,col="black")
min(WAGES$wage)
## [1] 20.08554
max(WAGES$wage)
## [1] 318.3424
# its evident that the distribution is right skewed and there's an outlier from $250 000
#with the most wages spread almost evenly on either side of $100 000
# The minimum wage is $20 000 and the max is $318 342.4
boxplot(WAGES$wage,horizontal = T ,
col="blue",
fill=T,
xlab="Wages per:1000",
main="Box plot of Wages")
#the box plot also indicates that the average wage is $110 000, with the min at below $25 000
#the max is at around $200 000 with outliers from above $200 000
##histogram of age
hist(WAGES$age,xlab="Age",main="Histogram of Ages",col="purple")
rug(WAGES$age, lwd=0.4,col="black")
##the rug plot makes it easy for us to read from the table the min age,
#which is 18 years
min(WAGES$age)
## [1] 18
max(WAGES$age)
## [1] 80
# and the oldest being 80 yrs of age
##this is a plot of wage as a function of age with jobclass as a selector##
ggplot(WAGES, aes(x=age,
y=wage,col=jobclass))+
geom_point()+
labs(x="Age",
y="Wage",
title="Wage as a function of age with Jobclass as a selector")+
geom_smooth(method = lm)
## `geom_smooth()` using formula 'y ~ x'
## its clear that Jobclass influences wages with Information being the most rewarding according to the scatter plot,
# those in the industrial sector earn less than those in the Information industry
#most 18 year old to 20 yrs are in the Industrial sector and earn less than $100 000
str(WAGES)
## 'data.frame': 3000 obs. of 11 variables:
## $ year : int 2006 2004 2003 2003 2005 2008 2009 2008 2006 2004 ...
## $ age : int 18 24 45 43 50 54 44 30 41 52 ...
## $ maritl : Factor w/ 5 levels "1. Never Married",..: 1 1 2 2 4 2 2 1 1 2 ...
## $ race : Factor w/ 4 levels "1. White","2. Black",..: 1 1 1 3 1 1 4 3 2 1 ...
## $ education : Factor w/ 5 levels "1. < HS Grad",..: 1 4 3 4 2 4 3 3 3 2 ...
## $ region : Factor w/ 9 levels "1. New England",..: 2 2 2 2 2 2 2 2 2 2 ...
## $ jobclass : Factor w/ 2 levels "1. Industrial",..: 1 2 1 2 2 2 1 2 2 2 ...
## $ health : Factor w/ 2 levels "1. <=Good","2. >=Very Good": 1 2 1 2 1 2 2 1 2 2 ...
## $ health_ins: Factor w/ 2 levels "1. Yes","2. No": 2 2 1 1 1 1 1 1 1 1 ...
## $ logwage : num 4.32 4.26 4.88 5.04 4.32 ...
## $ wage : num 75 70.5 131 154.7 75 ...
summary(WAGES$education)
## 1. < HS Grad 2. HS Grad 3. Some College 4. College Grad
## 268 971 650 685
## 5. Advanced Degree
## 426
##from the data in question, 268 candidates do not have high school grad.
##971 Graduated from high school,650 graduated at some College, 685 graduated from College
# and lastly 426 have an Advanced Degree
#3 # Modeling #
##model 1 with all the variables ##
names(WAGES)
## [1] "year" "age" "maritl" "race" "education"
## [6] "region" "jobclass" "health" "health_ins" "logwage"
## [11] "wage"
md1 <-lm(wage~age+maritl+race+education+logwage,data = WAGES)
md1
##
## Call:
## lm(formula = wage ~ age + maritl + race + education + logwage,
## data = WAGES)
##
## Coefficients:
## (Intercept) age
## -402.58279 -0.02934
## maritl2. Married maritl3. Widowed
## -1.25298 -3.58374
## maritl4. Divorced maritl5. Separated
## -1.35265 -2.28336
## race2. Black race3. Asian
## -0.46048 -0.20005
## race4. Other education2. HS Grad
## 0.84476 -1.98652
## education3. Some College education4. College Grad
## -2.90264 -1.20410
## education5. Advanced Degree logwage
## 4.67521 111.19343
summary(md1)
##
## Call:
## lm(formula = wage ~ age + maritl + race + education + logwage,
## data = WAGES)
##
## Residuals:
## Min 1Q Median 3Q Max
## -13.951 -5.405 -3.606 0.504 94.505
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -402.58279 3.48305 -115.583 < 2e-16 ***
## age -0.02934 0.02294 -1.279 0.20097
## maritl2. Married -1.25298 0.65717 -1.907 0.05667 .
## maritl3. Widowed -3.58374 2.99788 -1.195 0.23202
## maritl4. Divorced -1.35265 1.08208 -1.250 0.21138
## maritl5. Separated -2.28336 1.81787 -1.256 0.20919
## race2. Black -0.46048 0.79914 -0.576 0.56451
## race3. Asian -0.20005 0.97477 -0.205 0.83741
## race4. Other 0.84476 2.12386 0.398 0.69084
## education2. HS Grad -1.98652 0.88860 -2.236 0.02545 *
## education3. Some College -2.90264 0.95013 -3.055 0.00227 **
## education4. College Grad -1.20410 0.96929 -1.242 0.21424
## education5. Advanced Degree 4.67521 1.09073 4.286 1.87e-05 ***
## logwage 111.19343 0.79079 140.610 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 12.75 on 2986 degrees of freedom
## Multiple R-squared: 0.9071, Adjusted R-squared: 0.9067
## F-statistic: 2243 on 13 and 2986 DF, p-value: < 2.2e-16
anova(md1)
## Analysis of Variance Table
##
## Response: wage
## Df Sum Sq Mean Sq F value Pr(>F)
## age 1 199870 199870 1230.451 < 2.2e-16 ***
## maritl 4 222572 55643 342.553 < 2.2e-16 ***
## race 3 39689 13230 81.445 < 2.2e-16 ***
## education 4 1063370 265843 1636.597 < 2.2e-16 ***
## logwage 1 3211551 3211551 19771.160 < 2.2e-16 ***
## Residuals 2986 485034 162
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
confint(md1)
## 2.5 % 97.5 %
## (Intercept) -409.41221523 -395.75336989
## age -0.07431157 0.01563574
## maritl2. Married -2.54153652 0.03558026
## maritl3. Widowed -9.46185626 2.29437775
## maritl4. Divorced -3.47433552 0.76904188
## maritl5. Separated -5.84776391 1.28104772
## race2. Black -2.02740313 1.10644547
## race3. Asian -2.11132722 1.71123210
## race4. Other -3.31960967 5.00912517
## education2. HS Grad -3.72885623 -0.24418134
## education3. Some College -4.76561649 -1.03966341
## education4. College Grad -3.10464100 0.69644630
## education5. Advanced Degree 2.53655472 6.81386501
## logwage 109.64287703 112.74398742
fitted(md1)
## 231655 86582 161300 155159 11443 376662 450601
## 77.029408 68.667355 134.016177 154.068310 72.751429 132.118965 163.573732
## 377954 228963 81404 302778 305706 8690 153561
## 117.822981 124.150271 132.755611 121.503622 82.202266 94.124336 139.007357
## 449654 447660 160191 230312 301585 153682 158226
## 137.784867 92.708444 85.843599 195.430692 133.831412 103.925296 183.084963
## 11141 448410 305116 233002 8684 229379 86064
## 28.796493 87.254553 158.558211 99.586370 224.996850 85.654727 58.378900
## 378472 157244 82694 7690 377879 9747 233301
## 121.327498 67.600482 185.933752 105.378197 90.146310 118.821798 94.104950
## 157123 230823 80406 228851 153810 81383 303642
## 98.275973 91.985935 111.801103 110.790823 61.620021 -11.984287 117.915589
## 87492 8692 86929 380872 449480 305136 227963
## 20.126600 75.041357 81.595097 159.883623 215.573290 174.714531 62.931675
## 232863 8621 379668 84595 154634 450864 84377
## 123.284586 188.606898 105.253554 217.147416 -10.722723 128.309477 83.346820
## 234086 154482 85916 161065 12003 228071 13479
## 188.548222 151.158762 104.106943 117.568820 152.933046 121.339250 76.216110
## 81494 159076 159207 447501 153767 81071 376442
## 89.885214 136.774471 127.210754 156.079984 183.314349 104.082923 67.512468
## 87299 228621 232494 228400 451860 157058 159583
## 97.746634 83.543258 83.719285 106.487023 101.053734 111.267417 214.991319
## 233759 159224 374859 11710 86298 453021 161431
## 85.764480 118.540527 93.952818 139.363981 110.772642 65.163217 35.038503
## 305888 232199 86568 447500 452506 450908 82573
## 85.109522 76.293145 94.023641 63.915769 135.480017 138.013804 135.861646
## 159196 156110 14148 232000 453486 156065 229079
## 104.547012 77.945291 120.365230 83.807299 103.725550 102.123825 183.079645
## 450905 10660 449456 374660 87463 9273 377517
## 155.367689 147.129367 123.979740 127.529777 116.982061 62.662236 121.843412
## 231592 303825 156310 303376 230586 450109 379991
## 98.443290 92.787854 53.769355 132.250220 119.331960 119.417781 83.249971
## 87291 228517 160971 307464 449246 233043 377184
## 74.488293 117.374991 87.440283 97.852330 126.123004 174.890558 224.989423
## 8033 233687 447751 230398 378429 447412 13924
## 106.815109 95.374592 90.061668 160.200330 141.098708 98.220241 62.167771
## 87630 84600 451987 160246 307755 375007 303430
## 135.777318 95.904464 120.160067 85.083864 109.697123 142.559874 150.457137
## 379330 8339 83190 452580 302701 83222 159871
## 128.364212 144.481252 41.944432 112.677116 130.739184 90.302590 93.422764
## 82108 229714 159048 302868 10499 84127 11661
## 83.229468 99.301919 112.598804 48.163370 58.288375 132.331383 162.328927
## 86282 305327 81655 303953 374752 159109 159285
## 133.186996 169.333968 49.968544 105.083134 137.990233 83.973624 84.218122
## 159909 378138 9786 86191 154759 12122 306309
## 158.663159 146.493727 72.763084 133.074591 109.451641 27.080477 128.817812
## 377137 375944 304068 156557 306779 161021 85966
## 126.938639 77.251842 71.103792 141.077826 132.294993 65.012773 86.022423
## 453692 233313 9681 379875 305250 84642 451306
## 89.045409 131.868827 64.982386 76.365960 147.673841 148.055234 166.693839
## 228212 157989 88028 155697 234523 233149 13626
## 105.475289 145.607583 105.153406 143.050477 128.716267 133.568389 118.556606
## 234640 453255 154195 232628 85539 377464 230582
## 109.354972 123.725401 150.038880 106.727096 105.270580 111.214059 104.702630
## 9573 84164 11880 85545 153581 232176 450900
## 100.574157 150.340997 111.486665 59.726026 99.535439 172.801884 185.025728
## 377900 232371 12056 84397 233497 228458 230993
## 119.866688 159.933859 93.501594 124.970553 73.618393 131.629923 123.123069
## 153269 305585 302536 307024 233435 12288 303912
## -12.053777 119.038581 86.788203 239.352613 145.194302 143.023033 75.774805
## 14404 233441 377452 449474 381113 156406 378714
## 143.316412 73.232490 160.601374 110.234837 70.509503 134.859616 156.473640
## 376309 451901 450725 375024 159821 229865 83880
## 82.670898 113.728285 78.186867 72.424373 98.362730 103.805627 167.752777
## 9965 157250 453371 228243 307645 156420 160039
## 73.846962 103.630891 99.022304 101.533612 131.864626 102.365808 99.523277
## 233379 231082 301920 80687 450566 86450 234600
## 115.498797 123.005717 174.978572 51.728841 82.202266 210.459800 81.586169
## 307663 303900 453852 230477 227901 86826 8653
## 82.721796 39.547275 74.595529 133.816130 13.274171 122.312818 128.426829
## 305209 81173 451854 228591 302140 153731 228955
## 83.807299 63.117428 114.553338 102.239781 54.671767 102.011348 137.074111
## 9621 305165 378023 82989 82023 374706 379611
## 51.198449 125.232342 56.894025 114.582675 108.897180 71.534158 144.196437
## 452592 305871 157388 448936 377039 82375 449852
## 94.965650 72.826176 144.393238 117.045154 95.755984 98.836338 161.564396
## 301195 228628 85756 160269 301711 304988 156809
## 110.958582 104.898293 38.266965 -19.639014 122.859027 115.264093 116.046515
## 14133 306552 377157 82901 159765 229546 9730
## 123.240420 115.409951 99.298156 115.381445 125.320356 126.113722 31.877457
## 158570 83618 379620 449489 447879 10076 84867
## 13.974738 119.953948 131.140987 149.030031 109.006993 98.591163 89.853117
## 14063 12822 302239 84949 11129 450963 154245
## 150.897206 61.081118 130.064412 110.834574 123.713746 174.597179 57.152749
## 231844 87485 306574 154477 13319 452710 156407
## 86.230783 69.154885 92.495860 58.083010 148.163847 88.987759 12.714399
## 153297 13996 80386 12586 234325 305437 231481
## 64.611896 82.803164 72.943528 136.575690 148.312666 82.447656 62.058459
## 83198 231026 303072 305362 447780 87269 307318
## 96.592256 96.237931 75.216570 124.156542 80.054916 91.234261 138.311906
## 302976 302515 14041 228348 381272 87402 451721
## 131.100530 99.412692 69.143230 125.109495 65.839832 131.717937 122.078115
## 8318 447992 377619 153764 158574 374992 155488
## 93.159451 39.124325 87.494463 87.594953 150.345104 117.678719 78.881399
## 8969 86280 451302 448525 381232 304500 156397
## 101.864658 166.472811 139.694239 75.153042 72.972866 149.783114 106.590215
## 9066 82172 375305 13745 87094 87118 11498
## 90.009211 114.627587 84.443031 124.479259 138.027610 93.465506 81.468818
## 87260 303688 304050 378178 302298 157594 10835
## 123.680489 166.262151 112.067381 105.158724 226.820711 148.870810 168.835223
## 81344 449687 7980 449444 10723 154638 85115
## 140.374399 175.319507 95.699005 86.970877 148.392871 132.654100 107.392165
## 232201 452906 301654 307056 161096 87060 12303
## 114.933150 5.771612 96.164132 138.673760 183.929696 154.845104 87.671804
## 229331 159410 154322 378567 450843 85580 303657
## 47.045494 71.998069 94.952752 124.586908 150.205979 222.704006 104.291245
## 231767 82755 84630 154919 83800 375159 452406
## 63.204321 132.011316 217.147416 124.259886 131.512571 91.036038 120.531758
## 375122 87199 82912 379794 307692 7744 85617
## 65.247076 98.157364 131.943727 157.453072 164.098346 145.017899 119.603673
## 82419 158170 10787 86679 379950 380366 377229
## 72.511734 72.503552 134.164067 -66.621031 79.790874 108.933704 120.637145
## 14381 380704 154336 303935 449322 447585 154099
## 102.641584 108.966661 127.433199 97.403846 126.410556 132.197528 99.983426
## 83458 228692 10081 86122 452287 82373 448894
## 86.995718 131.893964 98.311348 81.286144 107.980751 123.790479 98.827752
## 81495 155436 231274 158044 153953 450724 160958
## 132.417662 108.966661 63.513274 133.313031 144.349186 109.384310 95.198564
## 376843 229069 9667 450052 448988 82603 7878
## 99.012365 147.520891 124.661487 97.981337 120.155683 152.052488 101.212578
## 14321 8396 447417 87860 232031 378256 155519
## 94.776725 81.468818 134.932298 151.325055 133.546771 146.347677 96.158710
## 304018 9841 448723 233955 8039 448678 306092
## 120.203086 90.683983 163.341884 115.205417 84.855957 160.222725 22.973308
## 153618 157194 306995 304167 12086 12979 451080
## 48.422094 83.072701 90.566631 91.153765 145.633191 114.955293 124.762935
## 85699 81085 228178 12945 450263 301266 157405
## 127.814517 217.088740 117.846480 65.627251 97.697767 91.204616 171.945555
## 161083 8459 451331 305396 451170 306067 303214
## 137.520702 189.252332 95.292922 149.607087 124.750971 83.744206 111.849249
## 452388 302942 11666 378911 82114 7969 379907
## 214.380138 112.514735 132.206979 155.544529 149.641743 58.193716 111.105272
## 232187 379987 448271 378868 11319 155212 160678
## 78.758084 141.328093 120.030643 80.221241 59.244964 116.564685 110.616230
## 86604 227990 8348 156680 158692 231182 306711
## 167.694101 104.693702 110.243764 68.359955 98.640911 129.901268 103.381677
## 12734 229031 449980 160714 302861 230508 12537
## 121.738139 73.522777 58.992485 146.378972 80.587352 131.717937 72.562228
## 450603 86119 448869 451086 154643 304493 303813
## 57.994996 104.547012 80.597138 72.353310 97.844456 122.893683 227.970679
## 376113 86394 301315 232504 10753 157040 305092
## 125.584397 111.447980 111.070825 112.589173 121.177192 127.926625 134.932298
## 12728 447357 159513 161380 14457 158761 154582
## 79.996240 113.998565 -59.899210 119.458907 108.702892 173.731197 232.811029
## 158274 378307 9863 155729 87848 305240 159441
## 103.601553 135.172403 90.537294 37.572557 104.576350 126.172398 95.639896
## 80586 83515 231410 81995 232366 229698 449667
## 132.471020 11.709656 115.811811 90.088536 225.046818 104.678504 175.271951
## 81457 83804 154652 159717 302069 13267 8550
## 89.363630 165.939434 88.394588 135.392003 133.440414 69.762429 110.689045
## 449709 157793 302529 157309 451256 159735 85268
## 180.964111 168.952575 142.598348 71.103792 60.974495 85.705804 111.251961
## 453542 158301 307764 231800 12439 7412 86091
## 116.075853 154.415047 111.800035 225.369535 90.378949 93.671586 112.452115
## 159115 10935 447841 234010 453198 376184 160130
## 41.764421 83.513920 112.908651 186.012557 95.814660 188.958953 -20.108421
## 306716 304809 11522 306077 301911 155698 450165
## 112.886332 108.078009 86.005007 83.004112 102.245276 132.642903 137.666471
## 159956 380945 301907 159358 233565 301859 302193
## 147.644503 112.387588 82.090232 96.422751 111.829373 121.765193 35.800147
## 161261 451254 305400 233567 380078 80581 87755
## 92.027485 60.857143 109.107633 222.777618 101.064526 189.017628 128.628253
## 13685 83327 159834 84809 87700 305809 380902
## 105.191672 97.068309 82.867335 154.068310 115.528135 127.240773 77.255121
## 158812 306821 231279 12575 232850 379119 81696
## 114.515261 72.086083 91.255543 -39.942951 97.798664 110.180929 222.909371
## 378745 304502 80930 9157 377201 160496 306557
## 98.244604 83.777961 91.818460 117.422162 81.029155 147.618258 147.955565
## 302928 7880 379439 155174 80508 81575 231191
## 81.732859 122.683000 82.508015 94.679409 116.030584 110.820821 61.213707
## 232830 85999 450673 447485 453584 8016 160160
## 76.087779 103.748243 105.470627 162.206257 30.887097 93.859269 115.831237
## 380311 11315 232256 80679 229791 450800 230173
## 148.854003 136.056862 138.107584 126.373286 91.388469 114.729365 133.546771
## 228889 7978 374363 380398 452862 228899 232593
## 94.195269 107.675717 76.950220 156.237311 116.051075 93.098765 67.136061
## 231255 306356 158824 380061 376529 304383 10445
## 112.452115 91.935811 117.798237 149.754256 155.750435 62.695946 109.897195
## 229647 377052 380800 450000 233715 304660 233026
## 105.499965 137.191463 14.245425 120.833132 143.941324 145.954011 139.036695
## 80647 87572 11809 233001 305553 379752 380738
## 125.761667 181.899850 164.466856 99.063517 116.268903 147.937882 102.466302
## 447577 87038 154076 374391 449807 307460 449365
## 84.443031 124.097866 130.801815 109.817460 120.240486 220.607031 119.897782
## 378727 156087 12157 301568 10832 160170 453712
## 116.697610 138.224936 75.358315 124.449363 123.745811 -36.087358 178.271209
## 87395 305387 229944 380031 231476 154504 231749
## 57.304756 150.603827 119.038581 145.063686 123.413689 106.069349 223.899087
## 377308 8330 154617 87791 230102 157248 447647
## 98.333392 97.957317 101.388589 72.538772 116.339145 100.769584 39.383049
## 231197 379516 451555 158257 81725 305274 379947
## 91.116602 146.924733 103.163474 136.566762 88.012843 149.708066 26.914152
## 84795 83423 301999 305108 375810 153403 154768
## 142.673922 119.674003 58.733855 89.221344 107.079151 100.710908 105.358771
## 302561 153724 84494 83214 378589 307823 303202
## 148.238436 150.566210 116.956366 130.286948 122.928698 46.465006 76.753999
## 452445 159137 451436 232410 307670 159052 155165
## 144.225775 66.756498 190.539966 102.158037 104.547012 173.973020 83.924743
## 13246 158241 379243 9196 450568 7781 10997
## 156.624965 58.371175 91.490247 72.972866 145.226190 150.251772 77.575461
## 153426 80273 374547 85217 377128 158403 228131
## 129.184007 124.704260 225.634330 39.588414 152.657829 178.130863 125.056315
## 452170 154530 81780 378629 305370 301646 12249
## 90.031903 94.232695 47.388621 129.570896 116.026105 99.967763 122.666102
## 302635 8793 12032 13257 156095 232674 378952
## 58.176342 101.776644 125.967072 144.548492 122.459697 75.065028 99.505326
## 304280 376160 86736 305599 9903 13558 378086
## 124.720741 108.438851 148.455457 91.431571 121.825780 107.862849 126.522406
## 80963 376772 453319 231608 87803 154604 304641
## 177.762975 124.127204 220.983191 167.391804 143.897834 153.738322 153.895892
## 452853 85681 452452 8297 233667 377125 380656
## 126.749361 99.371066 114.541683 119.930689 136.604705 90.303548 125.878926
## 374314 306069 306727 379612 153785 157154 306904
## 91.036038 97.197605 115.536115 136.147054 133.949372 103.704487 187.912365
## 9761 86702 158105 379806 449268 83615 378890
## 95.694725 100.779522 148.255590 80.309255 122.981697 90.553376 99.351759
## 230899 9311 7750 302750 231066 157343 9952
## 149.084675 169.392644 73.549922 130.104023 220.596517 114.515261 51.783762
## 233281 86503 14172 14341 231725 377627 375298
## 96.887741 114.142607 61.022442 118.891891 165.248736 135.855914 131.307206
## 84172 154047 375008 86259 230737 378052 155909
## 130.932863 131.293205 127.285568 141.406345 80.951772 -5.189227 116.485834
## 375457 155588 306550 82560 379734 376576 158927
## 73.908831 134.077590 86.503141 180.891361 110.944158 166.203475 54.832664
## 374739 83417 14351 159265 157150 451548 302614
## 138.508613 126.510241 101.653618 142.542191 137.608715 145.050163 131.058291
## 453033 84994 227948 380920 231461 160102 449353
## 156.884471 225.570822 102.734474 106.670425 100.349249 167.271715 162.487523
## 448411 306810 155681 10055 233682 157882 302173
## 97.663938 142.676660 77.119545 150.839067 121.708891 149.729756 90.889349
## 231216 9850 161403 377645 84260 155985 306353
## 95.255476 143.025977 53.886425 59.041459 153.538893 129.156336 124.938963
## 228023 156832 304488 305737 303148 302080 447857
## 79.526833 109.493937 39.779568 111.443444 104.070960 178.842263 109.565374
## 233741 85657 379124 157694 83479 450888 14252
## 161.354744 68.687089 105.411952 122.342156 104.041622 101.210802 86.258807
## 14421 301908 452061 304906 302424 159404 231750
## 129.075604 37.785735 147.902283 134.873623 226.527331 166.174137 176.719894
## 305745 376178 450343 160548 302678 302085 159635
## 129.696242 68.237081 123.452563 67.596974 122.224805 142.110990 39.646997
## 81174 82948 82251 379828 450063 9535 154111
## 98.763758 81.718067 91.497995 121.603291 138.526355 83.900723 34.945979
## 305404 85550 447980 14481 85819 450651 82222
## 105.486294 55.959561 182.207690 106.045678 113.629628 30.513303 103.777581
## 12508 377741 302139 153833 85624 230790 449764
## 54.368753 154.075447 106.963805 141.095283 106.510075 112.960463 82.364527
## 449202 13741 302523 81623 13718 10378 161366
## 163.771674 138.048908 158.440859 97.908736 71.983634 140.170443 137.726191
## 9215 157493 302363 11991 449684 11238 159751
## 81.396945 168.928555 124.334179 125.648349 98.040013 104.145209 135.508879
## 452407 233537 229847 9864 447299 231895 230128
## 123.863162 91.218844 82.055576 109.327643 104.359330 140.375808 84.276798
## 12999 160782 379257 161228 232829 234092 84421
## 64.214070 81.586169 120.218743 123.579617 104.928405 124.068528 122.981697
## 157953 86497 7737 13471 448820 85643 453480
## 126.665670 117.886251 107.651388 160.294830 129.650547 97.412435 113.233279
## 85241 156206 84713 155666 83567 449541 448368
## 38.839902 106.979482 147.996558 121.088869 72.805859 221.188556 133.685741
## 377037 231115 305375 303226 85015 228219 379558
## 102.827390 97.615071 108.770223 133.497023 183.044519 125.349116 79.702861
## 160043 82149 156798 9029 157633 9820 448635
## 69.091476 155.691759 71.279287 124.155767 133.137004 89.776790 221.511273
## 81776 86230 84040 11619 87714 14549 83620
## 110.616230 96.845550 68.824215 188.958953 107.687372 107.622050 57.199770
## 378744 10047 11784 12453 378962 230457 447527
## 114.677335 138.203638 98.890038 63.976566 131.071192 159.712237 83.396568
## 154701 453719 153784 160819 380247 81823 155141
## 117.995243 75.442345 73.085801 133.919425 46.675689 56.048135 86.094795
## 156716 7546 374359 301939 306511 452755 8667
## 98.173077 84.142249 132.658007 81.213704 60.885455 162.012798 104.860027
## 450499 156050 160046 87749 8363 234293 448089
## 149.846359 145.961924 -12.145083 116.281218 116.423410 136.721560 156.651358
## 453187 447835 307486 82464 155315 380158 375387
## 74.636668 145.106977 104.664364 216.707347 184.772692 89.136779 117.045247
## 85776 229893 229973 13960 234361 301929 306789
## 49.908503 123.763494 146.083911 118.547346 112.892183 111.330628 132.236317
## 230376 380304 306501 376743 230371 304137 374823
## 92.523812 152.527726 163.577488 96.093109 61.096356 176.730295 37.895274
## 451590 227916 7993 159388 304858 230749 86325
## 113.447425 84.344548 120.707785 144.897685 164.320167 97.241243 40.843903
## 154901 81954 451332 379839 449978 233080 307530
## 72.650242 164.378842 154.937902 92.936153 107.343192 116.982061 111.917386
## 161327 158949 448811 11623 10265 379315 230661
## 129.860615 115.545817 98.568027 37.301870 101.500445 120.277419 97.491520
## 81295 305243 228627 13060 375312 156535 304223
## 99.840473 140.214471 81.876464 97.596391 89.914552 147.432877 93.047385
## 307620 85969 13360 11113 305667 234017 12837
## 99.037434 39.470970 98.294352 63.314316 96.267719 126.909810 115.410783
## 302321 81373 160726 452148 229256 306650 452276
## 116.017177 78.264341 98.098689 106.639082 123.621813 136.591591 155.582478
## 302510 81228 228440 228053 10471 231759 155837
## 226.586007 177.772465 123.441214 68.840116 87.792338 70.583891 141.318866
## 302024 301193 158905 453630 303454 228501 304450
## 106.492392 117.150943 91.542763 121.543078 183.234514 89.770599 74.219548
## 378489 86991 153315 231642 234448 80744 374333
## 161.465080 44.767972 107.227846 96.962901 104.987081 95.936074 105.869650
## 304748 232443 451096 82862 380709 376073 301216
## 145.695597 77.026968 93.412554 132.500358 84.843849 103.998520 57.414032
## 233939 451070 449595 158200 9638 157436 452319
## 94.481801 91.702258 132.383006 62.695946 147.849868 128.579280 135.860425
## 302474 230090 306734 234336 8827 8301 85748
## 130.999616 131.764335 120.795490 124.769006 122.947041 149.489735 50.887744
## 376569 378593 158180 82969 228806 380329 304795
## 99.581953 91.768682 130.266629 141.286414 116.603935 119.778674 74.894904
## 14455 304663 87070 380220 12400 303868 7845
## 128.622758 105.411952 109.056552 100.188791 121.474284 93.119175 108.905258
## 234319 233042 233381 157856 82387 301852 82525
## 69.316461 112.288636 105.926270 47.353107 128.403252 82.861840 144.651420
## 449130 84343 452636 233211 233851 12233 12501
## 67.646705 78.744287 131.848417 37.484544 136.880767 111.839870 224.620775
## 153789 87826 8875 229950 85730 377504 13650
## 77.315930 85.906752 121.984684 123.628459 116.810451 45.590186 121.855580
## 155246 227999 157775 453565 8927 380898 85375
## 50.511669 120.408910 79.780836 126.803745 155.016987 39.180101 61.505040
## 153469 83341 8279 307337 13148 84841 85515
## 132.010132 82.603294 131.633491 92.201002 128.109873 108.984343 90.295944
## 86629 231027 157246 13588 376203 83057 230814
## 135.835961 72.650149 109.824106 94.227001 134.340461 135.669823 238.349905
## 305515 307267 88046 302698 232536 158406 452654
## 68.235155 86.598752 107.658034 109.985208 101.748916 133.626046 112.520581
## 155330 307313 159448 155833 307280 7401 11845
## 105.495998 136.650266 78.087696 133.986839 121.485753 100.928885 115.498797
## 307683 8589 375802 305144 453214 8360 377324
## 226.732697 98.028358 184.244610 90.266607 89.537077 103.205650 113.146081
## 302793 154537 232060 83048 376922 87672 234303
## 99.733961 114.876055 90.165954 92.360151 167.862767 99.155337 127.625206
## 374328 158629 231349 377297 230086 81256 306063
## 137.003284 107.795979 92.619481 85.001694 77.266776 118.541856 106.978472
## 378700 86261 450507 159849 301682 448787 82646
## 138.065982 95.682111 115.755898 65.927845 146.261817 106.881109 97.006540
## 81754 14268 85704 233733 229393 83536 375861
## 91.907623 99.527694 81.938224 120.560787 121.500857 105.935617 148.171783
## 14368 85295 231204 13498 302692 307635 83924
## 154.614438 166.291489 81.996900 7.808903 102.694100 122.694665 124.880287
## 80239 379220 453870 85521 9738 157529 307581
## 85.546303 91.881550 87.767023 74.868498 103.676453 90.879646 115.657301
## 380007 453715 381016 8356 156461 380325 156598
## 79.317915 160.578297 141.586744 153.824825 87.293594 103.815979 134.192205
## 450872 305335 449727 452029 232822 158958 233370
## 66.612488 142.451659 174.057441 77.692812 145.033354 107.169170 149.431059
## 161344 233394 233584 448801 302882 306349 452162
## 82.481503 131.546110 171.778093 98.239108 92.043250 133.074591 78.827073
## 231483 82643 305066 11473 86233 12787 233174
## 149.000693 174.250026 133.655384 148.854532 111.624007 127.339867 94.106415
## 303344 307057 301337 81731 157918 160058 159843
## 149.167018 125.072796 131.629488 59.197851 112.940716 39.901336 138.801992
## 157233 231489 452313 233665 157818 376459 13375
## 67.952307 135.538692 96.460470 154.503061 119.925364 92.415388 79.944722
## 154265 156078 303231 159873 228330 451634 159186
## 98.069351 150.697159 146.660691 100.720846 131.483233 119.567354 106.212906
## 160564 447672 452613 12504 302206 234624 159256
## 138.919344 138.673044 90.537294 79.868850 233.189629 83.509503 102.146382
## 14460 233287 452861 88065 7550 302313 82600
## 90.728111 179.545471 116.203282 99.012365 52.716003 124.298847 141.594027
## 380306 13488 153493 227880 378323 81976 155452
## 138.772654 92.611826 59.575871 83.981142 132.247276 113.258712 87.440283
## 450962 11853 156191 87661 82514 378030 157381
## 79.487905 142.529110 126.263867 42.490181 144.812534 159.887996 123.152407
## 86485 10930 307771 85202 233889 7496 453337
## 121.265206 125.281105 109.083807 143.472692 74.523734 92.431289 187.824352
## 376076 160307 161341 11390 301389 304303 87441
## 56.091691 112.053933 83.895405 75.743705 77.838728 149.459921 110.352188
## 12175 12033 82301 83227 153765 158059 375572
## 83.807299 141.794058 81.483921 79.377417 213.498142 135.883013 149.313708
## 448806 82280 153375 380151 230950 14546 450602
## 132.311269 174.978572 115.264093 138.502335 115.497965 94.957215 107.062204
## 81692 158659 306889 379968 10750 155530 86633
## 223.173412 215.578077 166.526192 110.606527 128.750923 123.739165 155.609064
## 378686 10144 87286 87895 375523 451283 14519
## 168.387703 101.368954 103.211463 107.139832 104.899067 231.163305 115.958501
## 380780 86239 10984 231862 449495 448715 448977
## 89.286800 141.846949 23.413644 111.574679 106.435722 136.219126 123.246938
## 234530 86190 230114 447347 155626 376579 451819
## 125.149989 147.409800 124.589160 146.795108 94.782884 155.427718 130.438652
## 155900 8505 234613 11832 11081 301246 375987
## 215.079333 76.623082 112.112608 155.697077 93.103028 134.550906 90.625307
## 156259 85655 448836 153902 305415 9743 230054
## 66.915632 113.944293 82.214450 60.753229 57.935170 123.155499 72.738163
## 12519 227962 83739 157490 82456 159012 88116
## 39.529645 59.516151 215.478211 144.563948 20.984209 77.692812 82.131935
## 376549 87170 11435 85129 448698 154709 379618
## 107.169170 168.102789 99.850411 122.283480 93.042100 125.173666 159.523536
## 161267 380753 153467 231484 379211 156236 450978
## 72.115421 104.291899 108.150790 115.188264 115.267635 150.486475 156.407945
## 84773 449829 305946 12507 154311 154975 307420
## 117.220511 162.371465 99.484681 81.674183 41.633516 113.605786 146.693775
## 228741 376605 304583 159573 375743 449387 83565
## 55.720566 168.837476 59.604165 112.426721 174.861220 122.058572 77.722243
## 7664 157200 230665 12813 302409 83416 83964
## 98.040013 131.541909 99.791735 108.761568 105.358771 88.812926 139.182656
## 13483 232794 447864 452049 87163 157204 80604
## 98.245378 90.566631 103.851084 14.062752 121.515277 132.324330 216.736685
## 161272 87121 231993 377133 449641 156429 12311
## 115.528135 61.120534 134.066724 123.980514 78.730325 145.480862 90.830673
## 379397 84236 451645 8988 307325 11919 11403
## 133.655384 125.537855 103.353736 121.025460 113.984262 103.637537 158.123460
## 88019 306940 155528 301789 378048 8841 85602
## 130.495553 160.558871 117.590706 89.190031 39.036312 130.586090 128.980308
## 304529 157296 155829 379034 153627 229223 380392
## 71.661212 103.190822 96.613492 91.207681 124.303231 59.491323 143.267326
## 158726 377495 230878 453110 85888 376196 228775
## 138.254274 77.751488 106.470346 103.727833 100.500047 74.404475 127.875170
## 153559 304567 83140 450085 378923 87254 9513
## 105.499965 125.232342 130.801815 147.335463 124.039190 133.225017 96.904601
## 156960 80462 304074 306048 448446 448106 86335
## 67.140571 111.736823 114.524000 14.949535 176.866025 -20.890842 160.088989
## 230002 447211 305589 8755 13308 448287 10187
## 118.481160 148.824665 105.711306 128.892295 124.537934 74.100615 158.118142
## 80524 377969 153484 11876 229679 229435 80558
## 111.017258 82.542308 106.377046 111.198603 101.474936 104.312309 86.759865
## 11650 82081 82799 155256 80446 159200 8197
## 169.275292 131.111649 97.863985 97.417271 109.378591 86.553500 145.052759
## 153388 88113 155513 158884 230315 86782 306149
## 124.039190 98.425607 118.645770 47.440315 105.499965 104.957743 88.870826
## 380883 7639 381143 9181 158451 229117 233600
## 96.458697 137.514180 145.519569 148.413935 91.877135 113.434496 72.151404
## 231346 379646 228164 85693 452344 160400 160533
## 71.397171 115.526628 78.488725 69.041042 71.282234 1.423090 104.863459
## 307204 450078 84607 10989 155859 234391 81772
## 29.867367 170.388122 127.399117 71.654942 123.929717 128.756553 72.370036
## 377896 153951 231716 229399 302102 81714 155433
## 100.446867 126.641805 132.441682 67.160506 168.361512 140.169628 -49.352658
## 87168 85320 7420 451424 229703 14417 9241
## 81.451019 91.102695 122.406118 167.926761 148.383765 72.115421 224.732809
## 377591 302226 376645 157321 154342 301885 84599
## 140.081020 134.507671 117.275440 170.081025 26.826138 85.818739 70.334360
## 374558 301209 378837 374851 153917 86617 374294
## 97.475786 126.733782 87.092660 74.614238 77.559922 134.338894 147.908544
## 375787 83031 155234 156931 84305 233131 451873
## 59.291275 138.400963 97.638210 101.112410 95.404852 118.353320 113.087405
## 452428 232403 158091 159901 374894 376018 85534
## 183.753668 152.490251 142.241024 37.616999 98.002703 84.796328 131.575448
## 378978 305552 12671 157620 156543 234246 157606
## 145.932398 164.249836 114.905392 149.812452 114.775488 63.225393 125.585679
## 230929 87063 157575 8274 229913 301692 304818
## 114.336317 21.943571 53.746428 68.031716 103.572215 96.603048 104.256047
## 448786 229605 231509 80950 87704 158664 81095
## 122.136791 93.030681 124.596610 149.607087 93.917945 124.231868 93.749658
## 302918 161349 306415 10603 86007 306146 234661
## 72.860925 67.474203 97.074484 65.320677 105.229765 102.525628 38.006356
## 84287 377509 377763 306688 302888 377799 381003
## 92.726419 125.061632 158.382183 47.447297 98.016625 53.491672 119.749336
## 380799 83368 11548 304155 9144 11624 153897
## 57.270101 148.619300 114.615493 104.517674 111.906039 138.919344 181.718505
## 157384 453498 229614 380993 159758 10899 374347
## 110.269492 83.538841 80.226427 75.266318 87.528297 70.543644 111.567885
## 374986 81794 303090 375451 154262 379725 88050
## 98.831329 67.978358 109.919613 41.810872 96.185078 110.133734 72.616394
## 451349 84848 306255 82384 378696 85794 450118
## 123.035055 147.638242 105.030559 99.576431 98.875614 127.804839 93.642249
## 9457 230105 153266 157526 234243 231448 449095
## 90.860011 115.899825 87.586973 177.786347 107.049813 149.583067 171.206789
## 303172 81506 80235 87943 83985 375234 156633
## 72.516866 89.724760 223.026723 109.330671 164.149457 128.666519 101.953624
## 14384 8450 160165 451015 232095 154723 304780
## 89.974427 114.334208 120.619772 86.705525 127.056499 43.792866 111.516003
## 377397 303182 11131 7535 375336 451744 232578
## 130.582149 114.112463 58.150614 118.003603 67.945671 147.012746 107.718543
## 374914 307821 305822 7495 449798 159599 448887
## 86.975308 137.162125 104.103563 152.915260 188.548222 49.467828 100.959745
## 453745 375738 229672 161522 378510 160189 230629
## 115.571612 117.841101 60.774447 96.112102 100.607248 124.880287 137.014939
## 233946 86943 230497 377005 80350 81917 301556
## 132.060289 104.899067 6.790628 142.199004 107.358009 81.492942 115.848920
## 8888 307676 7381 233790 303636 81716 158585
## 52.387534 67.180824 88.500373 106.504100 119.704341 107.373899 52.287412
## 307816 154833 450754 157064 377858 380391 452617
## 119.142640 138.484593 109.972942 116.781113 220.539121 149.460397 151.427280
## 452685 154958 161421 229694 7822 12679 447486
## 114.201283 82.172928 83.734481 117.803555 148.224652 59.256619 90.520672
## 13835 379762 81141 7699 85842 12364 84080
## 94.517146 73.315219 73.058981 133.555715 105.259162 104.329867 136.943646
## 451706 14152 85144 302797 81223 88062 452864
## 137.843543 95.139888 158.500024 104.188311 126.264375 101.095226 101.371704
## 12144 160944 8105 154672 453271 155921 154732
## 116.515172 115.841149 136.462584 131.140987 72.415446 110.545124 50.979091
## 233690 86143 156740 12718 449744 448117 154750
## 103.352339 147.782454 84.125599 155.486394 27.896443 72.626222 71.944889
## 83654 81277 379686 227939 80897 231662 154839
## 132.118965 117.632005 52.020554 114.166528 141.483239 130.743140 75.446329
## 305114 450873 447174 377920 161041 14541 376938
## 141.293932 123.569783 115.586810 60.980685 70.637985 134.016177 225.136112
## 447645 80720 447722 155179 8907 160862 155453
## 89.486861 115.733500 124.156542 110.088147 139.262615 84.521585 186.716667
## 378199 12156 447458 232327 301930 158517 12579
## 125.713883 102.741259 133.391342 155.016987 86.277804 91.735764 104.811053
## 13995 82195 306499 302319 447816 449074 229524
## 148.472610 89.970283 147.225034 150.498326 103.909760 123.168887 104.781715
## 232133 85388 13298 307289 7589 9082 305036
## 124.762935 79.761537 131.199663 158.616887 168.287505 71.587338 159.448873
## 302117 160497 450224 449975 80475 378718 13370
## 109.407929 135.832072 120.672952 113.918371 81.080779 137.814205 101.476619
## 380165 86118 159505 450919 80496 302736 81910
## 115.205417 165.914241 60.578380 72.659077 95.374592 59.893284 100.039568
## 159140 8846 7415 80565 452789 13535 156743
## 103.236384 116.957140 83.543258 95.845788 121.661781 155.633084 86.145893
## 87391 450392 155733 12600 80237 306346 81445
## 107.685544 110.665203 112.104004 103.865594 114.737107 148.183687 73.002297
## 231389 378598 306310 380028 86072 11321 307301
## 164.056125 124.728102 124.701304 112.200622 160.337863 73.890269 130.231213
## 447298 161253 377359 453728 14042 304908 160028
## 76.193476 53.373010 171.074752 214.761531 144.577830 175.348845 69.203859
## 13005 158124 86567 82851 305392 153650 304093
## 26.767462 81.243042 122.947041 108.995793 117.494946 109.006993 132.441682
## 233121 230850 157822 451294 14543 159847 83903
## 91.065376 87.983505 77.764979 20.069526 136.574418 50.096722 103.865594
## 378535 453171 301347 453420 155699 380739 9766
## 61.003832 114.012794 110.621982 158.695001 75.083644 144.974137 130.085612
## 234383 232723 81234 229581 87788 452608 8652
## 73.066133 115.269411 175.213275 45.828499 104.869729 98.630972 111.158452
## 451324 160285 84767 229001 230839 11453 87015
## 28.753889 141.124620 15.614605 122.163845 112.874656 74.925537 94.327354
## 157453 87789 10827 450748 83883 230302 160949
## 111.814594 72.003565 164.545475 142.028294 106.648010 90.603950 80.563164
## 302490 452615 156728 158466 8344 7436 374803
## 128.716267 121.056811 94.553677 117.162598 109.970795 124.420583 97.775971
## 12491 232762 230998 84524 13464 159550 234248
## 144.440843 139.182636 71.097521 142.280975 100.544819 71.485185 112.629036
## 234357 451267 155944 228029 159068 228443 376883
## 57.987545 147.198173 91.468657 103.366850 114.239548 93.647633 92.079234
## 233097 228418 80966 229478 374483 381181 12955
## 107.985668 125.203004 148.942017 122.664873 140.567069 117.942853 119.661323
## 161502 380218 156036 229899 305122 450849 376406
## 149.871128 224.842733 -54.692763 110.043884 123.621813 71.178689 218.381986
## 303218 156645 14338 14140 380621 447629 86490
## 144.264041 106.826910 115.212106 80.084254 79.570252 85.584035 91.824121
## 302168 158551 233702 378925 160680 158298 450290
## 143.023033 117.297047 129.072717 73.002204 82.808660 80.527124 112.088588
## 305059 301937 160924 12963 10344 8757 82071
## 75.379285 96.893988 98.069999 86.945970 105.163108 106.082307 91.372895
## 155631 9139 10933 449746 379247 13497 14109
## 92.394806 100.838198 132.486016 140.194467 112.306319 128.769447 95.257240
## 234415 234376 155250 85134 381020 159971 9591
## 77.794317 154.092330 139.709964 83.690040 74.314903 114.970714 88.975692
## 83666 301931 307750 453302 307225 230293 154660
## 131.558818 160.578236 114.882700 147.819588 160.709310 140.148406 16.891301
## 156739 8789 375928 447995 447215 448598 229234
## 111.212711 121.706517 71.845220 75.094274 144.959223 122.659645 225.340197
## 447888 82715 82946 80449 86044 157202 450096
## 81.601366 162.364853 75.006260 106.153070 107.504699 124.200669 122.636764
## 448535 450450 451844 451460 11973 452739 230033
## 135.141647 149.225694 75.706386 116.546409 111.765620 158.734238 156.501353
## 377968 447810 9620 83273 381222 301976 381289
## 105.151096 108.919059 52.786249 110.380092 112.728705 66.323688 158.352846
## 307040 450227 302539 86544 86015 84882 301497
## 103.237843 116.535347 76.356272 96.713161 89.914552 134.512878 105.036054
## 378528 7539 14035 379720 87842 12496 453550
## 74.153759 88.248084 174.861220 105.380735 120.531758 60.413167 79.732199
## 12905 307423 302880 229722 13420 305048 81872
## 96.334737 45.432004 121.471814 104.752378 96.462910 157.764377 90.527413
## 11889 301313 448972 304644 380216 154881 85010
## 91.388469 110.899906 60.861652 132.726273 154.092330 136.850346 125.798661
## 303653 374554 7830 14307 83763 161310 450610
## 83.865975 115.565712 152.332919 68.031623 87.712305 106.045678 89.250682
## 8736 379881 161031 156574 380839 380501 449794
## 109.055874 131.199663 72.738163 71.162467 142.449840 114.532927 149.519552
## 81288 231420 10519 381177 229249 453598 82185
## 175.477316 108.045803 135.465782 113.577735 90.977362 99.664445 101.298811
## 453746 448132 86463 84715 155547 83136 8414
## 144.284451 128.662909 99.859475 155.691759 109.882782 128.804281 99.860166
## 304459 378108 155401 228504 376032 305001 10568
## 132.823075 -29.328118 134.585514 115.727230 104.312309 94.753546 72.859137
## 158869 82571 233856 85706 87534 158028 376894
## 97.909545 114.846717 179.377498 158.440859 67.708906 137.085050 113.918371
## 450739 453840 85005 12029 233756 228877 233966
## 115.870309 102.249966 115.957516 168.016946 140.218463 133.876006 138.449937
## 376565 375596 7603 376986 448055 81116 228861
## 99.733060 97.805309 101.042363 224.701361 -20.750798 85.348568 61.243045
## 87034 305311 378766 13578 302454 160354 452525
## 88.752246 163.255366 97.550196 139.095371 88.022123 138.625964 119.361298
## 83954 302858 11897 305534 448547 154312 13095
## 135.215975 112.280031 153.537016 129.309298 151.153444 92.355440 86.131661
## 155937 233677 82261 450761 11935 449193 13380
## 98.563711 153.077231 20.896195 133.304348 134.785609 98.939786 105.798840
## 13510 303955 82964 155032 81944 228060 228305
## 134.066115 70.857433 116.914784 102.965047 102.887495 84.096261 123.504462
## 8471 375955 378357 228453 375260 84747 9001
## 147.937882 99.024329 160.646885 225.374056 128.221464 109.351081 90.910134
## 13523 377490 85233 8658 302756 228793 85808
## 90.683983 66.317219 105.840312 217.096283 93.022557 111.099776 132.617710
## 229152 449705 85799 155865 85689 450894 378221
## 103.337512 171.324141 72.675070 70.936039 -11.577724 99.174489 169.187278
## 230406 376602 156489 7568 453257 376581 379989
## 149.577273 -39.107349 131.277868 119.390636 133.299042 85.525267 106.251043
## 234332 11046 303385 450697 156124 161043 449651
## 88.724137 54.891340 119.951656 84.355017 106.785771 113.799555 114.772856
## 233230 231523 154395 304408 380248 83466 13091
## 120.408451 148.084572 155.574408 110.636318 132.396910 32.812703 80.963427
## 84078 14266 82469 450648 230082 302568 452618
## 162.771051 38.131750 132.735061 71.935433 145.754273 97.396861 132.666964
## 449703 228508 453301 8172 380101 306319 10780
## 109.291255 91.853458 109.318715 140.982075 168.258167 101.747306 104.823314
## 8168 234147 379279 13027 159780 153749 87231
## 82.656474 42.952078 110.174727 141.670921 113.871114 75.559697 116.251880
## 381130 83569 82380 87411 80378 306390 233582
## 98.069351 73.694606 73.249168 83.631364 99.564776 145.372880 143.697966
## 230156 80860 157459 228496 453835 376688 84683
## 149.929804 103.660229 47.982118 126.201736 57.892617 139.389776 46.629378
## 380971 448578 376787 231118 7373 156889 80853
## 110.117485 48.929031 -24.479857 116.427908 61.096356 96.642023 58.834234
## 379750 377519 11199 306981 232149 13294 229612
## 91.995637 175.154599 176.455294 81.826274 116.623948 124.692605 82.896673
## 12617 451199 7609 231686 234389 229901 153622
## 181.316166 153.828289 131.589196 219.138173 103.375425 92.699840 120.795799
## 86931 9860 82359 83774 379289 451529 157319
## 145.754273 141.817611 209.990393 118.499534 125.478122 109.230702 135.421341
## 10740 83212 234447 448296 229238 156703 303382
## 134.419547 115.469459 115.821514 139.899938 119.087769 111.548600 127.882982
## 83663 13264 228067 379994 374633 380994 452521
## 88.690627 97.879398 92.520762 110.293513 148.091747 81.527494 113.146081
## 301537 452259 380756 156099 379666 13066 233531
## 130.454560 111.281299 131.101840 89.914552 117.422130 82.378669 128.452226
## 159976 155361 301559 159911 378511 303173 155313
## 169.187278 84.673317 108.791932 132.020321 151.132285 119.838739 217.041739
## 231958 375616 307319 12456 448765 301777 11762
## 114.230620 104.070960 188.230822 115.440121 138.555532 118.833215 164.496194
## 379995 302475 303761 7976 157964 9336 379954
## 107.032275 158.499535 130.631123 135.420356 76.941394 114.659034 55.308717
## 230714 83126 82701 452203 154263 230644 304966
## 100.382695 119.220966 76.848858 104.312309 82.746717 78.087696 83.471894
## 156987 88084 160389 81881 83677 80890 306629
## 65.636435 149.841790 136.703358 182.815604 155.662422 90.683983 102.506882
## 12188 301793 447716 10043 156286 376933 160815
## 108.476844 54.499740 141.656847 93.815056 155.079808 174.732214 128.276198
## 84588 156257 306463 304367 156055 84965 86137
## 141.436218 55.836799 68.749010 172.743957 122.549988 97.258926 147.849868
## 7434 13145 376834 80861 307009 9407 448011
## -74.419644 116.318326 149.460397 82.055576 66.651591 100.158618 90.668785
## 301160 87472 86258 86622 234539 233141 160720
## 92.783344 107.951413 70.828095 58.541354 122.445538 107.049813 128.693336
## 380833 447332 13074 377769 159957 14047 229085
## 133.439887 84.076557 117.741967 126.455982 91.578260 39.178188 122.000257
## 156367 86170 231625 376206 374441 229681 84975
## 130.407539 133.185344 93.100776 117.338626 65.418186 98.930997 138.895324
## 80338 158704 86260 377704 450907 8898 86506
## 81.410142 65.564876 144.505272 82.231604 151.367796 98.450743 76.875427
## 81695 452011 233422 232655 161451 450319 305903
## 147.196491 168.404097 187.883028 98.010675 82.466307 82.051192 75.219373
## 12064 448531 450203 302905 377539 306049 234286
## 97.358595 110.870569 117.033285 98.480014 107.198508 87.017897 74.887758
## 82123 13073 12975 9152 85858 449352 156000
## 69.943775 -21.825399 96.669522 117.152327 118.175213 177.628062 113.907903
## 374878 374341 453736 83544 374646 14363 380303
## -4.581683 71.485185 104.370860 43.454092 130.935622 85.808944 82.891178
## 11668 156595 303371 12558 154495 232910 448457
## 202.381181 95.315916 120.939459 143.883423 82.368413 101.504409 125.888300
## 156591 374845 154639 376657 453155 302655 234441
## 164.290829 104.987081 104.760257 224.167961 84.566043 104.854531 129.778705
## 10756 157788 159478 82408 231687 451735 14361
## 105.563408 164.077568 83.714868 139.057249 225.310859 124.068528 124.645584
## 447846 87736 159033 452456 229915 85977 158370
## 119.397281 51.552814 123.123069 137.990108 83.690848 147.527151 148.025896
## 306799 86857 154144 155861 302734 87460 301952
## 102.119314 154.268357 94.108435 116.130161 226.732697 113.439901 156.828352
## 452190 302487 375314 80513 8245 450802 380599
## 116.157047 148.824665 116.734621 109.912120 89.094389 107.675717 77.530465
## 8760 228870 86333 82672 303408 379215 153433
## 129.309298 62.138433 40.194715 162.599556 95.201491 78.433296 117.363454
## 452035 12738 10025 302428 230517 451939 83710
## 157.625485 132.343038 123.035065 82.689142 140.111640 3.454565 153.427260
## 11155 10801 377849 155762 380873 11350 449916
## 152.657829 146.922628 78.864622 87.340615 157.541218 58.556928 118.997825
## 11955 452076 158386 8307 452919 304571 84662
## 94.320976 132.685280 155.105001 120.212473 90.390604 98.010675 90.654645
## 157527 155753 85476 86888 11885 379300 84104
## 178.212533 90.354620 97.333108 70.671905 128.593826 68.925500 83.597517
## 451062 379529 155117 234168 228808 85191 159708
## 169.216616 142.849950 99.757777 144.231093 106.433716 142.380338 60.219075
## 155806 378375 155162 230689 158165 448727 154715
## 124.850949 165.998110 120.776632 127.933846 4.740739 65.138314 71.357953
## 449784 82382 159218 81077 303201 375099 452764
## 107.794316 85.850390 86.905555 142.967301 93.427814 118.660281 215.631966
## 84935 302956 231714 377432 450157 155744 12978
## 158.499535 98.078278 141.132492 130.656125 118.038229 171.668156 109.732474
## 228951 156037 302728 233642 228903 449895 451041
## 77.722150 115.410783 144.730042 105.722961 130.407539 109.838263 133.831411
## 376582 160144 379821 161269 87217 160293 86674
## 52.082046 83.459107 218.846074 221.604074 109.239630 146.130038 123.387110
## 87761 303104 229277 452824 232086 233767 12838
## 98.675745 71.367058 187.734942 164.422063 67.228745 129.945030 119.782442
## 159042 375741 85607 86744 11797 452631 374872
## 94.371297 224.754719 171.069368 105.288441 155.457056 120.942489 133.225017
## 448646 379131 231134 9431 379883 376403 376258
## 106.939785 133.313031 141.868307 117.040737 138.467518 99.091793 125.015322
## 14511 449447 231149 13208 376577 9330 380510
## 70.554553 110.811893 219.578242 73.325014 135.078988 76.963875 93.947283
## 234379 449359 449768 304596 83073 80331 307248
## 128.858424 104.429660 161.377066 84.247460 87.553139 120.649109 70.099657
## 87597 161439 234656 153663 11542 81869 156792
## 120.030704 35.162602 123.680489 82.246800 47.486699 92.294986 109.230702
## 376283 452245 231515 306859 82001 375236 86010
## 92.553057 148.097906 116.269563 123.005717 149.615266 113.322621 109.025336
## 230943 228764 156896 453724 379194 452457 232552
## 115.264093 -40.608795 64.894373 161.095032 132.187343 123.595213 109.202012
## 450777 158588 377411 302723 153400 86089 160883
## -11.137656 103.774699 57.665701 123.213456 130.684464 121.177192 123.272496
## 379090 302129 86755 377441 87396 307386 84169
## 138.371626 59.579336 145.345828 76.424636 105.074320 98.734420 73.606592
## 449775 228357 449987 303856 304921 374988 229150
## 131.766910 162.423529 143.282657 129.548677 94.212350 85.596051 163.551628
## 84663 379349 157534 305469 231089 82956 379819
## 164.032105 145.482411 72.855607 64.839615 73.442365 97.646965 91.238657
## 449534 448935 375717 304731 10772 14158 85775
## 136.668698 90.857252 68.729691 135.215975 138.832651 121.906460 111.535056
## 161082 377328 155957 154985 87716 374629 232517
## 91.329417 122.872705 151.489176 40.929406 23.650853 128.716267 129.302276
## 84219 380749 453653 81828 377546 451614 160598
## 222.767999 147.042084 123.628459 101.286827 154.582237 134.046715 215.636753
## 7816 157421 9691 304770 81122 233881 377413
## 115.162824 34.019498 120.766461 139.042013 94.650886 99.041703 76.192443
## 303918 229437 447724 85017 9109 84346 301863
## 128.575985 83.572595 134.851226 122.666102 70.691795 129.613998 105.291820
## 452767 380912 450623 7899 13782 452871 13456
## 141.412665 114.075192 43.599348 105.016419 93.984660 135.806623 80.938008
## 306022 232102 375105 81175 375985 233063 85647
## 87.925367 154.657745 57.569918 92.708444 22.246982 87.440283 142.407123
## 11736 153843 10673 84898 375389 374477 160912
## 155.545070 80.904752 130.759594 67.888995 57.275418 57.387452 131.452585
## 13605 305951 84566 160765 449036 13295 7863
## 127.252428 67.619768 125.209075 88.394774 84.060653 136.013417 122.465732
## 87877 86166 160895 450033 156104 160718 81086
## 168.923237 124.244555 65.271404 213.170637 104.355787 95.937906 115.923667
## 87767 13125 231653 85304 375038 9595 87553
## 91.124052 126.808037 73.555207 120.766461 224.960085 225.026188 81.461742
## 81392 451374 158047 81515 153519 380550 304366
## 126.504397 168.185484 89.974427 12.933771 105.810974 90.119917 125.576121
## 304377 9064 378073 158940 380022 227841 12002
## 115.894329 81.630611 131.830904 121.374249 104.338503 144.791531 139.554347
## 304602 450489 158881 154684 9521 451147 448799
## 107.021844 75.295656 92.988059 90.886590 127.755001 63.467740 135.353299
## 86446 378317 7499 154659 159096 379777 161093
## 60.474724 180.661332 160.402269 59.056572 125.827999 107.431206 155.222353
## 8398 86001 9947 13597 8402 229336 9471
## 163.507184 115.987839 149.302112 137.135994 120.146873 110.224751 144.769313
## 307463 303301 307758 8704 450579 377548 379802
## 69.697108 94.568914 26.843821 156.084254 134.462963 106.485746 103.677912
## 155828 160072 158458 380862 229278 158416 374326
## 109.921047 82.891178 71.279819 84.409276 150.742713 123.328434 133.371952
## 84906 10154 304890 448330 302440 8594 160473
## 138.537951 81.102528 64.847941 4.518710 135.095867 137.726191 119.925364
## 452589 154916 453566 453173 231286 83337 8625
## 132.950937 121.478566 114.970714 81.098112 89.909542 130.479098 111.809757
## 304249 452699 13542 233331 12638 376869 11100
## 115.592212 115.518432 129.621209 112.805063 68.685479 164.173477 155.222353
## 379372 376009 304338 304116 452574 230268 159545
## 151.272156 99.927085 144.489817 148.589962 117.798237 47.564648 152.530832
## 229535 161425 376778 232700 306371 304010 154423
## 82.055576 13.109799 101.046236 107.548557 136.008099 85.554605 142.676296
## 377710 8072 306740 374463 155676 378483 11655
## 93.020510 86.236667 168.332174 109.096284 104.811053 126.724345 166.208793
## 159926 161488 380370 154590 86392 12146 301904
## 87.880352 72.954512 57.240763 96.548993 141.510158 138.286836 73.105414
## 375850 449254 378197 12275 447285 229216 379593
## 171.904436 103.842778 121.812615 72.248346 -5.305428 128.457544 91.173025
## 10380 378289 453516 8978 87747 13594 448361
## 71.837118 169.304630 125.073998 137.220801 96.422751 155.486394 84.012757
## 82431 227968 154580 155201 228062 301131 81508
## 141.652703 167.342046 85.114536 135.777285 85.689732 8.072164 122.885607
## 160105 10455 230783 380368 8521 302231 154400
## 74.900709 88.782812 105.740164 144.401803 68.829361 70.936039 41.516164
## 376389 231469 155163 229213 161447 11017 81252
## 130.044347 77.501479 141.133734 158.352846 -54.169690 121.519236 120.248081
## 227917 82223 450449 155027 301716 160957 307162
## 137.968934 147.360127 169.221934 -55.855363 93.243173 70.798758 84.210528
## 153288 10549 448079 85787 232991 232011 234060
## 44.044226 135.064846 74.925537 69.278195 113.518164 126.821287 225.369535
## 83770 228316 451479 233965 8562 231536 451622
## 72.086083 127.725663 92.699840 68.002285 225.172878 149.695101 120.707785
## 451993 159704 228435 11386 10964 227859 449407
## 106.963805 220.811950 134.221543 116.193204 219.105888 73.148893 220.631136
## 233646 450142 375066 377927 154494 80376 81068
## 132.467657 144.548492 132.232347 96.658697 78.387220 132.236317 132.364627
## 233828 85640 10274 153933 10377 87797 84394
## 189.164318 90.948024 155.867787 220.987978 89.885214 105.976018 86.366364
## 232457 377675 304688 233833 374782 154678 303392
## 135.489719 115.000581 39.792912 228.814967 83.425204 51.110953 162.306177
## 453674 302464 230110 86348 449111 156748 8312
## 80.377633 124.762935 98.949420 163.445347 68.325095 132.255024 157.834465
## 378918 154871 302382 305523 377010 157367 154310
## 165.562186 126.604924 137.308815 147.644503 139.895746 136.554957 44.308360
## 8265 154479 14202 161025 85939 158022 229664
## 91.642432 63.856401 132.220882 144.563948 98.069351 91.167530 124.317371
## 448419 301493 9698 451173 377766 379628 158239
## 62.638216 96.877533 122.976379 95.892972 145.062692 132.089627 112.459840
## 450366 10192 303306 230907 87177 85563 378239
## 110.849499 97.292354 105.133770 118.630975 166.320827 83.708598 79.937564
## 232251 448807 451298 234574 303467 160372 80668
## 29.272269 158.876347 149.671081 108.280837 99.193914 130.378201 75.970428
## 230140 87724 159738 13820 159737 158555 8911
## 123.181745 139.620324 39.558983 58.121276 115.712143 71.133130 111.990621
## 230355 155813 304171 154382 447429 307480 301212
## 122.461974 99.051642 123.035055 155.926463 110.733581 81.336082 114.188822
## 450515 160071 231742 379911 231151 7548 157269
## 115.381445 131.884262 158.194560 111.149524 189.222994 47.081102 62.979944
## 378112 158610 87409 451122 227949 451359 13067
## 169.128603 110.754640 84.096261 189.017628 105.044636 161.782512 109.853444
## 374802 86228 379346 376228 228763 85100 87786
## 115.117404 110.645567 113.292771 179.670877 73.607613 50.682379 88.751937
## 87346 10641 451408 159969 376315 233368 155264
## 127.678847 169.245954 130.295506 221.017316 94.036322 96.522833 138.409003
## 7747 302426 157328 9454 160476 84722 160518
## 127.955963 135.716008 65.218138 172.157199 151.835215 144.158535 54.319780
## 12284 375528 83300 9974 11998 11771 85840
## 71.660917 174.925858 111.105272 125.999825 117.099413 116.212630 90.537294
## 83877 305966 7951 451372 83243 10311 159643
## 145.541940 121.427263 78.029020 102.935709 126.812359 130.684464 140.361161
## 378452 153846 13108 11905 375715 82621 12425
## 133.498997 63.156241 115.146742 68.389200 69.255356 167.723439 117.859109
## 82295 379133 305527 13255 86181 157316 450927
## 87.599799 148.990991 159.546100 132.186569 137.520826 158.440859 221.393921
## 229450 85047 447600 450428 85993 378229 449815
## 112.680967 137.191463 129.038984 62.138433 94.546484 164.290829 141.548291
## 229998 448218 306163 11664 8194 14196 88022
## 159.026869 49.635141 57.270101 120.531758 179.289484 120.473082 102.598106
## 160061 7840 450384 160299 233831 449264 12477
## 140.325425 104.492134 81.779880 71.326840 122.874601 120.732318 94.606857
## 375640 161055 82687 301552 375238 453137 379538
## 164.437518 176.855394 147.511220 90.537294 46.138762 111.889656 29.477634
## 451582 447462 158645 87154 378986 160715 81037
## 146.460736 81.491510 82.808106 91.564589 135.661362 91.035264 85.471100
## 82804 154694 452218 157720 374624 153643 86198
## 93.073690 127.898313 112.045235 118.312643 42.398200 91.388469 122.917703
## 84791 232289 374507 305083 87712 306948 13141
## 134.203200 144.275886 113.703502 218.714778 23.944232 129.758866 28.682222
## 155887 228654 304515 83807 229996 301419 306410
## 83.748623 74.628698 110.691814 79.461512 134.456246 171.940237 100.035508
## 452996 14126 158400 87273 231271 155621 11861
## 102.590950 85.977444 233.415515 66.930856 84.462456 71.250481 77.955770
## 154008 161216 447422 156545 13641 304636 452513
## 93.143639 143.707395 103.963320 152.595465 94.487808 141.481993 88.896652
## 81809 231777 9019 9487 304371 305970 155402
## 78.886529 68.349923 89.959463 89.229383 166.584868 113.322109 143.634712
## 307501 155886 229104 87711 374720 156049 159113
## 72.826176 92.289109 124.394469 106.939750 139.621315 123.005717 57.346459
## 449072 87306 229074 302202 303505 11180 9111
## 98.444473 141.269893 125.085653 79.444137 56.389835 144.945340 225.760843
## 447235 304337 159650 234513 159500 12446 9781
## 114.853362 109.289378 155.310367 104.418006 126.690686 99.435264 120.042715
## 305890 306575 153588 306484 377256 379428 450934
## 109.882782 106.397733 154.338215 79.790874 153.185433 75.810577 86.138273
## 377314 234185 448466 12792 80262 82810 301634
## 127.398543 111.266875 71.604769 81.392447 110.049380 92.295264 111.648810
## 306030 231565 451279 307401 453377 159201 84893
## 119.417781 147.303870 65.476862 113.821643 155.064008 103.689567 123.599253
## 161391 161397 161416 306010 306687 232349 83445
## 58.580604 99.321179 103.177708 92.523720 103.513539 114.699221 84.843849
## 303155 450065 231998 80918 304411 155790 159561
## 94.271025 101.329930 42.556545 56.859370 92.205513 86.372976 98.699587
## 377472 450455 304184 154351 447182 13962 154728
## 86.745101 78.747270 156.857084 138.166763 92.611733 155.642929 123.666725
## 380298 230171 307415 161305 451605 301838 154752
## 106.294318 47.065904 87.234918 90.449280 156.243572 67.688589 24.504980
## 8804 158531 379706 306214 158084 305029 307412
## 135.861410 89.016071 104.752378 98.338514 133.634784 169.409891 137.181027
## 377739 451296 157053 303357 233408 449482 376816
## 151.241458 135.596011 124.590340 117.632005 108.479496 138.143110 152.540477
## 302281 10033 14375 453557
## 105.016419 61.159543 91.548923 92.476834
#our model is 0.9067 effective at predicting our data
##model 2 with logwage removed##
md2 <- lm(wage~age+maritl+race+education,data = WAGES)
md2
##
## Call:
## lm(formula = wage ~ age + maritl + race + education, data = WAGES)
##
## Coefficients:
## (Intercept) age
## 58.7874 0.3262
## maritl2. Married maritl3. Widowed
## 18.1584 1.7819
## maritl4. Divorced maritl5. Separated
## 4.6329 12.7795
## race2. Black race3. Asian
## -4.5226 -4.1096
## race4. Other education2. HS Grad
## -7.5714 11.1453
## education3. Some College education4. College Grad
## 24.1237 39.0124
## education5. Advanced Degree
## 63.5153
summary(md2)
##
## Call:
## lm(formula = wage ~ age + maritl + race + education, data = WAGES)
##
## Residuals:
## Min 1Q Median 3Q Max
## -114.041 -19.085 -3.404 14.344 219.768
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 58.78739 3.22523 18.227 < 2e-16 ***
## age 0.32621 0.06292 5.184 2.31e-07 ***
## maritl2. Married 18.15842 1.77346 10.239 < 2e-16 ***
## maritl3. Widowed 1.78188 8.27409 0.215 0.8295
## maritl4. Divorced 4.63286 2.98444 1.552 0.1207
## maritl5. Separated 12.77950 5.00898 2.551 0.0108 *
## race2. Black -4.52263 2.20435 -2.052 0.0403 *
## race3. Asian -4.10959 2.68946 -1.528 0.1266
## race4. Other -7.57144 5.85995 -1.292 0.1964
## education2. HS Grad 11.14532 2.43914 4.569 5.09e-06 ***
## education3. Some College 24.12369 2.56833 9.393 < 2e-16 ***
## education4. College Grad 39.01242 2.55631 15.261 < 2e-16 ***
## education5. Advanced Degree 63.51534 2.78025 22.845 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 35.18 on 2987 degrees of freedom
## Multiple R-squared: 0.2921, Adjusted R-squared: 0.2893
## F-statistic: 102.7 on 12 and 2987 DF, p-value: < 2.2e-16
anova(md2)
## Analysis of Variance Table
##
## Response: wage
## Df Sum Sq Mean Sq F value Pr(>F)
## age 1 199870 199870 161.503 < 2.2e-16 ***
## maritl 4 222572 55643 44.962 < 2.2e-16 ***
## race 3 39689 13230 10.690 5.481e-07 ***
## education 4 1063370 265843 214.812 < 2.2e-16 ***
## Residuals 2987 3696585 1238
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
confint(md2)
## 2.5 % 97.5 %
## (Intercept) 52.4634903 65.1112868
## age 0.2028345 0.4495942
## maritl2. Married 14.6810954 21.6357435
## maritl3. Widowed -14.4416169 18.0053716
## maritl4. Divorced -1.2189034 10.4846220
## maritl5. Separated 2.9581048 22.6008922
## race2. Black -8.8448315 -0.2004207
## race3. Asian -9.3829648 1.1637899
## race4. Other -19.0613793 3.9185061
## education2. HS Grad 6.3627431 15.9278909
## education3. Some College 19.0878153 29.1595737
## education4. College Grad 34.0001075 44.0247271
## education5. Advanced Degree 58.0639406 68.9667381
##this model is 0.2893 ,which is significantly lower that the previous model,
#this implies that removing Logwage as a factor will reduce the predictive strength of our model drastically
##model 3 with logwage included but race removed##
md3<-lm(wage~age+maritl+education+logwage, data = WAGES)
md3
##
## Call:
## lm(formula = wage ~ age + maritl + education + logwage, data = WAGES)
##
## Coefficients:
## (Intercept) age
## -402.6294 -0.0307
## maritl2. Married maritl3. Widowed
## -1.2165 -3.5727
## maritl4. Divorced maritl5. Separated
## -1.3075 -2.3145
## education2. HS Grad education3. Some College
## -2.0049 -2.9390
## education4. College Grad education5. Advanced Degree
## -1.2231 4.6452
## logwage
## 111.2045
summary(md3)
##
## Call:
## lm(formula = wage ~ age + maritl + education + logwage, data = WAGES)
##
## Residuals:
## Min 1Q Median 3Q Max
## -13.892 -5.414 -3.638 0.509 94.577
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -402.62942 3.46603 -116.164 < 2e-16 ***
## age -0.03070 0.02282 -1.345 0.17869
## maritl2. Married -1.21649 0.65304 -1.863 0.06259 .
## maritl3. Widowed -3.57265 2.99468 -1.193 0.23296
## maritl4. Divorced -1.30754 1.07907 -1.212 0.22571
## maritl5. Separated -2.31449 1.81629 -1.274 0.20266
## education2. HS Grad -2.00486 0.88610 -2.263 0.02373 *
## education3. Some College -2.93896 0.94728 -3.103 0.00194 **
## education4. College Grad -1.22307 0.96478 -1.268 0.20500
## education5. Advanced Degree 4.64523 1.08439 4.284 1.9e-05 ***
## logwage 111.20453 0.78942 140.869 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 12.74 on 2989 degrees of freedom
## Multiple R-squared: 0.9071, Adjusted R-squared: 0.9068
## F-statistic: 2919 on 10 and 2989 DF, p-value: < 2.2e-16
anova(md3)
## Analysis of Variance Table
##
## Response: wage
## Df Sum Sq Mean Sq F value Pr(>F)
## age 1 199870 199870 1231.46 < 2.2e-16 ***
## maritl 4 222572 55643 342.83 < 2.2e-16 ***
## education 4 1093761 273440 1684.76 < 2.2e-16 ***
## logwage 1 3220761 3220761 19844.17 < 2.2e-16 ***
## Residuals 2989 485122 162
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
confint(md3)
## 2.5 % 97.5 %
## (Intercept) -409.42546038 -395.83337538
## age -0.07544478 0.01404968
## maritl2. Married -2.49693682 0.06395657
## maritl3. Widowed -9.44450195 2.29919629
## maritl4. Divorced -3.42333349 0.80825633
## maritl5. Separated -5.87578882 1.24680655
## education2. HS Grad -3.74228839 -0.26742640
## education3. Some College -4.79633854 -1.08157643
## education4. College Grad -3.11476250 0.66863199
## education5. Advanced Degree 2.51901032 6.77145856
## logwage 109.65668060 112.75238844
## model 3 is 0.9068 which is slightly above that of model one
##this implies that race is not that significant factor in predicting wages as much as logwage is.
##model 4 with maritl status removed##
md4<-lm(wage~age+education+logwage,data=WAGES)
md4
##
## Call:
## lm(formula = wage ~ age + education + logwage, data = WAGES)
##
## Coefficients:
## (Intercept) age
## -401.61475 -0.04985
## education2. HS Grad education3. Some College
## -1.93794 -2.81696
## education4. College Grad education5. Advanced Degree
## -1.08399 4.81539
## logwage
## 110.92492
summary(md4)
##
## Call:
## lm(formula = wage ~ age + education + logwage, data = WAGES)
##
## Residuals:
## Min 1Q Median 3Q Max
## -13.253 -5.413 -3.703 0.464 93.886
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -401.61475 3.40112 -118.083 < 2e-16 ***
## age -0.04985 0.02072 -2.406 0.01621 *
## education2. HS Grad -1.93794 0.88411 -2.192 0.02846 *
## education3. Some College -2.81696 0.94384 -2.985 0.00286 **
## education4. College Grad -1.08399 0.96088 -1.128 0.25936
## education5. Advanced Degree 4.81539 1.07932 4.462 8.44e-06 ***
## logwage 110.92492 0.76853 144.333 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 12.74 on 2993 degrees of freedom
## Multiple R-squared: 0.907, Adjusted R-squared: 0.9068
## F-statistic: 4862 on 6 and 2993 DF, p-value: < 2.2e-16
## model 4 is 0.9068 which is =model 3 but > model 1 and 2 making it the better mdel so far since it predicts the same accuracy
# with less variable to compute
##model 5 with race age education and logwage##
md5<-lm(wage~logwage+education,data = WAGES)
summary(md5)
##
## Call:
## lm(formula = wage ~ logwage + education, data = WAGES)
##
## Residuals:
## Min 1Q Median 3Q Max
## -12.457 -5.467 -3.776 0.398 93.155
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -402.0169 3.3997 -118.250 < 2e-16 ***
## logwage 110.5426 0.7525 146.896 < 2e-16 ***
## education2. HS Grad -1.9120 0.8847 -2.161 0.0308 *
## education3. Some College -2.6807 0.9429 -2.843 0.0045 **
## education4. College Grad -0.9899 0.9609 -1.030 0.3030
## education5. Advanced Degree 4.8695 1.0799 4.509 6.76e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 12.75 on 2994 degrees of freedom
## Multiple R-squared: 0.9068, Adjusted R-squared: 0.9066
## F-statistic: 5824 on 5 and 2994 DF, p-value: < 2.2e-16
md5
##
## Call:
## lm(formula = wage ~ logwage + education, data = WAGES)
##
## Coefficients:
## (Intercept) logwage
## -402.0169 110.5426
## education2. HS Grad education3. Some College
## -1.9120 -2.6807
## education4. College Grad education5. Advanced Degree
## -0.9899 4.8695
##removing Age as a factor reduces our predictive power from 0.9068 to 0.9066
## making model 4 the better model since its predictive power is 0.9068 with fewer variables
##model 6 wage as a function of log wage
md6<-lm(wage~logwage,data=WAGES)
md6
##
## Call:
## lm(formula = wage ~ logwage, data = WAGES)
##
## Coefficients:
## (Intercept) logwage
## -413.2 112.8
summary(md6)
##
## Call:
## lm(formula = wage ~ logwage, data = WAGES)
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.991 -6.422 -4.445 0.709 94.909
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -413.164 3.136 -131.7 <2e-16 ***
## logwage 112.780 0.672 167.8 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 12.94 on 2998 degrees of freedom
## Multiple R-squared: 0.9038, Adjusted R-squared: 0.9038
## F-statistic: 2.817e+04 on 1 and 2998 DF, p-value: < 2.2e-16
anova(md6)
## Analysis of Variance Table
##
## Response: wage
## Df Sum Sq Mean Sq F value Pr(>F)
## logwage 1 4719715 4719715 28166 < 2.2e-16 ***
## Residuals 2998 502371 168
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##making a prediction using logwage as the main factor##
predict(md6,list(logwage=7))
## 1
## 376.2964
##an individual with a log wage of 7 earns around $ 376 296
## it should be noted that logwage and education are directly proportional so the higher the log wage the higher the level of education
min(WAGES$logwage)
## [1] 3
# the minimum log wage is 3 for those who did not graduate from high school
max(WAGES$logwage)
## [1] 5.763128
# the max is 5.76
predict(md6,list(logwage=5.76))
## 1
## 236.4491
#which gives us an estimate of around $ 236 449 of which is acceptable since in our data
# the box plot show that the max is around $200 000 with a few outliers attributed to
# the difference in ages,marital status, education and race but logwage being the main driving force behind individual earnings
#based on the graphs we can estimate that an individual with a logwage of 5.76
# is likely to be from 30 years of age
##plot of logwage and education race as a selector
ggplot(WAGES,aes(x=logwage,
y=education, col=race))+
geom_point()+
labs(x="Logwage",y="Education",title="Logwage vs Education :per Race" )
#It is clear that the higher the Logwage the higher the wage and most whites have,
#a higher logwage with a few exceptions of blacks having the highest logwages in the group as well as the highest wages
#As expected the higher your Education Level the higher your Logwage and thus, the higher the wage
##plot of wage and education with Log wage as a selector
ggplot(WAGES,aes(x=WAGES$wage,
y=WAGES$education,
col=logwage))+
geom_point()+
labs(x="Wage",
y="Education",
title="Wage as a function of Education:logwage as a selector")
## Warning: Use of `WAGES$wage` is discouraged. Use `wage` instead.
## Warning: Use of `WAGES$education` is discouraged. Use `education` instead.
# the lowest wages have a logwage of about 3 and are between the amounts of $20 000 to $100 000
#with the highest logwage being 5 and associated with the wages from $150 000 till above $300 000 and log wage is directly,
#proportional to Education levels