HW 1

Some questions on this homework involve random sampling, and so each student may obtain slightly different results. Because of this, I need to see both your code and resulting output. For simplicity and to ensure that your output matches your textual explanations and answers, I will accept copies of your output placed in Microsoft Word for this assignment. However if you feel more comfortable doing so, you can also alternatively submit an HTML document produced in R Markdown. Just be sure that the HTML document displays your output and that your written answers match the displayed output. Be sure to use either R or R Markdown to answer all of the following questions.

Part 1: Association Analysis

  1. Load the bob_ross csv file into R. This data contains information about various paintings done by Bob Ross. Bob Ross was an American artist know for his TV show called The Joy of Painting. This dataset lists possible elements of each painting, such as a barn or tree, and whether they were present or absent.
bob_ross <- read.csv("C:/Users/raze1/OneDrive/Desktop/UIndy/MSDA 622/Homework/Homework 1/bob_ross.csv")
summary(bob_ross)
##    EPISODE             TITLE            APPLE_FRAME       AURORA_BOREALIS   
##  Length:403         Length:403         Min.   :0.000000   Min.   :0.000000  
##  Class :character   Class :character   1st Qu.:0.000000   1st Qu.:0.000000  
##  Mode  :character   Mode  :character   Median :0.000000   Median :0.000000  
##                                        Mean   :0.002481   Mean   :0.004963  
##                                        3rd Qu.:0.000000   3rd Qu.:0.000000  
##                                        Max.   :1.000000   Max.   :1.000000  
##       BARN             BEACH            BOAT              BRIDGE       
##  Min.   :0.00000   Min.   :0.000   Min.   :0.000000   Min.   :0.00000  
##  1st Qu.:0.00000   1st Qu.:0.000   1st Qu.:0.000000   1st Qu.:0.00000  
##  Median :0.00000   Median :0.000   Median :0.000000   Median :0.00000  
##  Mean   :0.04218   Mean   :0.067   Mean   :0.004963   Mean   :0.01737  
##  3rd Qu.:0.00000   3rd Qu.:0.000   3rd Qu.:0.000000   3rd Qu.:0.00000  
##  Max.   :1.00000   Max.   :1.000   Max.   :1.000000   Max.   :1.00000  
##     BUILDING            BUSHES           CABIN            CACTUS        
##  Min.   :0.000000   Min.   :0.0000   Min.   :0.0000   Min.   :0.000000  
##  1st Qu.:0.000000   1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.000000  
##  Median :0.000000   Median :0.0000   Median :0.0000   Median :0.000000  
##  Mean   :0.002481   Mean   :0.2978   Mean   :0.1712   Mean   :0.009926  
##  3rd Qu.:0.000000   3rd Qu.:1.0000   3rd Qu.:0.0000   3rd Qu.:0.000000  
##  Max.   :1.000000   Max.   :1.0000   Max.   :1.0000   Max.   :1.000000  
##   CIRCLE_FRAME          CIRRUS            CLIFF             CLOUDS      
##  Min.   :0.000000   Min.   :0.00000   Min.   :0.00000   Min.   :0.0000  
##  1st Qu.:0.000000   1st Qu.:0.00000   1st Qu.:0.00000   1st Qu.:0.0000  
##  Median :0.000000   Median :0.00000   Median :0.00000   Median :0.0000  
##  Mean   :0.004963   Mean   :0.06948   Mean   :0.01985   Mean   :0.4442  
##  3rd Qu.:0.000000   3rd Qu.:0.00000   3rd Qu.:0.00000   3rd Qu.:1.0000  
##  Max.   :1.000000   Max.   :1.00000   Max.   :1.00000   Max.   :1.0000  
##     CONIFER          CUMULUS         DECIDUOUS       DIANE_ANDRE      
##  Min.   :0.0000   Min.   :0.0000   Min.   :0.0000   Min.   :0.000000  
##  1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.000000  
##  Median :1.0000   Median :0.0000   Median :1.0000   Median :0.000000  
##  Mean   :0.5261   Mean   :0.2134   Mean   :0.5633   Mean   :0.002481  
##  3rd Qu.:1.0000   3rd Qu.:0.0000   3rd Qu.:1.0000   3rd Qu.:0.000000  
##  Max.   :1.0000   Max.   :1.0000   Max.   :1.0000   Max.   :1.000000  
##       DOCK          DOUBLE_OVAL_FRAME       FARM              FENCE        
##  Min.   :0.000000   Min.   :0.000000   Min.   :0.000000   Min.   :0.00000  
##  1st Qu.:0.000000   1st Qu.:0.000000   1st Qu.:0.000000   1st Qu.:0.00000  
##  Median :0.000000   Median :0.000000   Median :0.000000   Median :0.00000  
##  Mean   :0.002481   Mean   :0.002481   Mean   :0.002481   Mean   :0.05955  
##  3rd Qu.:0.000000   3rd Qu.:0.000000   3rd Qu.:0.000000   3rd Qu.:0.00000  
##  Max.   :1.000000   Max.   :1.000000   Max.   :1.000000   Max.   :1.00000  
##       FIRE          FLORIDA_FRAME         FLOWERS             FOG         
##  Min.   :0.000000   Min.   :0.000000   Min.   :0.00000   Min.   :0.00000  
##  1st Qu.:0.000000   1st Qu.:0.000000   1st Qu.:0.00000   1st Qu.:0.00000  
##  Median :0.000000   Median :0.000000   Median :0.00000   Median :0.00000  
##  Mean   :0.002481   Mean   :0.002481   Mean   :0.02978   Mean   :0.05707  
##  3rd Qu.:0.000000   3rd Qu.:0.000000   3rd Qu.:0.00000   3rd Qu.:0.00000  
##  Max.   :1.000000   Max.   :1.000000   Max.   :1.00000   Max.   :1.00000  
##      FRAMED           GRASS            GUEST         HALF_CIRCLE_FRAME 
##  Min.   :0.0000   Min.   :0.0000   Min.   :0.00000   Min.   :0.000000  
##  1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.00000   1st Qu.:0.000000  
##  Median :0.0000   Median :0.0000   Median :0.00000   Median :0.000000  
##  Mean   :0.1315   Mean   :0.3524   Mean   :0.05459   Mean   :0.002481  
##  3rd Qu.:0.0000   3rd Qu.:1.0000   3rd Qu.:0.00000   3rd Qu.:0.000000  
##  Max.   :1.0000   Max.   :1.0000   Max.   :1.00000   Max.   :1.000000  
##  HALF_OVAL_FRAME        HILLS              LAKE            LAKES  
##  Min.   :0.000000   Min.   :0.00000   Min.   :0.0000   Min.   :0  
##  1st Qu.:0.000000   1st Qu.:0.00000   1st Qu.:0.0000   1st Qu.:0  
##  Median :0.000000   Median :0.00000   Median :0.0000   Median :0  
##  Mean   :0.002481   Mean   :0.04467   Mean   :0.3548   Mean   :0  
##  3rd Qu.:0.000000   3rd Qu.:0.00000   3rd Qu.:1.0000   3rd Qu.:0  
##  Max.   :1.000000   Max.   :1.00000   Max.   :1.0000   Max.   :0  
##    LIGHTHOUSE            MILL               MOON             MOUNTAIN    
##  Min.   :0.000000   Min.   :0.000000   Min.   :0.000000   Min.   :0.000  
##  1st Qu.:0.000000   1st Qu.:0.000000   1st Qu.:0.000000   1st Qu.:0.000  
##  Median :0.000000   Median :0.000000   Median :0.000000   Median :0.000  
##  Mean   :0.002481   Mean   :0.004963   Mean   :0.007444   Mean   :0.397  
##  3rd Qu.:0.000000   3rd Qu.:0.000000   3rd Qu.:0.000000   3rd Qu.:1.000  
##  Max.   :1.000000   Max.   :1.000000   Max.   :1.000000   Max.   :1.000  
##    MOUNTAINS          NIGHT            OCEAN           OVAL_FRAME     
##  Min.   :0.0000   Min.   :0.0000   Min.   :0.00000   Min.   :0.00000  
##  1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.00000   1st Qu.:0.00000  
##  Median :0.0000   Median :0.0000   Median :0.00000   Median :0.00000  
##  Mean   :0.2457   Mean   :0.0273   Mean   :0.08933   Mean   :0.09429  
##  3rd Qu.:0.0000   3rd Qu.:0.0000   3rd Qu.:0.00000   3rd Qu.:0.00000  
##  Max.   :1.0000   Max.   :1.0000   Max.   :1.00000   Max.   :1.00000  
##    PALM_TREES           PATH            PERSON            PORTRAIT       
##  Min.   :0.00000   Min.   :0.0000   Min.   :0.000000   Min.   :0.000000  
##  1st Qu.:0.00000   1st Qu.:0.0000   1st Qu.:0.000000   1st Qu.:0.000000  
##  Median :0.00000   Median :0.0000   Median :0.000000   Median :0.000000  
##  Mean   :0.02233   Mean   :0.1216   Mean   :0.002481   Mean   :0.007444  
##  3rd Qu.:0.00000   3rd Qu.:0.0000   3rd Qu.:0.000000   3rd Qu.:0.000000  
##  Max.   :1.00000   Max.   :1.0000   Max.   :1.000000   Max.   :1.000000  
##  RECTANGLE_3D_FRAME RECTANGULAR_FRAME      RIVER            ROCKS       
##  Min.   :0.000000   Min.   :0.000000   Min.   :0.0000   Min.   :0.0000  
##  1st Qu.:0.000000   1st Qu.:0.000000   1st Qu.:0.0000   1st Qu.:0.0000  
##  Median :0.000000   Median :0.000000   Median :0.0000   Median :0.0000  
##  Mean   :0.002481   Mean   :0.002481   Mean   :0.3127   Mean   :0.1911  
##  3rd Qu.:0.000000   3rd Qu.:0.000000   3rd Qu.:1.0000   3rd Qu.:0.0000  
##  Max.   :1.000000   Max.   :1.000000   Max.   :1.0000   Max.   :1.0000  
##  SEASHELL_FRAME          SNOW        SNOWY_MOUNTAIN    SPLIT_FRAME      
##  Min.   :0.000000   Min.   :0.0000   Min.   :0.0000   Min.   :0.000000  
##  1st Qu.:0.000000   1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.000000  
##  Median :0.000000   Median :0.0000   Median :0.0000   Median :0.000000  
##  Mean   :0.002481   Mean   :0.1861   Mean   :0.2705   Mean   :0.002481  
##  3rd Qu.:0.000000   3rd Qu.:0.0000   3rd Qu.:1.0000   3rd Qu.:0.000000  
##  Max.   :1.000000   Max.   :1.0000   Max.   :1.0000   Max.   :1.000000  
##    STEVE_ROSS       STRUCTURE           SUN            TOMB_FRAME      
##  Min.   :0.0000   Min.   :0.0000   Min.   :0.00000   Min.   :0.000000  
##  1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.00000   1st Qu.:0.000000  
##  Median :0.0000   Median :0.0000   Median :0.00000   Median :0.000000  
##  Mean   :0.0273   Mean   :0.2109   Mean   :0.09926   Mean   :0.002481  
##  3rd Qu.:0.0000   3rd Qu.:0.0000   3rd Qu.:0.00000   3rd Qu.:0.000000  
##  Max.   :1.0000   Max.   :1.0000   Max.   :1.00000   Max.   :1.000000  
##       TREE            TREES         TRIPLE_FRAME        WATERFALL      
##  Min.   :0.0000   Min.   :0.0000   Min.   :0.000000   Min.   :0.00000  
##  1st Qu.:1.0000   1st Qu.:1.0000   1st Qu.:0.000000   1st Qu.:0.00000  
##  Median :1.0000   Median :1.0000   Median :0.000000   Median :0.00000  
##  Mean   :0.8958   Mean   :0.8362   Mean   :0.002481   Mean   :0.09677  
##  3rd Qu.:1.0000   3rd Qu.:1.0000   3rd Qu.:0.000000   3rd Qu.:0.00000  
##  Max.   :1.0000   Max.   :1.0000   Max.   :1.000000   Max.   :1.00000  
##      WAVES            WINDMILL         WINDOW_FRAME          WINTER      
##  Min.   :0.00000   Min.   :0.000000   Min.   :0.000000   Min.   :0.0000  
##  1st Qu.:0.00000   1st Qu.:0.000000   1st Qu.:0.000000   1st Qu.:0.0000  
##  Median :0.00000   Median :0.000000   Median :0.000000   Median :0.0000  
##  Mean   :0.08437   Mean   :0.002481   Mean   :0.002481   Mean   :0.1712  
##  3rd Qu.:0.00000   3rd Qu.:0.000000   3rd Qu.:0.000000   3rd Qu.:0.0000  
##  Max.   :1.00000   Max.   :1.000000   Max.   :1.000000   Max.   :1.0000  
##   WOOD_FRAMED      
##  Min.   :0.000000  
##  1st Qu.:0.000000  
##  Median :0.000000  
##  Mean   :0.002481  
##  3rd Qu.:0.000000  
##  Max.   :1.000000
  1. To perform association analysis on this dataset, we need to first remove all non-binary columns from the dataset, and then convert the dataset into a matrix of transactions. Do this in R.
library(arules)
## Warning: package 'arules' was built under R version 4.2.2
## Loading required package: Matrix
## 
## Attaching package: 'arules'
## The following objects are masked from 'package:base':
## 
##     abbreviate, write
bob_ross2 <- subset(bob_ross, select = -c(EPISODE,TITLE))
bob_ross2 <- as.matrix(bob_ross2)
summary(bob_ross2)
##   APPLE_FRAME       AURORA_BOREALIS         BARN             BEACH      
##  Min.   :0.000000   Min.   :0.000000   Min.   :0.00000   Min.   :0.000  
##  1st Qu.:0.000000   1st Qu.:0.000000   1st Qu.:0.00000   1st Qu.:0.000  
##  Median :0.000000   Median :0.000000   Median :0.00000   Median :0.000  
##  Mean   :0.002481   Mean   :0.004963   Mean   :0.04218   Mean   :0.067  
##  3rd Qu.:0.000000   3rd Qu.:0.000000   3rd Qu.:0.00000   3rd Qu.:0.000  
##  Max.   :1.000000   Max.   :1.000000   Max.   :1.00000   Max.   :1.000  
##       BOAT              BRIDGE           BUILDING            BUSHES      
##  Min.   :0.000000   Min.   :0.00000   Min.   :0.000000   Min.   :0.0000  
##  1st Qu.:0.000000   1st Qu.:0.00000   1st Qu.:0.000000   1st Qu.:0.0000  
##  Median :0.000000   Median :0.00000   Median :0.000000   Median :0.0000  
##  Mean   :0.004963   Mean   :0.01737   Mean   :0.002481   Mean   :0.2978  
##  3rd Qu.:0.000000   3rd Qu.:0.00000   3rd Qu.:0.000000   3rd Qu.:1.0000  
##  Max.   :1.000000   Max.   :1.00000   Max.   :1.000000   Max.   :1.0000  
##      CABIN            CACTUS          CIRCLE_FRAME          CIRRUS       
##  Min.   :0.0000   Min.   :0.000000   Min.   :0.000000   Min.   :0.00000  
##  1st Qu.:0.0000   1st Qu.:0.000000   1st Qu.:0.000000   1st Qu.:0.00000  
##  Median :0.0000   Median :0.000000   Median :0.000000   Median :0.00000  
##  Mean   :0.1712   Mean   :0.009926   Mean   :0.004963   Mean   :0.06948  
##  3rd Qu.:0.0000   3rd Qu.:0.000000   3rd Qu.:0.000000   3rd Qu.:0.00000  
##  Max.   :1.0000   Max.   :1.000000   Max.   :1.000000   Max.   :1.00000  
##      CLIFF             CLOUDS          CONIFER          CUMULUS      
##  Min.   :0.00000   Min.   :0.0000   Min.   :0.0000   Min.   :0.0000  
##  1st Qu.:0.00000   1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0000  
##  Median :0.00000   Median :0.0000   Median :1.0000   Median :0.0000  
##  Mean   :0.01985   Mean   :0.4442   Mean   :0.5261   Mean   :0.2134  
##  3rd Qu.:0.00000   3rd Qu.:1.0000   3rd Qu.:1.0000   3rd Qu.:0.0000  
##  Max.   :1.00000   Max.   :1.0000   Max.   :1.0000   Max.   :1.0000  
##    DECIDUOUS       DIANE_ANDRE            DOCK          DOUBLE_OVAL_FRAME 
##  Min.   :0.0000   Min.   :0.000000   Min.   :0.000000   Min.   :0.000000  
##  1st Qu.:0.0000   1st Qu.:0.000000   1st Qu.:0.000000   1st Qu.:0.000000  
##  Median :1.0000   Median :0.000000   Median :0.000000   Median :0.000000  
##  Mean   :0.5633   Mean   :0.002481   Mean   :0.002481   Mean   :0.002481  
##  3rd Qu.:1.0000   3rd Qu.:0.000000   3rd Qu.:0.000000   3rd Qu.:0.000000  
##  Max.   :1.0000   Max.   :1.000000   Max.   :1.000000   Max.   :1.000000  
##       FARM              FENCE              FIRE          FLORIDA_FRAME     
##  Min.   :0.000000   Min.   :0.00000   Min.   :0.000000   Min.   :0.000000  
##  1st Qu.:0.000000   1st Qu.:0.00000   1st Qu.:0.000000   1st Qu.:0.000000  
##  Median :0.000000   Median :0.00000   Median :0.000000   Median :0.000000  
##  Mean   :0.002481   Mean   :0.05955   Mean   :0.002481   Mean   :0.002481  
##  3rd Qu.:0.000000   3rd Qu.:0.00000   3rd Qu.:0.000000   3rd Qu.:0.000000  
##  Max.   :1.000000   Max.   :1.00000   Max.   :1.000000   Max.   :1.000000  
##     FLOWERS             FOG              FRAMED           GRASS       
##  Min.   :0.00000   Min.   :0.00000   Min.   :0.0000   Min.   :0.0000  
##  1st Qu.:0.00000   1st Qu.:0.00000   1st Qu.:0.0000   1st Qu.:0.0000  
##  Median :0.00000   Median :0.00000   Median :0.0000   Median :0.0000  
##  Mean   :0.02978   Mean   :0.05707   Mean   :0.1315   Mean   :0.3524  
##  3rd Qu.:0.00000   3rd Qu.:0.00000   3rd Qu.:0.0000   3rd Qu.:1.0000  
##  Max.   :1.00000   Max.   :1.00000   Max.   :1.0000   Max.   :1.0000  
##      GUEST         HALF_CIRCLE_FRAME  HALF_OVAL_FRAME        HILLS        
##  Min.   :0.00000   Min.   :0.000000   Min.   :0.000000   Min.   :0.00000  
##  1st Qu.:0.00000   1st Qu.:0.000000   1st Qu.:0.000000   1st Qu.:0.00000  
##  Median :0.00000   Median :0.000000   Median :0.000000   Median :0.00000  
##  Mean   :0.05459   Mean   :0.002481   Mean   :0.002481   Mean   :0.04467  
##  3rd Qu.:0.00000   3rd Qu.:0.000000   3rd Qu.:0.000000   3rd Qu.:0.00000  
##  Max.   :1.00000   Max.   :1.000000   Max.   :1.000000   Max.   :1.00000  
##       LAKE            LAKES     LIGHTHOUSE            MILL         
##  Min.   :0.0000   Min.   :0   Min.   :0.000000   Min.   :0.000000  
##  1st Qu.:0.0000   1st Qu.:0   1st Qu.:0.000000   1st Qu.:0.000000  
##  Median :0.0000   Median :0   Median :0.000000   Median :0.000000  
##  Mean   :0.3548   Mean   :0   Mean   :0.002481   Mean   :0.004963  
##  3rd Qu.:1.0000   3rd Qu.:0   3rd Qu.:0.000000   3rd Qu.:0.000000  
##  Max.   :1.0000   Max.   :0   Max.   :1.000000   Max.   :1.000000  
##       MOON             MOUNTAIN       MOUNTAINS          NIGHT       
##  Min.   :0.000000   Min.   :0.000   Min.   :0.0000   Min.   :0.0000  
##  1st Qu.:0.000000   1st Qu.:0.000   1st Qu.:0.0000   1st Qu.:0.0000  
##  Median :0.000000   Median :0.000   Median :0.0000   Median :0.0000  
##  Mean   :0.007444   Mean   :0.397   Mean   :0.2457   Mean   :0.0273  
##  3rd Qu.:0.000000   3rd Qu.:1.000   3rd Qu.:0.0000   3rd Qu.:0.0000  
##  Max.   :1.000000   Max.   :1.000   Max.   :1.0000   Max.   :1.0000  
##      OCEAN           OVAL_FRAME        PALM_TREES           PATH       
##  Min.   :0.00000   Min.   :0.00000   Min.   :0.00000   Min.   :0.0000  
##  1st Qu.:0.00000   1st Qu.:0.00000   1st Qu.:0.00000   1st Qu.:0.0000  
##  Median :0.00000   Median :0.00000   Median :0.00000   Median :0.0000  
##  Mean   :0.08933   Mean   :0.09429   Mean   :0.02233   Mean   :0.1216  
##  3rd Qu.:0.00000   3rd Qu.:0.00000   3rd Qu.:0.00000   3rd Qu.:0.0000  
##  Max.   :1.00000   Max.   :1.00000   Max.   :1.00000   Max.   :1.0000  
##      PERSON            PORTRAIT        RECTANGLE_3D_FRAME RECTANGULAR_FRAME 
##  Min.   :0.000000   Min.   :0.000000   Min.   :0.000000   Min.   :0.000000  
##  1st Qu.:0.000000   1st Qu.:0.000000   1st Qu.:0.000000   1st Qu.:0.000000  
##  Median :0.000000   Median :0.000000   Median :0.000000   Median :0.000000  
##  Mean   :0.002481   Mean   :0.007444   Mean   :0.002481   Mean   :0.002481  
##  3rd Qu.:0.000000   3rd Qu.:0.000000   3rd Qu.:0.000000   3rd Qu.:0.000000  
##  Max.   :1.000000   Max.   :1.000000   Max.   :1.000000   Max.   :1.000000  
##      RIVER            ROCKS        SEASHELL_FRAME          SNOW       
##  Min.   :0.0000   Min.   :0.0000   Min.   :0.000000   Min.   :0.0000  
##  1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.000000   1st Qu.:0.0000  
##  Median :0.0000   Median :0.0000   Median :0.000000   Median :0.0000  
##  Mean   :0.3127   Mean   :0.1911   Mean   :0.002481   Mean   :0.1861  
##  3rd Qu.:1.0000   3rd Qu.:0.0000   3rd Qu.:0.000000   3rd Qu.:0.0000  
##  Max.   :1.0000   Max.   :1.0000   Max.   :1.000000   Max.   :1.0000  
##  SNOWY_MOUNTAIN    SPLIT_FRAME         STEVE_ROSS       STRUCTURE     
##  Min.   :0.0000   Min.   :0.000000   Min.   :0.0000   Min.   :0.0000  
##  1st Qu.:0.0000   1st Qu.:0.000000   1st Qu.:0.0000   1st Qu.:0.0000  
##  Median :0.0000   Median :0.000000   Median :0.0000   Median :0.0000  
##  Mean   :0.2705   Mean   :0.002481   Mean   :0.0273   Mean   :0.2109  
##  3rd Qu.:1.0000   3rd Qu.:0.000000   3rd Qu.:0.0000   3rd Qu.:0.0000  
##  Max.   :1.0000   Max.   :1.000000   Max.   :1.0000   Max.   :1.0000  
##       SUN            TOMB_FRAME            TREE            TREES       
##  Min.   :0.00000   Min.   :0.000000   Min.   :0.0000   Min.   :0.0000  
##  1st Qu.:0.00000   1st Qu.:0.000000   1st Qu.:1.0000   1st Qu.:1.0000  
##  Median :0.00000   Median :0.000000   Median :1.0000   Median :1.0000  
##  Mean   :0.09926   Mean   :0.002481   Mean   :0.8958   Mean   :0.8362  
##  3rd Qu.:0.00000   3rd Qu.:0.000000   3rd Qu.:1.0000   3rd Qu.:1.0000  
##  Max.   :1.00000   Max.   :1.000000   Max.   :1.0000   Max.   :1.0000  
##   TRIPLE_FRAME        WATERFALL           WAVES            WINDMILL       
##  Min.   :0.000000   Min.   :0.00000   Min.   :0.00000   Min.   :0.000000  
##  1st Qu.:0.000000   1st Qu.:0.00000   1st Qu.:0.00000   1st Qu.:0.000000  
##  Median :0.000000   Median :0.00000   Median :0.00000   Median :0.000000  
##  Mean   :0.002481   Mean   :0.09677   Mean   :0.08437   Mean   :0.002481  
##  3rd Qu.:0.000000   3rd Qu.:0.00000   3rd Qu.:0.00000   3rd Qu.:0.000000  
##  Max.   :1.000000   Max.   :1.00000   Max.   :1.00000   Max.   :1.000000  
##   WINDOW_FRAME          WINTER        WOOD_FRAMED      
##  Min.   :0.000000   Min.   :0.0000   Min.   :0.000000  
##  1st Qu.:0.000000   1st Qu.:0.0000   1st Qu.:0.000000  
##  Median :0.000000   Median :0.0000   Median :0.000000  
##  Mean   :0.002481   Mean   :0.1712   Mean   :0.002481  
##  3rd Qu.:0.000000   3rd Qu.:0.0000   3rd Qu.:0.000000  
##  Max.   :1.000000   Max.   :1.0000   Max.   :1.000000
class(bob_ross2)
## [1] "matrix" "array"
  1. Perform association analysis to determine rules with a support of at least 30% and confidence of at least 90%. Bob Ross included trees in a large number of his drawings. Display all of the rules that you find in your output, and using these rules, describe some of the types of landscapes in which Bob Ross tended to draw tree(s).
br_basket_rules <- apriori(bob_ross2, parameter = list(sup = .3, conf = 0.9, target = "rules"))
## Apriori
## 
## Parameter specification:
##  confidence minval smax arem  aval originalSupport maxtime support minlen
##         0.9    0.1    1 none FALSE            TRUE       5     0.3      1
##  maxlen target  ext
##      10  rules TRUE
## 
## Algorithmic control:
##  filter tree heap memopt load sort verbose
##     0.1 TRUE TRUE  FALSE TRUE    2    TRUE
## 
## Absolute minimum support count: 120 
## 
## set item appearances ...[0 item(s)] done [0.00s].
## set transactions ...[66 item(s), 403 transaction(s)] done [0.00s].
## sorting and recoding items ... [9 item(s)] done [0.00s].
## creating transaction tree ... done [0.00s].
## checking subsets of size 1 2 3 4 done [0.00s].
## writing ... [31 rule(s)] done [0.00s].
## creating S4 object  ... done [0.00s].
inspect(br_basket_rules)
##      lhs                           rhs     support   confidence coverage 
## [1]  {RIVER}                    => {TREES} 0.3002481 0.9603175  0.3126551
## [2]  {RIVER}                    => {TREE}  0.3126551 1.0000000  0.3126551
## [3]  {GRASS}                    => {TREE}  0.3374690 0.9577465  0.3523573
## [4]  {LAKE}                     => {TREES} 0.3325062 0.9370629  0.3548387
## [5]  {LAKE}                     => {TREE}  0.3523573 0.9930070  0.3548387
## [6]  {MOUNTAIN}                 => {TREES} 0.3672457 0.9250000  0.3970223
## [7]  {MOUNTAIN}                 => {TREE}  0.3870968 0.9750000  0.3970223
## [8]  {DECIDUOUS}                => {TREES} 0.5136476 0.9118943  0.5632754
## [9]  {DECIDUOUS}                => {TREE}  0.5632754 1.0000000  0.5632754
## [10] {CONIFER}                  => {TREES} 0.5161290 0.9811321  0.5260546
## [11] {CONIFER}                  => {TREE}  0.5260546 1.0000000  0.5260546
## [12] {TREES}                    => {TREE}  0.8362283 1.0000000  0.8362283
## [13] {TREE}                     => {TREES} 0.8362283 0.9335180  0.8957816
## [14] {RIVER, TREES}             => {TREE}  0.3002481 1.0000000  0.3002481
## [15] {RIVER, TREE}              => {TREES} 0.3002481 0.9603175  0.3126551
## [16] {GRASS, TREES}             => {TREE}  0.3126551 1.0000000  0.3126551
## [17] {GRASS, TREE}              => {TREES} 0.3126551 0.9264706  0.3374690
## [18] {LAKE, TREES}              => {TREE}  0.3325062 1.0000000  0.3325062
## [19] {LAKE, TREE}               => {TREES} 0.3325062 0.9436620  0.3523573
## [20] {CONIFER, MOUNTAIN}        => {TREES} 0.3126551 0.9767442  0.3200993
## [21] {CONIFER, MOUNTAIN}        => {TREE}  0.3200993 1.0000000  0.3200993
## [22] {MOUNTAIN, TREES}          => {TREE}  0.3672457 1.0000000  0.3672457
## [23] {MOUNTAIN, TREE}           => {TREES} 0.3672457 0.9487179  0.3870968
## [24] {CLOUDS, TREES}            => {TREE}  0.3424318 1.0000000  0.3424318
## [25] {CLOUDS, TREE}             => {TREES} 0.3424318 0.9387755  0.3647643
## [26] {DECIDUOUS, TREES}         => {TREE}  0.5136476 1.0000000  0.5136476
## [27] {DECIDUOUS, TREE}          => {TREES} 0.5136476 0.9118943  0.5632754
## [28] {CONIFER, TREES}           => {TREE}  0.5161290 1.0000000  0.5161290
## [29] {CONIFER, TREE}            => {TREES} 0.5161290 0.9811321  0.5260546
## [30] {CONIFER, MOUNTAIN, TREES} => {TREE}  0.3126551 1.0000000  0.3126551
## [31] {CONIFER, MOUNTAIN, TREE}  => {TREES} 0.3126551 0.9767442  0.3200993
##      lift     count
## [1]  1.148392 121  
## [2]  1.116343 126  
## [3]  1.069174 136  
## [4]  1.120583 134  
## [5]  1.108537 142  
## [6]  1.106157 148  
## [7]  1.088435 156  
## [8]  1.090485 207  
## [9]  1.116343 227  
## [10] 1.173283 208  
## [11] 1.116343 212  
## [12] 1.116343 337  
## [13] 1.116343 337  
## [14] 1.116343 121  
## [15] 1.148392 121  
## [16] 1.116343 126  
## [17] 1.107916 126  
## [18] 1.116343 134  
## [19] 1.128474 134  
## [20] 1.168035 126  
## [21] 1.116343 129  
## [22] 1.116343 148  
## [23] 1.134520 148  
## [24] 1.116343 138  
## [25] 1.122631 138  
## [26] 1.116343 207  
## [27] 1.090485 207  
## [28] 1.116343 208  
## [29] 1.173283 208  
## [30] 1.116343 126  
## [31] 1.168035 126

Bob Ross predominantly painted naturescapes, which naturally included a lot of trees. The landscapes thay he typically included trees in, based on the analysis above, were landscapes where mountains, lakes, and open skies with clouds were pictured. Additionally, it should be noted that the data includes trees, but all sub types of trees (deciduous and conifer), so for future analysis, deciding to be precise or not when defining tress might be helpful.

Part 2: Predicting a Numeric Column of Data
  1. Load the nhanes_train csv file into R. This data contains information about the weight, age, height, and pulse of various individuals. Use this data in completing the next question.
nhanes_train <- read.csv("C:/Users/raze1/OneDrive/Desktop/UIndy/MSDA 622/Homework/Homework 1/nhanes_train.csv")
summary(nhanes_train)
##       Age            Weight           Height          Pulse       
##  Min.   :16.00   Min.   : 39.30   Min.   :139.9   Min.   : 40.00  
##  1st Qu.:30.00   1st Qu.: 67.50   1st Qu.:162.2   1st Qu.: 64.00  
##  Median :44.00   Median : 79.40   Median :169.7   Median : 72.00  
##  Mean   :45.15   Mean   : 82.63   Mean   :169.5   Mean   : 72.32  
##  3rd Qu.:58.00   3rd Qu.: 94.65   3rd Qu.:176.7   3rd Qu.: 80.00  
##  Max.   :80.00   Max.   :223.00   Max.   :199.9   Max.   :122.00
  1. Develop analytical models to predict a person’s weight based on his/her age, height, and pulse (i.e., use the variable Weight as your target variable). In particular, create a regression model, a decision tree, a bagging model using 100 bootstrapped samples, a random forest with 200 trees, and a boosting model with 200 trees each having 5 splits and a shrinkage/weight of 0.03.
nhanes_train_reg <- lm(Weight ~ ., data = nhanes_train)
summary(nhanes_train_reg)
## 
## Call:
## lm(formula = Weight ~ ., data = nhanes_train)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -43.860 -13.096  -3.099  10.227 116.080 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -112.64017    6.78932 -16.591  < 2e-16 ***
## Age            0.12471    0.02045   6.097 1.22e-09 ***
## Height         1.01324    0.03522  28.768  < 2e-16 ***
## Pulse          0.24685    0.03019   8.177 4.32e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 18.67 on 2867 degrees of freedom
## Multiple R-squared:  0.2311, Adjusted R-squared:  0.2303 
## F-statistic: 287.2 on 3 and 2867 DF,  p-value: < 2.2e-16
library(rpart)
## Warning: package 'rpart' was built under R version 4.2.1
library(rpart.plot)
## Warning: package 'rpart.plot' was built under R version 4.2.1
nhanes_train_regtree <- rpart(formula = Weight ~., data = nhanes_train)
prp(nhanes_train_regtree, digits = 4, extra = 1)

library(ipred)
## Warning: package 'ipred' was built under R version 4.2.1
nhanes_train_bagging <- bagging(formula = Weight ~., data = nhanes_train, nbagg = 100)
summary(nhanes_train_bagging)
##        Length Class      Mode   
## y      2871   -none-     numeric
## X         3   data.frame list   
## mtrees  100   -none-     list   
## OOB       1   -none-     logical
## comb      1   -none-     logical
## call      4   -none-     call
library(randomForest)
## Warning: package 'randomForest' was built under R version 4.2.2
## randomForest 4.7-1.1
## Type rfNews() to see new features/changes/bug fixes.
nhanes_train_rf <- randomForest(Weight ~., data = nhanes_train, importance = TRUE, ntree = 200)
summary(nhanes_train_rf)
##                 Length Class  Mode     
## call               5   -none- call     
## type               1   -none- character
## predicted       2871   -none- numeric  
## mse              200   -none- numeric  
## rsq              200   -none- numeric  
## oob.times       2871   -none- numeric  
## importance         6   -none- numeric  
## importanceSD       3   -none- numeric  
## localImportance    0   -none- NULL     
## proximity          0   -none- NULL     
## ntree              1   -none- numeric  
## mtry               1   -none- numeric  
## forest            11   -none- list     
## coefs              0   -none- NULL     
## y               2871   -none- numeric  
## test               0   -none- NULL     
## inbag              0   -none- NULL     
## terms              3   terms  call
library(gbm)
## Warning: package 'gbm' was built under R version 4.2.2
## Loaded gbm 2.1.8.1
nhanes_train_boost <- gbm(Weight~., data = nhanes_train, distribution = "gaussian", n.trees = 200, shrinkage = 0.03, interaction.depth = 5)
summary(nhanes_train_boost)

##           var  rel.inf
## Height Height 64.65771
## Pulse   Pulse 18.08281
## Age       Age 17.25948
  1. Load the nhanes_test csv file into R, and use this data to calculate the mean squared error (MSE) for each of the models that you developed in the previous question. Based on your results, which model is best for predicting body weight?
nhanes_test <- read.csv("C:/Users/raze1/OneDrive/Desktop/UIndy/MSDA 622/Homework/Homework 1/nhanes_test.csv")
summary(nhanes_test)
##       Age            Weight           Height          Pulse       
##  Min.   :16.00   Min.   : 37.00   Min.   :140.0   Min.   : 40.00  
##  1st Qu.:30.00   1st Qu.: 66.90   1st Qu.:162.1   1st Qu.: 64.00  
##  Median :44.00   Median : 79.35   Median :169.3   Median : 72.00  
##  Mean   :45.33   Mean   : 81.91   Mean   :169.5   Mean   : 72.52  
##  3rd Qu.:59.00   3rd Qu.: 93.50   3rd Qu.:176.6   3rd Qu.: 80.00  
##  Max.   :80.00   Max.   :188.50   Max.   :199.5   Max.   :128.00
regression_pred <- predict(nhanes_train_reg, nhanes_test)
regression_pred
##         1         2         3         4         5         6         7         8 
##  82.14586  89.33741  90.20501  85.64830  84.37376  84.37376  86.07717  89.39954 
##         9        10        11        12        13        14        15        16 
##  89.39954  89.39954  89.39954  78.98367  79.91240  73.84526  73.84526  72.90300 
##        17        18        19        20        21        22        23        24 
##  72.90300  64.16983  69.55827  75.56820  75.56820  83.58530  83.58530  83.58530 
##        25        26        27        28        29        30        31        32 
##  83.58530  73.39076  73.39076  82.60612  82.13333  91.96404  81.52459  81.86528 
##        33        34        35        36        37        38        39        40 
##  86.46176  89.64465  89.64465  89.64465  59.55078  73.20451  73.20451  90.27108 
##        41        42        43        44        45        46        47        48 
##  83.13654  88.51347  85.63292  71.96074  73.61677  78.85527  71.89961  72.03211 
##        49        50        51        52        53        54        55        56 
##  77.12682  80.34622  82.00289  80.09947  80.09947  80.09947  88.06510  91.58971 
##        57        58        59        60        61        62        63        64 
##  91.58971  81.19065  88.08746  89.96586  92.68357  99.58263  74.60027  76.67210 
##        65        66        67        68        69        70        71        72 
##  82.91296  70.69129  73.99850  90.58262  75.71340  75.48491  73.85613  85.38864 
##        73        74        75        76        77        78        79        80 
##  88.38096  96.30026 106.00706  96.34232  96.34232  96.09023  81.38286  94.85567 
##        81        82        83        84        85        86        87        88 
##  72.74385  81.50530  80.45267  80.45267  67.19707  67.19707  91.70663  67.03850 
##        89        90        91        92        93        94        95        96 
##  96.39318  96.39318  96.39318  99.92456  62.14398  74.09263  91.90395  81.03129 
##        97        98        99       100       101       102       103       104 
##  81.03129  84.71833 101.40811  92.70735  76.83843  77.34998  86.52371  88.21483 
##       105       106       107       108       109       110       111       112 
##  88.21483  93.53129  93.53129  88.04604  76.00939  76.00939 103.98571  98.24018 
##       113       114       115       116       117       118       119       120 
##  98.24018  61.26527  87.26661  97.06715  94.25121  87.02048  89.21024  89.21024 
##       121       122       123       124       125       126       127       128 
##  83.57997  81.64477  86.04087  80.92298  76.59968  70.10632  75.99214  74.98075 
##       129       130       131       132       133       134       135       136 
##  86.68226  78.52710  83.59844  89.31956  89.31956  66.89821  63.10532  86.83016 
##       137       138       139       140       141       142       143       144 
##  86.83016  79.10920  72.14388  95.00438  90.17897  71.17719  71.17719  81.21855 
##       145       146       147       148       149       150       151       152 
##  81.21855  79.65788  91.39773  91.39773  96.73713  98.89080  86.08989  88.24418 
##       153       154       155       156       157       158       159       160 
##  88.24418  66.50029  96.83846  89.90392  94.34597  75.50296  78.62823  80.08082 
##       161       162       163       164       165       166       167       168 
##  62.44261  79.97169  72.40867  76.26433  74.23807 101.97994  71.11200  78.58761 
##       169       170       171       172       173       174       175       176 
##  88.32417  81.61421  74.15458  87.64300  96.33185  87.96624  80.71009  80.71009 
##       177       178       179       180       181       182       183       184 
##  86.03390  82.29168  76.87988  82.35136  78.62064  80.18213  72.12070  64.46684 
##       185       186       187       188       189       190       191       192 
##  81.13302  89.46764 105.58104 105.58104  87.22048  66.34976  81.39001  80.32530 
##       193       194       195       196       197       198       199       200 
##  83.26102  75.96611  69.46475  69.46475  86.82788  77.92694  87.81222  72.25302 
##       201       202       203       204       205       206       207       208 
##  72.25302  87.30947  97.41748  91.17765  63.58817  88.79940  86.75527  91.63400 
##       209       210       211       212       213       214       215       216 
##  82.70458  82.70458  68.64963  97.13998  78.33225  89.42047  89.42047  72.05529 
##       217       218       219       220       221       222       223       224 
##  74.11048 100.89122 104.46691  75.20986  73.65287  73.63258  74.19889  85.30023 
##       225       226       227       228       229       230       231       232 
##  85.30023  86.52431  74.08422  79.70629  70.23987  97.41462  80.76649  74.21407 
##       233       234       235       236       237       238       239       240 
##  81.29976  71.86349  95.02776  95.02776  76.49056  82.42459  82.42459  82.42459 
##       241       242       243       244       245       246       247       248 
##  83.44070  64.52324  64.52324  84.81925  88.52926 101.22475  67.59701  80.90637 
##       249       250       251       252       253       254       255       256 
##  78.74000  78.74000  93.65312  85.29183  93.98866  93.98866  82.47341  73.96239 
##       257       258       259       260       261       262       263       264 
##  89.10604  92.39005  87.38351  90.17425  90.17425  89.23361  69.58761  64.45063 
##       265       266       267       268       269       270       271       272 
##  75.70521  90.00769  82.99542  81.41914  85.92171  85.92171  92.11520  86.57046 
##       273       274       275       276       277       278       279       280 
##  86.57046  71.15176  90.62385  90.62385  70.20805  75.87422  83.70777  90.42859 
##       281       282       283       284       285       286       287       288 
##  90.42859  79.57623  83.01654  69.99782  85.16752  85.16752  85.16752 115.30551 
##       289       290       291       292       293       294       295       296 
##  83.40851  73.26050  88.92451  88.92451  89.23588  77.29338  87.38968  67.79249 
##       297       298       299       300       301       302       303       304 
##  67.79249  78.99536  81.28111  77.76103 105.40405 107.09312  87.16550  87.16550 
##       305       306       307       308       309       310       311       312 
##  78.06170  79.95693  70.71672  80.21620  97.65684  69.02889  69.02889  93.03039 
##       313       314       315       316       317       318       319       320 
##  93.03039  91.07836  96.27710  81.10431  95.38035  92.46264  78.66759  82.24532 
##       321       322       323       324       325       326       327       328 
##  72.09711  74.40378  74.40378  85.54430  85.54430  94.05594  95.65169  95.65169 
##       329       330       331       332       333       334       335       336 
##  85.55805  85.55805  95.27984  79.65274  74.00096  81.80518  70.74547  81.79921 
##       337       338       339       340       341       342       343       344 
##  89.00615  89.00615  83.83535  86.01155  76.34966  69.74042  82.50521  92.95963 
##       345       346       347       348       349       350       351       352 
##  72.52826  75.93943  95.26138  85.45877  95.52412  95.52412  94.93114 100.82190 
##       353       354       355       356       357       358       359       360 
## 100.82190 100.82190  98.62313  98.62313  92.80848  92.80848  79.81046  96.32878 
##       361       362       363       364       365       366       367       368 
##  80.35133  88.25421  71.94638  84.82273  80.19834  88.95057  90.97991  90.97991 
##       369       370       371       372       373       374       375       376 
##  85.76214  85.76214  68.46483  83.22184  81.51248  73.64713 101.73055 101.73055 
##       377       378       379       380       381       382       383       384 
##  78.45182  86.69066  79.52250  83.07603  95.97064  88.50610  80.31955  75.27385 
##       385       386       387       388       389       390       391       392 
##  69.17678  84.11265  70.19821  70.19821  90.71471  63.12296  93.84038  80.13004 
##       393       394       395       396       397       398       399       400 
##  80.13004  91.32185  89.73018  82.45598  76.13244  81.98976  90.93521  84.49251 
##       401       402       403       404       405       406       407       408 
##  98.13743  81.52315  78.39173  78.39173  78.39173  72.04974  89.00245  86.26178 
##       409       410       411       412       413       414       415       416 
##  72.17199  94.65056  65.55842  90.13301  91.98005  70.47616  84.21664  75.74500 
##       417       418       419       420       421       422       423       424 
##  84.78293  84.78293  74.81215  76.95822  80.46251  96.13123  91.07304  74.64357 
##       425       426       427       428       429       430       431       432 
##  74.64357  81.74876  80.30192  93.07080  70.25482  74.64829  74.79370  68.18178 
##       433       434       435       436       437       438       439       440 
##  85.07974  85.07974 106.99940 106.99940  74.66613  77.08437  77.08437  82.95439 
##       441       442       443       444       445       446       447       448 
##  81.47658  93.29130  90.78035  77.08560  77.08560  77.08560  77.78891  96.11586 
##       449       450       451       452       453       454       455       456 
##  93.50522  69.56628  74.65668  70.72248  70.72248  75.23757  75.23757  70.11986 
##       457       458       459       460       461       462       463       464 
##  94.22476  65.33609  65.33609  91.21293  95.16517  95.16517  95.16517  80.14769 
##       465       466       467       468       469       470       471       472 
##  91.76427  79.26241  85.91865  85.91865  90.01631  82.53883  82.53883  76.13449 
##       473       474       475       476       477       478       479       480 
##  97.62320  85.96088  85.96088  85.96088  85.96088  55.90022  92.47290  92.99082 
##       481       482       483       484       485       486       487       488 
##  92.99082  67.25940  58.18127  58.18127  82.96466  96.13452  66.92918  66.92918 
##       489       490       491       492       493       494       495       496 
##  64.55729  71.86062  71.86062  77.07513  67.37694  72.33609 104.82030  87.15032 
##       497       498       499       500       501       502       503       504 
##  97.01710  97.01710  80.61634  80.61634  89.29905  63.80925  81.01694  96.12447 
##       505       506       507       508       509       510       511       512 
##  73.22687  61.98830  85.59846  89.54272  89.54272  90.31988  77.30343  92.00156 
##       513       514       515       516       517       518       519       520 
##  86.18877  70.79755  70.79755  64.27690  72.75449  72.02411  83.02843  77.72144 
##       521       522       523       524       525       526       527       528 
##  96.54948  78.00223  80.75602  68.94829  85.83269  75.71566  90.31495  70.18734 
##       529       530       531       532       533       534       535       536 
##  70.18734 102.03759  71.40365  78.16364  89.35319  74.31417  92.55680  67.39928 
##       537       538       539       540       541       542       543       544 
##  92.50695  92.50695  98.21804  70.67304  69.64750  69.64750  65.56786  84.75444 
##       545       546       547       548       549       550       551       552 
##  84.75444  90.17978  90.17978  96.07752  69.37962  82.32040  84.81944  89.04901 
##       553       554       555       556       557       558       559       560 
##  75.51342  85.38370  85.68174  81.58447  84.65065  85.37570  85.37570  84.36186 
##       561       562       563       564       565       566       567       568 
##  84.36186  94.80337  76.44851  93.36964  76.15277  92.99881  92.99881  92.99881 
##       569       570       571       572       573       574       575       576 
##  95.14200  95.14200  77.22406  89.25145  89.25145  62.66333  64.27957  64.27957 
##       577       578       579       580       581       582       583       584 
##  83.72868  71.21125  76.97587  82.48920  82.48920  82.48920  88.43388  75.03572 
##       585       586       587       588       589       590       591       592 
##  86.66197  71.40344  81.21117  94.76275  86.06733 105.86206 105.86206  77.21993 
##       593       594       595       596       597       598       599       600 
##  82.12596  81.77439  73.62418  78.16857  78.16857  71.31010  82.63216  99.21097 
##       601       602       603       604       605       606       607       608 
##  98.05127  84.74132  89.44118  71.11197  71.11197  73.96731  79.31964  79.31964 
##       609       610       611       612       613       614       615       616 
##  79.31964  83.04259  97.92718  97.92718  81.99775  79.30651  81.14861 108.12154 
##       617       618       619       620       621       622       623       624 
## 103.34578  71.79581  72.31760  69.68032  73.86864 103.69753 107.26685 113.87486 
##       625       626       627       628       629       630       631       632 
##  96.37062  99.97192  98.28264  80.29249  93.06116  97.52908  92.40687  88.52127 
##       633       634       635       636       637       638       639       640 
##  71.16490  71.16490  65.41753  78.46681  71.50437  71.50437  86.03268  76.70060 
##       641       642       643       644       645       646       647       648 
##  79.60004  79.95240  99.01037  72.94381  81.43185  86.20004  78.79231  74.04484 
##       649       650       651       652       653       654       655       656 
##  79.46734  79.46734  70.81354  86.90910  79.10920  79.10920  85.48749  69.09902 
##       657       658       659       660       661       662       663       664 
##  88.76329  71.00081  93.99668  82.51997  70.46301  78.61571 105.33246 105.33246 
##       665       666       667       668       669       670       671       672 
##  85.25860  85.25860  85.25860  93.84817  78.95067  74.10249  90.12461  90.12461 
##       673       674       675       676       677       678       679       680 
##  62.70248  81.71226  62.88628  86.94480  86.94480  69.02334  91.93287  87.01023 
##       681       682       683       684       685       686       687       688 
##  82.37166  75.17274  71.19279  73.52632  89.77489  69.03075  60.89712  91.27323 
##       689       690       691       692       693       694       695       696 
##  72.16132  80.96423 103.50187  93.92325  93.12618  87.04673  83.21139  82.60631 
##       697       698       699       700       701       702       703       704 
##  86.88039  68.97924  71.21904  81.62364  81.62364  77.96368  73.72138  86.93454 
##       705       706       707       708       709       710       711       712 
##  79.86259 100.82169  68.52926  68.52926  97.64578  64.83501  84.82500 101.55087 
##       713       714       715       716       717       718       719       720 
##  83.68416  74.99900  83.73832  91.31712  88.76330  78.76175  95.42220  74.98548 
##       721       722       723       724       725       726       727       728 
##  87.77056  76.84028  70.04725  68.15287  68.15287  76.15029  88.58423  76.76008 
##       729       730       731       732       733       734       735       736 
##  73.22646 102.49395 102.49395 102.49395  83.92642  81.05241  81.48089  81.48089 
##       737       738       739       740       741       742       743       744 
##  74.11293  84.12085  97.73786  75.06218  78.91989  63.68454  87.08489  98.59460 
##       745       746       747       748       749       750       751       752 
##  72.73605  72.73605  72.73605  70.73088  84.96201  71.37143  71.85303  85.39109 
##       753       754       755       756       757       758       759       760 
##  79.06471  79.66730  64.30234  74.75471  73.93470  92.69442  88.42610  88.05443 
##       761       762       763       764       765       766       767       768 
##  92.16362  92.16362  77.33171  75.77331  83.22225  52.02920  81.03909  73.72858 
##       769       770       771       772       773       774       775       776 
##  79.42322  79.42322  79.42322  79.42322  97.73725  97.73725  76.63065  87.56587 
##       777       778       779       780       781       782       783       784 
##  61.70730  92.87350  78.95865  78.95865  72.73131  97.22038  88.23596  80.31382 
##       785       786       787       788       789       790       791       792 
##  70.33276  68.37376  79.23125  96.77160  96.77160  71.06030  94.22414  94.22414 
##       793       794       795       796       797       798       799       800 
##  92.81709  88.71654  88.71654  88.71654  66.38420  66.38420  66.38420  84.73637 
##       801       802       803       804       805       806       807       808 
##  74.77053  74.77053  70.59798  82.01890  82.01890  82.35403  61.13544  72.68250 
##       809       810       811       812       813       814       815       816 
##  80.53861  71.33104 103.44730 103.44730  79.44147  81.50508  81.50508  74.23539 
##       817       818       819       820       821       822       823       824 
##  74.23539  91.15180  86.81803  84.07162  76.88747  76.88747  76.88747  82.66068 
##       825       826       827       828       829       830       831       832 
##  82.66068  90.38736  90.38736  91.91993  91.91993  89.21331  86.54730  87.33388 
##       833       834       835       836       837       838       839       840 
##  95.43736  75.79873  72.47636  71.18828  71.18828  80.78207  89.91418  70.62156 
##       841       842       843       844       845       846       847       848 
##  70.62156  70.62156  79.43924  74.64253  74.53322  89.72957 111.27100  85.96315 
##       849       850       851       852       853       854       855       856 
##  85.96315  95.99423  97.84576  81.98238  76.60460  76.60460  79.08581 101.78242 
##       857       858       859       860       861       862       863       864 
##  91.22831  91.22831  87.74986  87.74986  87.64668  56.01695  69.29367  75.10342 
##       865       866       867       868       869       870       871       872 
##  75.10342  75.10342  95.27717  83.43989  61.37993  85.84768  85.84768  73.33618 
##       873       874       875       876       877       878       879       880 
##  97.56537  89.39217  80.74597  85.57569  76.10354  94.35419  73.50008  73.50008 
##       881       882       883       884       885       886       887       888 
##  77.46136  70.16376  77.04129  79.30632  79.30632  79.30632  87.99946  99.74631 
##       889       890       891       892       893       894       895       896 
##  80.57164  70.30918  91.17949  91.18728  91.18728  91.18728  92.36728  82.29661 
##       897       898       899       900       901       902       903       904 
##  74.45075  74.45075  84.84633  76.43068  86.25954  86.25954  91.36716  76.00159 
##       905       906       907       908       909       910       911       912 
##  74.29302  85.47785  85.12096  85.12096  85.12096  78.24097  84.76756  65.59411 
##       913       914       915       916       917       918       919       920 
##  75.99481  73.65329  97.96020  97.96020 103.04589  83.38104  93.00292  76.04343 
##       921       922       923       924       925       926       927       928 
##  66.76017  83.85564  85.68523  80.41884  81.87819  87.39378  95.71816 106.71387 
##       929       930       931       932       933       934       935       936 
##  80.61595 107.18892  71.34580  69.86245  93.96960  84.26647  84.26647  74.67988 
##       937       938       939       940       941       942       943       944 
##  81.32050  81.32050  81.32050  83.59865  82.50479  82.50479  76.12896  85.67661 
##       945       946       947       948       949       950       951       952 
##  91.12535  79.02367  89.87293  77.62545  73.63710  81.53155  98.42868  79.72761 
##       953       954       955       956       957       958       959       960 
##  66.96611  62.64036  77.32967  94.60359  74.24830  96.21985  79.72207  83.64787 
##       961       962       963       964       965       966       967       968 
##  83.64787  88.60003  55.45104  82.76488  82.76488  72.14615  71.44999  71.44999 
##       969       970       971       972       973       974       975       976 
##  68.93249  86.46957  80.84219  74.86609  79.69890  86.62546  68.28065  76.48996 
##       977       978       979       980       981       982       983       984 
##  71.41063  62.78043  85.07933  85.64358  95.78872  70.18981  76.00180  96.53737 
##       985       986       987       988       989       990       991       992 
##  96.53737  96.53737  90.99306  88.06716  84.11572  70.25278  96.71377  75.62294 
##       993       994       995       996       997       998       999      1000 
##  77.07719  58.49876  58.49876  78.59706  77.81763  78.13472  75.67239  70.16970 
##      1001      1002      1003      1004      1005      1006      1007      1008 
##  84.57763 101.10945  92.56440  80.79501  80.79501  76.69588  68.81003  87.02560 
##      1009      1010      1011      1012      1013      1014      1015      1016 
##  87.02560  72.68413  80.85265  81.75183  67.67785  86.08416  83.35436  85.69772 
##      1017      1018      1019      1020      1021      1022      1023      1024 
##  85.69772  78.03300  75.63282  75.63282  77.11923  77.11923  91.07018  71.69961 
##      1025      1026      1027      1028      1029      1030      1031      1032 
##  76.68257 104.38795  80.28387  75.09235  82.76222  72.19579  86.45376  92.23130 
##      1033      1034      1035      1036      1037      1038      1039      1040 
##  83.57772  78.93774  87.21720  79.59756  79.59756  73.38808  81.98812  76.76767 
##      1041      1042      1043      1044      1045      1046      1047      1048 
##  76.76767  78.73015  78.73015  66.25110  83.68622  97.99735  83.24769  92.28689 
##      1049      1050      1051      1052      1053      1054      1055      1056 
##  93.21130  68.16598  89.57922  89.57922  92.75125  88.06142 103.20200  92.28338 
##      1057      1058      1059      1060      1061      1062      1063      1064 
##  93.04457  89.22009  80.07875  78.55807  79.96635  89.04697  89.04697  89.04697 
##      1065      1066      1067      1068      1069      1070      1071      1072 
##  75.17377  81.28417  90.73830  90.73830  82.70968  73.82804  84.30093  97.57666 
##      1073      1074      1075      1076      1077      1078      1079      1080 
##  87.44056  87.44056  80.35935  77.00990  79.82605  62.22888  99.78958  99.78958 
##      1081      1082      1083      1084      1085      1086      1087      1088 
##  81.12193  67.41571  90.38736  75.58317  95.68207  65.61463  83.70057  86.91343 
##      1089      1090      1091      1092      1093      1094      1095      1096 
##  70.95445  78.39317  99.42367  99.42367  87.18868  64.50479  78.05966  95.17340 
##      1097      1098      1099      1100      1101      1102      1103      1104 
##  73.50788  92.98302  69.61283  84.19366  95.24579  81.93542  78.88275  94.48810 
##      1105      1106      1107      1108      1109      1110      1111      1112 
## 105.84380 105.84380  88.03641  85.11113  83.84210  83.84210  86.17666  70.57953 
##      1113      1114      1115      1116      1117      1118      1119      1120 
##  91.33025  83.40892  77.22998  71.97038  83.84867  78.08058  85.67456  85.67456 
##      1121      1122      1123      1124      1125      1126      1127      1128 
##  66.04598  66.04598  88.68291  76.68728  76.68728  92.10452  87.72133  79.29873 
##      1129      1130      1131      1132      1133      1134      1135      1136 
##  71.39297  79.40025  87.37616  91.69719  72.97212  92.41386  92.41386  78.95331 
##      1137      1138      1139      1140      1141      1142      1143      1144 
##  91.87339  90.17179  92.85299  92.85299  89.58456  91.91051  91.91051  69.26783 
##      1145      1146      1147      1148      1149      1150      1151      1152 
##  69.26783  63.24500  71.94843  58.44381  73.07694  80.78516  79.15310  74.73133 
##      1153      1154      1155      1156      1157      1158      1159      1160 
##  74.73133  83.60438  83.60438  87.18643  87.18643  85.90572  79.79754  76.98899 
##      1161      1162      1163      1164      1165      1166      1167      1168 
##  65.78837  73.63749  79.33791  79.33791  77.65129  71.58005  84.53639  84.40391 
##      1169      1170      1171      1172      1173      1174      1175      1176 
##  70.77910  76.00713 109.66273  82.47607  82.47607  97.62526  87.53471  69.66494 
##      1177      1178      1179      1180      1181      1182      1183      1184 
##  73.72036  73.72036  77.38894  77.38894  77.38894  76.94263  76.94263  76.94263 
##      1185      1186      1187      1188      1189      1190      1191      1192 
##  74.45364  96.13721  99.58981  99.58981  77.11923  77.11923  76.61753  65.68990 
##      1193      1194      1195      1196      1197      1198      1199      1200 
##  85.31336  78.14375  89.33741  87.87846  87.87846  73.54909  63.33401  97.46221 
##      1201      1202      1203      1204      1205      1206      1207      1208 
##  83.74099  87.91477  66.64858  82.33085  64.52570  80.76650  81.41115  72.56435 
##      1209      1210      1211      1212      1213      1214      1215      1216 
##  74.54901  74.54901  67.97913  78.56094  76.18863  84.54625  94.73342  94.73342 
##      1217      1218      1219      1220      1221      1222      1223      1224 
##  75.71054  92.21674  74.34985  74.34985  76.71599  93.76222  93.76222  96.10827 
##      1225      1226      1227      1228      1229      1230      1231      1232 
##  74.40051  94.20320  67.49795  88.59757  80.86472  85.37388  89.78413  89.04718 
##      1233      1234      1235      1236      1237      1238      1239      1240 
##  77.69846  78.22539 103.99104  84.76509  76.41487  83.94219  83.94219  78.41594 
##      1241      1242      1243      1244      1245      1246      1247      1248 
##  78.41594  80.21065  99.72212  91.54582  89.04142  89.04142  81.86279  69.82061 
##      1249      1250      1251      1252      1253      1254      1255      1256 
##  69.82061  89.25453  89.25453  58.13982  80.09393  80.09393  95.24518  97.86443 
##      1257      1258      1259      1260      1261      1262      1263      1264 
##  90.67286  85.40135  87.89773  85.19912  76.12137  85.73179  85.73179  85.73179 
##      1265      1266      1267      1268      1269      1270      1271      1272 
##  77.79999  79.81336  72.62999  92.99328  92.99328  81.45339  78.34782  82.06052 
##      1273      1274      1275      1276      1277      1278      1279      1280 
##  83.31498  82.43240  72.05835  91.57700  67.33734  67.33734  67.48605  80.59030 
##      1281      1282      1283      1284      1285      1286      1287      1288 
##  80.59030  68.77413  94.48935  80.06767  79.84411  79.84411  79.84411  79.84411 
##      1289      1290      1291      1292      1293      1294      1295      1296 
##  81.38243  86.00704  96.67192  80.87028  80.87028  72.01917  83.18023  81.97458 
##      1297      1298      1299      1300      1301      1302      1303      1304 
##  65.18328  93.87072  93.87072  76.54226  82.34830  77.92246  80.62886  94.40157 
##      1305      1306      1307      1308      1309      1310      1311      1312 
##  80.51442  70.82954  81.12830  86.13175  83.74940  88.70135  93.56533  84.25109 
##      1313      1314      1315      1316      1317      1318      1319      1320 
##  84.25109  76.08507  87.53756  82.71811  82.71811  82.71811  73.79891  86.37315 
##      1321      1322      1323      1324      1325      1326      1327      1328 
##  59.66009  94.04775  89.66270  89.48959  75.36307  89.24367  89.24367  80.52693 
##      1329      1330      1331      1332      1333      1334      1335      1336 
##  98.92688  75.54522  75.54522  72.21629  72.21629  81.10637  81.10637  66.23838 
##      1337      1338      1339      1340      1341      1342      1343      1344 
##  66.23838  98.97386  78.57387  69.86512  78.55625  78.55625  91.01807  90.26510 
##      1345      1346      1347      1348      1349      1350      1351      1352 
##  91.72569  76.33385  74.26370  70.71509  70.71509  70.71509  88.90688  92.48952 
##      1353      1354      1355      1356      1357      1358      1359      1360 
##  90.04421  83.64028  83.64028  73.90189  79.88349  69.86532  86.62626  71.85242 
##      1361      1362      1363      1364      1365      1366      1367      1368 
##  80.97467  80.97467  65.86403  85.99390  95.65828  76.92417  89.01517  86.37644 
##      1369      1370      1371      1372      1373      1374      1375      1376 
##  86.37644  83.39927  83.39927  66.59957  86.71857  86.55756  86.55756  86.55756 
##      1377      1378      1379      1380      1381      1382      1383      1384 
##  73.17804  90.60026  75.03779  89.62085  66.63546  81.42653  77.52924  77.85679 
##      1385      1386      1387      1388      1389      1390      1391      1392 
##  85.58123  83.27128 105.38580  81.48969  77.51181  82.79072  94.33100  64.95768 
##      1393      1394      1395      1396      1397      1398      1399      1400 
##  99.39168  76.58145  86.47489  93.31796  73.95725  69.36118  83.99860  83.99860 
##      1401      1402      1403      1404      1405      1406      1407      1408 
##  86.10364  83.55906  83.55906  79.34036  71.10195  76.64811  76.64811  73.19262 
##      1409      1410      1411      1412      1413      1414      1415      1416 
##  91.19591  80.13494  91.05990  79.77477  99.52171  93.41129  55.37085  82.61946 
##      1417      1418      1419      1420      1421      1422      1423      1424 
##  90.89909  90.24708  82.48346  82.48346  76.03586  82.99132  75.48226  73.03979 
##      1425      1426      1427      1428      1429      1430      1431      1432 
##  85.04262  85.04262  71.08388  86.74769  89.91952  89.08286 103.66636 103.66636 
##      1433      1434      1435      1436      1437      1438      1439      1440 
##  81.80064  81.80064  81.80064  75.65843  58.16363  89.15074  68.44454  72.25547 
##      1441      1442      1443      1444      1445      1446      1447      1448 
##  72.25547  80.53533  95.32620  81.15928  66.26728  86.87691  86.87691  68.04355 
##      1449      1450      1451      1452      1453      1454      1455      1456 
##  77.65641  76.68769  85.12609  85.12609  81.57730  81.75716  81.75716  79.36907 
##      1457      1458      1459      1460      1461      1462      1463      1464 
##  87.43687  87.43687  87.43687  87.43687  80.23155  80.23155  62.59070  87.52651 
##      1465      1466      1467      1468      1469      1470      1471      1472 
##  72.21630  68.09051  78.55560  70.69910  99.84927  97.06676  97.06676  89.34335 
##      1473      1474      1475      1476      1477      1478      1479      1480 
##  84.23530  84.23530  67.43622  69.14313  71.30437  71.30437  83.39601  72.31823 
##      1481      1482      1483      1484      1485      1486      1487      1488 
##  90.43946  90.33054  99.55801  99.55801  88.56865  88.56865  88.56865  92.86140 
##      1489      1490      1491      1492      1493      1494      1495      1496 
##  99.81070  99.81070  99.81070  99.81070  77.53213  60.36097  64.35239  70.46487 
##      1497      1498      1499      1500      1501      1502      1503      1504 
##  70.46487  78.37634  78.37634  93.37499  93.37499  82.29415  82.83667 100.75892 
##      1505      1506      1507      1508      1509      1510      1511      1512 
##  79.92779  87.21513  87.21513  83.29469  76.91617  73.29969  85.65405  85.65405 
##      1513      1514      1515      1516      1517      1518      1519      1520 
##  66.64839  89.49328  68.11411  79.29319  70.97701  92.41179  58.70409  85.00899 
##      1521      1522      1523      1524      1525      1526      1527      1528 
##  85.00899  84.40144  79.88656  83.57199  83.57199  81.99038  76.03070  99.81954 
##      1529      1530      1531      1532      1533      1534      1535      1536 
##  85.15524  69.95127  72.99284  92.09162  92.09162  67.22496  68.34791 103.12014 
##      1537      1538      1539      1540      1541      1542      1543      1544 
##  77.66707  75.07429  76.60194  76.60194  84.20352  84.20352  84.20352  77.65148 
##      1545      1546      1547      1548      1549      1550      1551      1552 
##  91.84509  90.39740  66.32738  66.58666  81.67801  92.94322  92.94322  70.97415 
##      1553      1554      1555      1556      1557      1558      1559      1560 
##  85.94918  91.54357  84.40657  84.40657  91.66560  91.66560  78.49796  68.76020 
##      1561      1562      1563      1564      1565      1566      1567      1568 
##  82.31241  81.81952  81.81952  90.83144  82.39260  73.55421  66.69310  97.11905 
##      1569      1570      1571      1572      1573      1574      1575      1576 
##  70.22611  63.32296  86.36802  76.70902 107.17556  91.62889  73.30215  61.90462 
##      1577      1578      1579      1580      1581      1582      1583      1584 
##  91.43938  69.65735  97.29360  91.55628  79.57132  71.33616  69.58392  80.43381 
##      1585      1586      1587      1588      1589      1590      1591      1592 
##  80.43381  93.78868  74.84333  74.84333  90.41322  90.67328  90.67328  90.67328 
##      1593      1594      1595      1596      1597      1598      1599      1600 
##  90.67328 100.84958  79.15843  86.33192 102.82972 101.94919  70.99075  88.94728 
##      1601      1602      1603      1604      1605      1606      1607      1608 
##  88.12153  79.08029  79.08029  79.08029  82.55629  73.43772  76.99679  81.82630 
##      1609      1610      1611      1612      1613      1614      1615      1616 
##  81.13055  91.58254  47.63082  84.97082  84.97082  73.43504  86.36004  87.76072 
##      1617      1618      1619      1620      1621      1622      1623      1624 
##  87.76072  87.76072  95.55695  67.98099  94.19604  75.90806  75.90806  81.71020 
##      1625      1626      1627      1628      1629      1630      1631      1632 
##  69.47356  73.36492  88.17607  77.46956  77.46956  94.78881  58.25673  68.07780 
##      1633      1634      1635      1636      1637      1638      1639      1640 
##  68.07780  90.89379  81.93847  90.58958  83.99308  72.08932  63.75389  91.59585 
##      1641      1642      1643      1644      1645      1646      1647      1648 
##  70.65807  94.91002  88.12665  87.58371 101.23704  79.98974  79.98974  77.96573 
##      1649      1650      1651      1652      1653      1654      1655      1656 
##  77.96573  93.76531  94.97320  79.60988  92.51003  83.99081  83.99081  86.42299 
##      1657      1658      1659      1660      1661      1662      1663      1664 
##  75.73391  87.95619  72.26019  89.30888  89.30888  85.91618  84.20495  84.20495 
##      1665      1666      1667      1668      1669      1670      1671      1672 
##  84.20495  90.01058  90.01058  90.01058  85.08015  75.21992  75.21992  75.21992 
##      1673      1674      1675      1676      1677      1678      1679      1680 
##  65.99943  72.20584  72.20584  86.81742  86.81742  87.29493  87.29493  94.47418 
##      1681      1682      1683      1684      1685      1686      1687      1688 
##  78.11934  79.77746  96.09987  96.09987  80.35586  69.63910  76.02271  72.48231 
##      1689      1690      1691      1692      1693      1694      1695      1696 
##  85.82838  68.81372  79.36107  90.17957  72.75430  88.99240  94.86450  74.59372 
##      1697      1698      1699      1700      1701      1702      1703      1704 
##  77.51939  95.47120  88.78401  86.63284  86.63284  74.33364  80.71459  83.71041 
##      1705      1706      1707      1708      1709      1710      1711      1712 
##  83.71041  83.71041  81.53072  95.28926  82.42705  77.80738  77.80738  70.92021 
##      1713      1714      1715      1716      1717      1718      1719      1720 
## 104.74913  80.26273  89.77141  89.77141  86.05093  86.05093  86.05093  86.46197 
##      1721      1722      1723      1724      1725      1726      1727      1728 
##  72.33321  72.33321  99.37916  86.17809  77.69621  74.60150  88.77171  99.22266 
##      1729      1730      1731      1732      1733      1734      1735      1736 
##  70.23164  75.78110  75.78110  88.57357  95.21995  85.83043  85.83043  92.34883 
##      1737      1738      1739      1740      1741      1742      1743      1744 
##  90.83450  74.09982  64.24553  95.99731  92.83472  92.83472  75.57290  92.53793 
##      1745      1746      1747      1748      1749      1750      1751      1752 
##  92.53793  92.53793  93.49416  93.49416  84.25827  71.28899  71.81612  78.31174 
##      1753      1754      1755      1756      1757      1758      1759      1760 
##  72.68660  85.21408  94.34945  94.34945  83.96539  85.65652  79.67614  68.88633 
##      1761      1762      1763      1764      1765      1766      1767      1768 
##  68.96859  68.96859 106.00256 106.00256 106.00256  79.71983  88.02820  90.52006 
##      1769      1770      1771      1772      1773      1774      1775      1776 
##  84.58338  81.66816  81.66816  92.87369  92.87369  87.36118  87.36118  81.11475 
##      1777      1778      1779      1780      1781      1782      1783      1784 
##  79.51635  63.25587  63.25587  81.81583  81.81583  96.01761  74.18863  74.18863 
##      1785      1786      1787      1788      1789      1790      1791      1792 
##  74.18863  56.54777  56.54777  81.67327  91.57946  91.57946  85.49488  80.90185 
##      1793      1794      1795      1796      1797      1798      1799      1800 
##  62.72299  94.03522  80.96400  80.96400  94.23234  93.77454  93.77454  93.77454 
##      1801      1802      1803      1804      1805      1806      1807      1808 
##  67.64912  85.42206  85.42206  85.39602  87.81302  74.88969  74.88969 102.72265 
##      1809      1810      1811      1812      1813      1814      1815      1816 
## 102.72265 107.31873  75.11327  86.53129  86.53129  86.53129  89.74332  89.74332 
##      1817      1818      1819      1820      1821      1822      1823      1824 
##  73.53125  98.03609  93.82152  81.84229  89.34314  94.16526  94.16526  94.16526 
##      1825      1826      1827      1828      1829      1830      1831      1832 
##  66.34770  80.54683  72.60867  79.93293  81.16420  81.16420  86.33644  75.77310 
##      1833      1834      1835      1836      1837      1838      1839      1840 
##  95.58566  95.58566  95.58566  61.98051  91.06811  91.06811  76.76030  83.64295 
##      1841      1842      1843      1844      1845      1846      1847      1848 
## 100.97472 100.97472  71.97507  92.41937  69.28323 109.14320 109.14320  86.28229 
##      1849      1850      1851      1852      1853      1854      1855      1856 
##  82.75912  92.14104  92.14104  71.85550  71.85550  76.60975  69.85773  69.85773 
##      1857      1858      1859      1860      1861      1862      1863      1864 
##  64.73369  64.73369  64.73369  64.73369  93.23017  66.97840  81.58324  81.58324 
##      1865      1866      1867      1868      1869      1870      1871      1872 
##  66.15469  75.12620  73.72610  73.72610  89.36098  89.36098  76.29860  90.80024 
##      1873      1874      1875      1876      1877      1878      1879      1880 
##  74.81463  74.81463  88.38385  69.54557  65.71574  76.29245  80.97016  81.86197 
##      1881      1882      1883      1884      1885      1886      1887      1888 
##  81.86197  65.88517  91.22380  86.57294  70.94317  95.75487  91.45187  89.69142 
##      1889      1890      1891      1892      1893      1894      1895      1896 
##  89.35033  83.79926  76.06416  76.06416  76.06416  74.87450  74.87450 109.09049 
##      1897      1898      1899      1900      1901      1902      1903      1904 
##  91.67832  66.91626  66.91626  73.18031  73.18031  73.18031  73.18031  87.05145 
##      1905      1906      1907      1908      1909      1910      1911      1912 
##  87.05145  77.38935  77.88572  76.59949  84.99605  84.99605  64.86700  90.01262 
##      1913      1914      1915      1916      1917      1918      1919      1920 
##  72.68662  84.07653  82.60098  78.41552  78.41552  78.41552  71.69962  63.60189 
##      1921      1922      1923      1924      1925      1926      1927      1928 
##  81.56130  64.52919  76.62819  79.00543  83.32809  78.34475  93.41149  84.52593 
##      1929      1930      1931      1932      1933      1934      1935      1936 
##  84.52593  84.52593  57.50603  94.61260  76.66143  81.65029  87.60811  79.99815 
##      1937      1938      1939      1940      1941      1942      1943      1944 
##  80.07670  80.07670  70.26467  70.26467  87.70657  87.70657  87.70657  81.62118 
##      1945      1946      1947      1948      1949      1950      1951      1952 
##  88.02573  72.92290  72.92290  83.12298  94.24752  66.70542  66.70542  71.29472 
##      1953      1954      1955      1956      1957      1958      1959      1960 
##  71.29472  71.29472  68.44166  77.14775  84.03287  81.75491  87.92132  87.92132 
##      1961      1962      1963      1964      1965      1966      1967      1968 
##  85.14435  78.33001 106.35801  92.11724  77.17050  82.92690  80.36899  89.97181 
##      1969      1970      1971      1972      1973      1974      1975      1976 
##  89.97181  75.32084  86.97822 105.95826  82.94885  97.52661  92.71002  82.31875 
##      1977      1978      1979      1980      1981      1982      1983      1984 
##  95.67468  95.67468  70.28313  96.21186  96.21186  87.92175  87.25165  87.41244 
##      1985      1986      1987      1988      1989      1990      1991      1992 
##  70.86338  86.23019  86.23019  70.85458  87.46947  87.46947  87.46947  87.46947 
##      1993      1994      1995      1996      1997      1998      1999      2000 
##  83.55741  78.41020  75.94497  88.96083  79.12458  71.03118  71.03118  86.64636 
##      2001      2002      2003      2004      2005      2006      2007      2008 
##  86.64636  86.64636  86.64636  71.56980  75.52677  80.24203  86.25380  76.70921 
##      2009      2010      2011      2012      2013      2014      2015      2016 
##  84.64100 102.18752 100.31753 100.31753  87.98410  73.88670  73.88670  79.50444 
##      2017      2018      2019      2020      2021      2022      2023      2024 
##  86.72922  86.72922  77.05648  87.30906  65.86180  79.94914  93.03983  93.03983 
##      2025      2026      2027      2028      2029      2030      2031      2032 
##  83.59863  86.79179  94.53980  64.66397  87.27215  82.93903  88.54056  97.59387 
##      2033      2034      2035      2036      2037      2038      2039      2040 
##  95.13975  69.03402  84.40923  84.40923  80.88156  65.97031  65.97031  93.87709 
##      2041      2042      2043      2044      2045      2046      2047      2048 
##  75.19652  96.83046  85.64563  76.01820  89.67295  89.74496  84.70603  75.69002 
##      2049      2050      2051      2052      2053      2054      2055      2056 
##  80.51995  80.63153  73.81163  91.37702  91.37702  64.95500  85.12609  68.57867 
##      2057      2058      2059      2060      2061      2062      2063      2064 
##  68.57867 106.05363  65.17590  94.57550  94.57550  73.12267  87.25430  79.87774 
##      2065      2066      2067      2068      2069      2070      2071      2072 
##  72.66035  90.77994  90.77994  90.77994 104.20909 104.20909 104.20909 104.20909 
##      2073      2074      2075      2076      2077      2078      2079      2080 
##  87.55541  98.46766  74.59577  74.59577  70.91425  70.91425  70.91425  70.91425 
##      2081      2082      2083      2084      2085      2086      2087      2088 
##  80.33290  70.23184  76.89033  82.83624  82.83624  82.83624  89.94001  91.56674 
##      2089      2090      2091      2092      2093      2094      2095      2096 
##  90.02287  90.02287  80.59788  78.85691  60.66802  83.89933  83.89933  71.11466 
##      2097      2098      2099      2100      2101      2102      2103      2104 
##  67.75331  76.54739  90.50160  81.09178  81.20582  81.20582  90.38243  95.49294 
##      2105      2106      2107      2108      2109      2110      2111      2112 
##  67.28259  93.32002  95.82072 110.36400  67.86202  86.64597  68.05236  78.18189 
##      2113      2114      2115      2116      2117      2118      2119      2120 
##  99.28336  67.60727  71.97714  71.97714  71.97714  73.57782  77.94807  95.71366 
##      2121      2122      2123      2124      2125      2126      2127      2128 
##  88.95816  74.38327  95.37255  95.37255  85.54287  76.04548  89.82083  95.57088 
##      2129      2130      2131      2132      2133      2134      2135      2136 
##  90.65790  74.66939  87.63603  87.63603  87.63603  77.97700  88.93046  88.93046 
##      2137      2138      2139      2140      2141      2142      2143      2144 
##  93.54955  70.20252  73.48694  73.48694  80.50906  89.82599  93.41376  93.41376 
##      2145      2146      2147      2148      2149      2150      2151      2152 
##  78.96829  67.04693  96.88011  78.29616  73.37946  79.80616  79.80616  92.81175 
##      2153      2154      2155      2156      2157      2158      2159      2160 
##  84.26401  87.09000  91.65780  64.97838  74.17816  74.17816  74.17816  74.17816 
##      2161      2162      2163      2164      2165      2166      2167      2168 
##  87.95845  81.32048  63.83530  77.01216  77.01216  71.48117  76.09798  79.64617 
##      2169      2170      2171      2172      2173      2174      2175      2176 
##  85.31869  93.60327  87.67437  91.29866  91.09067  88.52969  84.04600  72.04237 
##      2177      2178      2179      2180      2181      2182      2183      2184 
##  80.61839  90.27844  79.53727  75.79936  78.28528  78.28528  78.28528  78.28528 
##      2185      2186      2187      2188      2189      2190      2191      2192 
##  85.13676  87.04818  87.75109  86.19902  93.70194  93.73824  69.71497  66.09275 
##      2193      2194      2195      2196      2197      2198      2199      2200 
##  89.70374  78.58392  58.25201  58.25201  82.24862  82.11754  82.11754  83.80929 
##      2201      2202      2203      2204      2205      2206      2207      2208 
##  69.03894  81.38222  82.52796  82.74415  82.90436  75.51096  78.21021  86.26958 
##      2209      2210      2211      2212      2213      2214      2215      2216 
##  90.85481  90.85481  90.85481  90.85481  75.53169  75.53169  68.74278  68.74278 
##      2217      2218      2219      2220      2221      2222      2223      2224 
##  72.04051  74.98035  74.98035  76.23912  78.99763  73.06710  77.99977  87.67993 
##      2225      2226      2227      2228      2229      2230      2231      2232 
##  75.99461  88.53257  74.67411  79.75530  83.42698  83.42698  79.84410  67.49056 
##      2233      2234      2235      2236      2237      2238      2239      2240 
##  72.99385  68.05442 102.76510  82.64262 102.19840 102.19840  91.96137  91.96137 
##      2241      2242      2243      2244      2245      2246      2247      2248 
##  86.36823  84.42748  75.17028  77.92143  77.92143  94.70882  95.32148  84.02466 
##      2249      2250      2251      2252      2253      2254      2255      2256 
##  90.39557  98.40428  85.08444  64.29230  80.98800  80.98800  62.90001  90.60497 
##      2257      2258      2259      2260      2261      2262      2263      2264 
##  85.06169  78.79786  77.59221  73.68180  74.14411  73.33147  85.30782  84.29542 
##      2265      2266      2267      2268      2269      2270      2271      2272 
##  84.29542  82.05500  82.05500  75.43281  75.43281  99.64148  88.87836  88.22305 
##      2273      2274      2275      2276      2277      2278      2279      2280 
##  88.22305  88.22305  88.22305  87.60772  87.60772  82.96753  75.12044 101.05244 
##      2281      2282      2283      2284      2285      2286      2287      2288 
##  86.19903  85.18579  81.41096  76.53426 104.87958 104.87958  93.99133  87.68893 
##      2289      2290      2291      2292      2293      2294      2295      2296 
##  87.68893  74.54429  88.27802  75.17848  89.61101  71.13291  77.93701  82.79030 
##      2297      2298      2299      2300      2301      2302      2303      2304 
##  82.79030  82.43750  77.06938  79.03371  78.48279  81.33322  87.15811  74.86937 
##      2305      2306      2307      2308      2309      2310      2311      2312 
##  74.86937  73.68182  94.79190  94.79190  87.20221  80.29659  81.96370  90.38244 
##      2313      2314      2315      2316      2317      2318      2319      2320 
##  90.06965  96.95785  96.95785  91.08391  67.53281  78.49880  73.04208  72.04748 
##      2321      2322      2323      2324      2325      2326      2327      2328 
##  86.11410  74.17528  93.31510  66.54522  66.54522  66.54522  87.84400  77.16047 
##      2329      2330      2331      2332      2333      2334      2335      2336 
##  74.74447  74.74447  81.86034  75.28185  77.56617  77.56617  96.00162  96.00162 
##      2337      2338      2339      2340      2341      2342      2343      2344 
##  96.00162  77.32658  81.77255  77.06733  84.34503  80.83419  73.34910  78.75827 
##      2345      2346      2347      2348      2349      2350      2351      2352 
##  80.80546  72.06861  77.60472  75.90846  78.67006 104.97843 104.97843 104.97843 
##      2353      2354      2355      2356      2357      2358      2359      2360 
##  80.96381  80.96381  67.87823  90.63575  90.63575  90.63575  96.66924  71.90985 
##      2361      2362      2363      2364      2365      2366      2367      2368 
##  94.04795  94.04795  73.39381  73.39381  73.39381  73.39381  67.40710  88.51390 
##      2369      2370      2371      2372      2373      2374      2375      2376 
##  70.24785 100.43650 100.43650 100.43650 100.43650  91.16616  91.16616  63.49442 
##      2377      2378      2379      2380      2381      2382      2383      2384 
##  63.49442  71.20654  79.84164  86.39899  69.08530  69.08530  69.08530  96.29821 
##      2385      2386      2387      2388      2389      2390      2391      2392 
##  80.87335  92.15868  90.40786  90.40786  97.03804  85.54984  87.86740  85.34065 
##      2393      2394      2395      2396      2397      2398      2399      2400 
##  85.34065  85.34065  95.32352  75.20926  64.83787  71.53103  71.27895  76.89257 
##      2401      2402      2403      2404      2405      2406      2407      2408 
##  94.05594  73.85102  70.67325  69.64709  90.04175  90.04175  80.70741  82.58745 
##      2409      2410      2411      2412      2413      2414      2415      2416 
##  82.58745  95.82215  88.48845  88.48845  73.66088  92.91820  92.91820 102.80388 
##      2417      2418      2419      2420      2421      2422      2423      2424 
##  73.76281  82.80405  79.96102 110.06270 110.06270 110.06270  85.46903  85.10003 
##      2425      2426      2427      2428      2429      2430      2431      2432 
##  80.17228  80.59480  73.56918  88.03269  84.69783  95.27410  57.47201  91.08577 
##      2433      2434      2435      2436      2437      2438      2439      2440 
##  91.08577  91.08577  84.71545  84.71545  94.59415  88.71941  88.71941  73.80978 
##      2441      2442      2443      2444      2445      2446      2447      2448 
##  57.04330  83.44543  66.94190  65.61279  76.80235  76.80235  86.13666  81.28152 
##      2449      2450      2451      2452      2453      2454      2455      2456 
##  81.45239  81.45239  83.61444  75.92446  77.97883  77.97883  78.81219  78.50372 
##      2457      2458      2459      2460      2461      2462      2463      2464 
##  71.25494  69.56380  69.56380  85.79865  85.79865  85.79865  80.84998  67.78449 
##      2465      2466      2467      2468      2469      2470      2471      2472 
##  76.35006  97.23371  61.10202  79.72781 101.55639  85.70574  90.03662  88.34755 
##      2473      2474      2475      2476      2477      2478      2479      2480 
## 101.06064  65.37016  87.68833  86.81783  86.81783  90.35045  90.35045  90.35045 
##      2481      2482      2483      2484      2485      2486      2487      2488 
##  73.35466  73.35466  77.63815  83.24749  66.72488 108.35373  78.54802  86.39080 
##      2489      2490      2491      2492      2493      2494      2495      2496 
##  75.50318  75.50318  75.50318  82.07365  71.75706  89.67049  73.12267  90.37670 
##      2497      2498      2499      2500      2501      2502      2503      2504 
##  76.29818  76.29818  76.29818  98.41290  82.26257  64.67399 103.09470 103.09470 
##      2505      2506      2507      2508      2509      2510      2511      2512 
## 103.09470 103.09470  77.39100  85.91596  89.57657  89.59769  89.59769  72.90669 
##      2513      2514      2515      2516      2517      2518      2519      2520 
##  99.98669  99.98669 102.43466  83.58613  88.88533  88.88533  79.79016  75.67463 
##      2521      2522      2523      2524      2525      2526      2527      2528 
##  82.34378  82.34378  77.49580  84.70315  83.37466  70.45480  79.80083  73.06831 
##      2529      2530      2531      2532      2533      2534      2535      2536 
##  75.90540  75.90540  94.48954  94.48954  93.64307  93.64307  69.75909  69.75909 
##      2537      2538      2539      2540      2541      2542      2543      2544 
##  74.97254  74.97254  88.31739 102.08046  93.77247  72.69749  72.69749  78.76113 
##      2545      2546      2547      2548      2549      2550      2551      2552 
##  69.64997  86.28270  81.87306  81.87306  81.87306  89.42867  89.42867  89.42867 
##      2553      2554      2555      2556      2557      2558      2559      2560 
##  73.12042  90.89952  84.25870  82.88446  69.36364  74.78364  80.21126  80.21126 
##      2561      2562      2563      2564      2565      2566      2567      2568 
##  98.62394  99.25465  99.25465  88.34263 100.70437 100.70437  69.03608  78.87045 
##      2569      2570      2571      2572      2573      2574      2575      2576 
##  82.80262  93.79545  76.56871  71.90493  71.90493  90.02903  89.70127  89.70127 
##      2577      2578      2579      2580      2581      2582      2583      2584 
##  76.77362  79.22590  87.45860  87.45860  96.50149  74.83758  77.85987  94.55170 
##      2585      2586      2587      2588      2589      2590      2591      2592 
##  76.78409  76.26905  86.77580  70.15657  74.33118  80.29125  83.27848  92.48152 
##      2593      2594      2595      2596      2597      2598      2599      2600 
##  61.40618  89.36468  84.02752  87.62331  68.35367  74.77010  90.35906  78.86983 
##      2601      2602      2603      2604      2605      2606      2607      2608 
##  73.41084  86.96286  88.21360  83.42265  83.42265  83.42265  83.72807  81.76990 
##      2609      2610      2611      2612      2613      2614      2615      2616 
##  62.93059  90.23660  73.83747  87.45490  80.20058  80.20058  86.19901  86.19901 
##      2617      2618      2619      2620      2621      2622      2623      2624 
##  76.53672  78.50351  78.50351  99.01304  99.01304  62.52834  85.88726  69.86779 
##      2625      2626      2627      2628      2629      2630      2631      2632 
##  69.86779  88.48086  84.95524  62.06831  80.54865  77.56330  77.56330  77.56330 
##      2633      2634      2635      2636      2637      2638      2639      2640 
##  78.13492  90.08565  88.65419  91.54888  91.54888  83.20915  71.20653  75.50565 
##      2641      2642      2643      2644      2645      2646      2647      2648 
##  82.64263  82.64263  98.32942  89.21782  64.80136  70.54814  74.48994  87.04160 
##      2649      2650      2651      2652      2653      2654      2655      2656 
##  94.65037  83.45322  83.45322  81.13794  81.13794  93.28248  77.46503  83.78796 
##      2657      2658      2659      2660      2661      2662      2663      2664 
##  83.78796  83.78796  87.45941  80.00019  79.07022  79.07022  89.80281  85.30106 
##      2665      2666      2667      2668      2669      2670      2671      2672 
##  80.22644  80.22644  88.07228 106.27514  82.50478  82.50478  70.99506  70.99506 
##      2673      2674      2675      2676      2677      2678      2679      2680 
##  72.00381  72.00381  72.00381  75.96220  75.96220  62.75378  78.29307  89.78474 
##      2681      2682      2683      2684      2685      2686      2687      2688 
##  80.55399  80.55399  80.55399  91.10749  91.10749  91.10749  71.68915  76.82573 
##      2689      2690      2691      2692      2693      2694      2695      2696 
##  76.55499  72.08113  72.08113  72.08113  89.51093  89.51093  76.09491  74.52870 
##      2697      2698      2699      2700      2701      2702      2703      2704 
##  83.20134  94.96992  94.96992  81.33504  85.38596  82.21683  61.27081  97.59431 
##      2705      2706      2707      2708      2709      2710      2711      2712 
##  97.59431  92.62183  92.62183  98.40715  64.63810  79.21564  79.21564 105.51830 
##      2713      2714      2715      2716      2717      2718      2719      2720 
##  91.57966  91.57966  97.86503  97.86503  75.79135  73.75481  88.37646  88.37646 
##      2721      2722      2723      2724      2725      2726      2727      2728 
##  77.22260  79.43615  82.42951  74.05285 101.23171  86.48248  79.23350  77.32702 
##      2729      2730      2731      2732      2733      2734      2735      2736 
##  77.32702  77.32702  94.50269  94.50269  65.63821  65.63821  94.34207  94.34207 
##      2737      2738      2739      2740      2741      2742      2743      2744 
##  94.34207  68.97617  99.46798  99.46798  85.78388  73.11816  73.08965  83.53096 
##      2745      2746      2747      2748      2749      2750      2751      2752 
##  83.53096  95.32641  98.04123  70.26796  70.26796  82.43752  69.81590  69.81590 
##      2753      2754      2755      2756      2757      2758      2759      2760 
##  87.47500  83.30247  77.12128  77.12128  77.12128 103.22661  75.80921  75.80921 
##      2761      2762      2763      2764      2765      2766      2767      2768 
##  75.80921  83.09449  93.49456  78.85712  87.78390  87.78390  82.26830  78.84152 
##      2769      2770      2771      2772      2773      2774      2775      2776 
##  78.84152  88.05136  88.05136  88.05136  75.87462  74.21733  79.65193 101.08074 
##      2777      2778      2779      2780      2781      2782      2783      2784 
## 101.08074 101.08074  97.73213  78.37389  78.37389  78.84893  78.84893  83.38019 
##      2785      2786      2787      2788      2789      2790      2791      2792 
##  65.87983  86.71345  86.71345  87.57100  87.57100  87.57100  63.82177  63.82177 
##      2793      2794      2795      2796      2797      2798      2799      2800 
##  63.82177  66.32678  77.85865  84.85536  92.69977  77.57416  82.75399  91.11816 
##      2801      2802      2803      2804      2805      2806      2807      2808 
##  87.84338  91.00596  77.32966  77.32966  87.70104  87.70104  90.39741  69.92480 
##      2809      2810      2811      2812      2813      2814      2815      2816 
##  69.92480  96.45859  85.52154  85.52154  73.74886  72.82730  85.89012  85.89012 
##      2817      2818      2819      2820      2821      2822      2823      2824 
##  85.89012  81.29116  84.24535 106.20007 106.20007  90.05999  78.04407  85.42207 
##      2825      2826      2827      2828      2829      2830      2831      2832 
##  85.98467  85.98467  85.46842  79.17895  72.02412  72.02412  94.30230  81.57997 
##      2833      2834      2835      2836      2837      2838      2839      2840 
##  89.98187  84.14669 103.58864  82.35897  83.12565  85.19605  94.06950  74.89502 
##      2841      2842      2843      2844      2845      2846      2847      2848 
##  70.92040  79.05155 112.98100 112.98100  78.41100  78.41100  93.72840  71.35913 
##      2849      2850      2851      2852      2853      2854      2855      2856 
##  74.38327  93.19244  93.19244  98.59503  74.67391  83.53834  61.70482  79.22715 
##      2857      2858      2859      2860      2861      2862      2863      2864 
##  67.13984  67.13984  85.83332  88.03885  83.92558  83.92558  74.49505  95.46402 
##      2865      2866      2867      2868      2869      2870      2871      2872 
##  68.99998  88.38879  75.45642  87.28507  87.28507  87.28507  87.12160  84.63794
MSE_reg <- mean((regression_pred - nhanes_test$Weight)^2)
MSE_reg
## [1] 332.8215
dec_tree_pred <- predict(nhanes_train_regtree, nhanes_test)
dec_tree_pred
##         1         2         3         4         5         6         7         8 
##  79.66708  88.16752  98.24776  88.16752  71.91270  71.91270  88.16752  98.24776 
##         9        10        11        12        13        14        15        16 
##  98.24776  98.24776  98.24776  88.16752  70.00833  71.91270  71.91270  71.91270 
##        17        18        19        20        21        22        23        24 
##  71.91270  71.91270  71.91270  71.91270  71.91270  88.16752  88.16752  88.16752 
##        25        26        27        28        29        30        31        32 
##  88.16752  71.91270  71.91270  79.66708  79.66708  88.16752  79.66708  79.66708 
##        33        34        35        36        37        38        39        40 
##  88.16752  88.16752  88.16752  88.16752  71.91270  71.91270  71.91270  90.39030 
##        41        42        43        44        45        46        47        48 
##  71.91270  98.24776  79.66708  71.91270  71.91270  71.91270  71.91270  71.91270 
##        49        50        51        52        53        54        55        56 
##  71.91270  90.39030  88.16752  90.39030  90.39030  90.39030  88.16752  98.24776 
##        57        58        59        60        61        62        63        64 
##  98.24776  90.39030  88.16752  88.16752  88.16752  98.24776  71.91270  71.91270 
##        65        66        67        68        69        70        71        72 
##  90.39030  71.91270  71.91270  88.16752  71.91270  71.91270  71.91270  79.66708 
##        73        74        75        76        77        78        79        80 
##  98.24776  98.24776  98.24776  88.16752  88.16752  88.16752  71.91270  98.24776 
##        81        82        83        84        85        86        87        88 
##  71.91270  71.91270  90.39030  90.39030  71.91270  71.91270  88.16752  71.91270 
##        89        90        91        92        93        94        95        96 
##  98.24776  98.24776  98.24776  98.24776  71.91270  71.91270  98.24776  79.66708 
##        97        98        99       100       101       102       103       104 
##  79.66708  79.66708  98.24776  98.24776  79.66708  79.66708  88.16752  88.16752 
##       105       106       107       108       109       110       111       112 
##  88.16752  88.16752  88.16752  88.16752  71.91270  71.91270  98.24776  98.24776 
##       113       114       115       116       117       118       119       120 
##  98.24776  71.91270  88.16752  98.24776  88.16752  88.16752  88.16752  88.16752 
##       121       122       123       124       125       126       127       128 
##  88.16752  79.66708  88.16752  90.39030  71.91270  71.91270  71.91270  70.00833 
##       129       130       131       132       133       134       135       136 
##  88.16752  79.66708  79.66708  88.16752  88.16752  71.91270  71.91270  88.16752 
##       137       138       139       140       141       142       143       144 
##  88.16752  79.66708  71.91270  88.16752  88.16752  71.91270  71.91270  79.66708 
##       145       146       147       148       149       150       151       152 
##  79.66708  71.91270  98.24776  98.24776  98.24776  98.24776  88.16752  90.39030 
##       153       154       155       156       157       158       159       160 
##  90.39030  71.91270  98.24776  88.16752  98.24776  71.91270  79.66708  71.91270 
##       161       162       163       164       165       166       167       168 
##  71.91270  79.66708  71.91270  71.91270  71.91270  98.24776  71.91270  71.91270 
##       169       170       171       172       173       174       175       176 
##  88.16752  71.91270  71.91270  88.16752  98.24776  88.16752  71.91270  71.91270 
##       177       178       179       180       181       182       183       184 
##  90.39030  79.66708  71.91270  88.16752  71.91270  79.66708  71.91270  71.91270 
##       185       186       187       188       189       190       191       192 
##  79.66708  88.16752  98.24776  98.24776  90.39030  71.91270  79.66708  71.91270 
##       193       194       195       196       197       198       199       200 
##  88.16752  71.91270  71.91270  71.91270  88.16752  79.66708  88.16752  71.91270 
##       201       202       203       204       205       206       207       208 
##  71.91270  70.00833  98.24776  88.16752  71.91270  98.24776  88.16752  98.24776 
##       209       210       211       212       213       214       215       216 
##  79.66708  79.66708  71.91270  98.24776  71.91270  88.16752  88.16752  71.91270 
##       217       218       219       220       221       222       223       224 
##  71.91270  98.24776  98.24776  71.91270  71.91270  71.91270  71.91270  88.16752 
##       225       226       227       228       229       230       231       232 
##  88.16752  88.16752  71.91270  79.66708  71.91270  98.24776  79.66708  71.91270 
##       233       234       235       236       237       238       239       240 
##  90.39030  71.91270  88.16752  88.16752  70.00833  90.39030  90.39030  90.39030 
##       241       242       243       244       245       246       247       248 
##  70.00833  71.91270  71.91270  88.16752  98.24776  88.16752  71.91270  88.16752 
##       249       250       251       252       253       254       255       256 
##  79.66708  79.66708  88.16752  88.16752  98.24776  98.24776  79.66708  71.91270 
##       257       258       259       260       261       262       263       264 
##  88.16752  98.24776  98.24776  88.16752  88.16752  88.16752  71.91270  71.91270 
##       265       266       267       268       269       270       271       272 
##  79.66708  98.24776  79.66708  90.39030  90.39030  90.39030  88.16752  88.16752 
##       273       274       275       276       277       278       279       280 
##  88.16752  71.91270  88.16752  88.16752  71.91270  71.91270  79.66708  88.16752 
##       281       282       283       284       285       286       287       288 
##  88.16752  88.16752  79.66708  71.91270  88.16752  88.16752  88.16752  98.24776 
##       289       290       291       292       293       294       295       296 
##  88.16752  71.91270  88.16752  88.16752  88.16752  71.91270  90.39030  71.91270 
##       297       298       299       300       301       302       303       304 
##  71.91270  70.00833  79.66708  71.91270  98.24776  98.24776  88.16752  88.16752 
##       305       306       307       308       309       310       311       312 
##  70.00833  71.91270  70.00833  71.91270  98.24776  71.91270  71.91270  88.16752 
##       313       314       315       316       317       318       319       320 
##  88.16752  98.24776  88.16752  79.66708  98.24776  98.24776  70.00833  90.39030 
##       321       322       323       324       325       326       327       328 
##  71.91270  71.91270  71.91270  88.16752  88.16752  98.24776  98.24776  98.24776 
##       329       330       331       332       333       334       335       336 
##  90.39030  90.39030  88.16752  71.91270  71.91270  79.66708  71.91270  71.91270 
##       337       338       339       340       341       342       343       344 
##  90.39030  90.39030  90.39030  88.16752  79.66708  71.91270  71.91270  98.24776 
##       345       346       347       348       349       350       351       352 
##  71.91270  79.66708  98.24776  88.16752  88.16752  88.16752  98.24776  98.24776 
##       353       354       355       356       357       358       359       360 
##  98.24776  98.24776  98.24776  98.24776  88.16752  88.16752  70.00833  98.24776 
##       361       362       363       364       365       366       367       368 
##  70.00833  88.16752  71.91270  90.39030  71.91270  88.16752  88.16752  88.16752 
##       369       370       371       372       373       374       375       376 
##  88.16752  88.16752  71.91270  88.16752  79.66708  79.66708  98.24776  98.24776 
##       377       378       379       380       381       382       383       384 
##  79.66708  88.16752  71.91270  79.66708  98.24776  88.16752  79.66708  79.66708 
##       385       386       387       388       389       390       391       392 
##  71.91270  88.16752  71.91270  71.91270  88.16752  71.91270  88.16752  79.66708 
##       393       394       395       396       397       398       399       400 
##  79.66708  98.24776  88.16752  71.91270  71.91270  88.16752  88.16752  90.39030 
##       401       402       403       404       405       406       407       408 
##  98.24776  71.91270  79.66708  79.66708  79.66708  71.91270  88.16752  88.16752 
##       409       410       411       412       413       414       415       416 
##  71.91270  98.24776  71.91270  88.16752  88.16752  71.91270  88.16752  71.91270 
##       417       418       419       420       421       422       423       424 
##  88.16752  88.16752  71.91270  71.91270  79.66708  98.24776  88.16752  71.91270 
##       425       426       427       428       429       430       431       432 
##  71.91270  79.66708  71.91270  98.24776  71.91270  71.91270  71.91270  71.91270 
##       433       434       435       436       437       438       439       440 
##  90.39030  90.39030  98.24776  98.24776  71.91270  79.66708  79.66708  79.66708 
##       441       442       443       444       445       446       447       448 
##  71.91270  98.24776  88.16752  71.91270  71.91270  71.91270  79.66708  98.24776 
##       449       450       451       452       453       454       455       456 
##  98.24776  71.91270  71.91270  71.91270  71.91270  71.91270  71.91270  71.91270 
##       457       458       459       460       461       462       463       464 
##  88.16752  71.91270  71.91270  88.16752  98.24776  98.24776  98.24776  79.66708 
##       465       466       467       468       469       470       471       472 
##  88.16752  79.66708  79.66708  79.66708  88.16752  70.00833  70.00833  70.00833 
##       473       474       475       476       477       478       479       480 
##  98.24776  70.00833  70.00833  70.00833  70.00833  71.91270  98.24776  88.16752 
##       481       482       483       484       485       486       487       488 
##  88.16752  71.91270  71.91270  71.91270  79.66708  98.24776  71.91270  71.91270 
##       489       490       491       492       493       494       495       496 
##  71.91270  71.91270  71.91270  71.91270  71.91270  71.91270  98.24776  88.16752 
##       497       498       499       500       501       502       503       504 
##  98.24776  98.24776  90.39030  90.39030  88.16752  71.91270  71.91270  98.24776 
##       505       506       507       508       509       510       511       512 
##  71.91270  71.91270  88.16752  88.16752  88.16752  88.16752  71.91270  88.16752 
##       513       514       515       516       517       518       519       520 
##  88.16752  71.91270  71.91270  71.91270  71.91270  71.91270  71.91270  79.66708 
##       521       522       523       524       525       526       527       528 
##  98.24776  79.66708  88.16752  71.91270  88.16752  79.66708  88.16752  71.91270 
##       529       530       531       532       533       534       535       536 
##  71.91270  98.24776  71.91270  70.00833  88.16752  71.91270  88.16752  71.91270 
##       537       538       539       540       541       542       543       544 
##  98.24776  98.24776  98.24776  71.91270  71.91270  71.91270  71.91270  88.16752 
##       545       546       547       548       549       550       551       552 
##  88.16752  88.16752  88.16752  88.16752  71.91270  79.66708  88.16752  88.16752 
##       553       554       555       556       557       558       559       560 
##  71.91270  88.16752  88.16752  79.66708  88.16752  88.16752  88.16752  88.16752 
##       561       562       563       564       565       566       567       568 
##  88.16752  98.24776  70.00833  98.24776  71.91270  88.16752  88.16752  88.16752 
##       569       570       571       572       573       574       575       576 
##  98.24776  98.24776  71.91270  98.24776  98.24776  71.91270  71.91270  71.91270 
##       577       578       579       580       581       582       583       584 
##  90.39030  71.91270  71.91270  79.66708  79.66708  79.66708  88.16752  71.91270 
##       585       586       587       588       589       590       591       592 
##  90.39030  71.91270  90.39030  98.24776  70.00833  98.24776  98.24776  70.00833 
##       593       594       595       596       597       598       599       600 
##  71.91270  88.16752  71.91270  79.66708  79.66708  71.91270  79.66708  98.24776 
##       601       602       603       604       605       606       607       608 
##  98.24776  79.66708  98.24776  71.91270  71.91270  71.91270  79.66708  79.66708 
##       609       610       611       612       613       614       615       616 
##  79.66708  79.66708  98.24776  98.24776  88.16752  79.66708  79.66708  98.24776 
##       617       618       619       620       621       622       623       624 
##  98.24776  71.91270  71.91270  71.91270  70.00833  98.24776  98.24776 133.65333 
##       625       626       627       628       629       630       631       632 
##  98.24776  98.24776  98.24776  71.91270  88.16752  98.24776  88.16752  98.24776 
##       633       634       635       636       637       638       639       640 
##  71.91270  71.91270  71.91270  79.66708  71.91270  71.91270  88.16752  79.66708 
##       641       642       643       644       645       646       647       648 
##  79.66708  88.16752  98.24776  71.91270  70.00833  90.39030  79.66708  79.66708 
##       649       650       651       652       653       654       655       656 
##  79.66708  79.66708  71.91270  88.16752  79.66708  79.66708  88.16752  71.91270 
##       657       658       659       660       661       662       663       664 
##  98.24776  71.91270  88.16752  79.66708  71.91270  71.91270 133.65333 133.65333 
##       665       666       667       668       669       670       671       672 
##  79.66708  79.66708  79.66708  88.16752  71.91270  71.91270  88.16752  88.16752 
##       673       674       675       676       677       678       679       680 
##  71.91270  79.66708  71.91270  88.16752  88.16752  71.91270  88.16752  88.16752 
##       681       682       683       684       685       686       687       688 
##  88.16752  71.91270  71.91270  71.91270  88.16752  71.91270  71.91270  88.16752 
##       689       690       691       692       693       694       695       696 
##  71.91270  71.91270  98.24776  98.24776  88.16752  90.39030  79.66708  90.39030 
##       697       698       699       700       701       702       703       704 
##  88.16752  71.91270  71.91270  79.66708  79.66708  71.91270  71.91270  88.16752 
##       705       706       707       708       709       710       711       712 
##  71.91270  98.24776  71.91270  71.91270  98.24776  71.91270  79.66708  98.24776 
##       713       714       715       716       717       718       719       720 
##  88.16752  71.91270  88.16752  98.24776  88.16752  71.91270  88.16752  79.66708 
##       721       722       723       724       725       726       727       728 
##  88.16752  79.66708  71.91270  71.91270  71.91270  71.91270  88.16752  79.66708 
##       729       730       731       732       733       734       735       736 
##  71.91270  98.24776  98.24776  98.24776  71.91270  79.66708  79.66708  79.66708 
##       737       738       739       740       741       742       743       744 
##  71.91270  79.66708  98.24776  71.91270  71.91270  71.91270  88.16752  98.24776 
##       745       746       747       748       749       750       751       752 
##  71.91270  71.91270  71.91270  71.91270  88.16752  70.00833  71.91270  88.16752 
##       753       754       755       756       757       758       759       760 
##  71.91270  88.16752  71.91270  70.00833  71.91270  98.24776  88.16752  88.16752 
##       761       762       763       764       765       766       767       768 
##  98.24776  98.24776  70.00833  71.91270  70.00833  71.91270  79.66708  71.91270 
##       769       770       771       772       773       774       775       776 
##  79.66708  79.66708  79.66708  79.66708  98.24776  98.24776  79.66708  88.16752 
##       777       778       779       780       781       782       783       784 
##  71.91270  88.16752  90.39030  90.39030  71.91270  98.24776  88.16752  79.66708 
##       785       786       787       788       789       790       791       792 
##  71.91270  71.91270  79.66708  88.16752  88.16752  71.91270  98.24776  98.24776 
##       793       794       795       796       797       798       799       800 
##  88.16752  88.16752  88.16752  88.16752  71.91270  71.91270  71.91270  88.16752 
##       801       802       803       804       805       806       807       808 
##  71.91270  71.91270  71.91270  79.66708  79.66708  79.66708  71.91270  71.91270 
##       809       810       811       812       813       814       815       816 
##  90.39030  71.91270  98.24776  98.24776  70.00833  90.39030  90.39030  71.91270 
##       817       818       819       820       821       822       823       824 
##  71.91270  88.16752  88.16752  90.39030  71.91270  71.91270  71.91270  79.66708 
##       825       826       827       828       829       830       831       832 
##  79.66708  88.16752  88.16752  98.24776  98.24776  88.16752  88.16752  98.24776 
##       833       834       835       836       837       838       839       840 
##  98.24776  79.66708  71.91270  71.91270  71.91270  79.66708  88.16752  71.91270 
##       841       842       843       844       845       846       847       848 
##  71.91270  71.91270  71.91270  79.66708  71.91270  88.16752  98.24776  90.39030 
##       849       850       851       852       853       854       855       856 
##  90.39030  98.24776  98.24776  79.66708  79.66708  79.66708  79.66708  98.24776 
##       857       858       859       860       861       862       863       864 
##  98.24776  98.24776  88.16752  88.16752  88.16752  71.91270  71.91270  71.91270 
##       865       866       867       868       869       870       871       872 
##  71.91270  71.91270  98.24776  88.16752  71.91270  88.16752  88.16752  71.91270 
##       873       874       875       876       877       878       879       880 
##  98.24776  88.16752  79.66708  88.16752  71.91270  98.24776  71.91270  71.91270 
##       881       882       883       884       885       886       887       888 
##  79.66708  71.91270  71.91270  79.66708  79.66708  79.66708  88.16752  88.16752 
##       889       890       891       892       893       894       895       896 
##  79.66708  71.91270  98.24776  98.24776  98.24776  98.24776  88.16752  79.66708 
##       897       898       899       900       901       902       903       904 
##  71.91270  71.91270  90.39030  71.91270  90.39030  90.39030  88.16752  71.91270 
##       905       906       907       908       909       910       911       912 
##  71.91270  90.39030  88.16752  88.16752  88.16752  79.66708  88.16752  71.91270 
##       913       914       915       916       917       918       919       920 
##  71.91270  71.91270  98.24776  98.24776 133.65333  71.91270  98.24776  71.91270 
##       921       922       923       924       925       926       927       928 
##  71.91270  79.66708  90.39030  71.91270  79.66708  88.16752  98.24776  98.24776 
##       929       930       931       932       933       934       935       936 
##  71.91270  98.24776  71.91270  71.91270  98.24776  88.16752  88.16752  71.91270 
##       937       938       939       940       941       942       943       944 
##  71.91270  71.91270  71.91270  79.66708  79.66708  79.66708  71.91270  88.16752 
##       945       946       947       948       949       950       951       952 
##  88.16752  90.39030  88.16752  71.91270  71.91270  71.91270  98.24776  79.66708 
##       953       954       955       956       957       958       959       960 
##  71.91270  71.91270  71.91270  98.24776  71.91270  98.24776  79.66708  79.66708 
##       961       962       963       964       965       966       967       968 
##  79.66708  88.16752  71.91270  90.39030  90.39030  71.91270  71.91270  71.91270 
##       969       970       971       972       973       974       975       976 
##  71.91270  79.66708  71.91270  79.66708  71.91270  79.66708  71.91270  71.91270 
##       977       978       979       980       981       982       983       984 
##  71.91270  71.91270  79.66708  88.16752  98.24776  71.91270  71.91270  88.16752 
##       985       986       987       988       989       990       991       992 
##  88.16752  88.16752  90.39030  88.16752  79.66708  71.91270  88.16752  71.91270 
##       993       994       995       996       997       998       999      1000 
##  79.66708  71.91270  71.91270  71.91270  79.66708  79.66708  71.91270  71.91270 
##      1001      1002      1003      1004      1005      1006      1007      1008 
##  88.16752  98.24776  88.16752  79.66708  79.66708  71.91270  71.91270  88.16752 
##      1009      1010      1011      1012      1013      1014      1015      1016 
##  88.16752  71.91270  71.91270  90.39030  71.91270  88.16752  79.66708  88.16752 
##      1017      1018      1019      1020      1021      1022      1023      1024 
##  88.16752  79.66708  71.91270  71.91270  71.91270  71.91270  88.16752  71.91270 
##      1025      1026      1027      1028      1029      1030      1031      1032 
##  71.91270  98.24776  71.91270  71.91270  71.91270  71.91270  88.16752  98.24776 
##      1033      1034      1035      1036      1037      1038      1039      1040 
##  79.66708  71.91270  88.16752  70.00833  70.00833  71.91270  90.39030  79.66708 
##      1041      1042      1043      1044      1045      1046      1047      1048 
##  79.66708  90.39030  90.39030  71.91270  88.16752  88.16752  88.16752  88.16752 
##      1049      1050      1051      1052      1053      1054      1055      1056 
##  98.24776  71.91270  88.16752  88.16752  98.24776  88.16752 133.65333  98.24776 
##      1057      1058      1059      1060      1061      1062      1063      1064 
##  98.24776  88.16752  70.00833  79.66708  79.66708  88.16752  88.16752  88.16752 
##      1065      1066      1067      1068      1069      1070      1071      1072 
##  71.91270  70.00833  88.16752  88.16752  88.16752  71.91270  90.39030  98.24776 
##      1073      1074      1075      1076      1077      1078      1079      1080 
##  88.16752  88.16752  71.91270  79.66708  70.00833  71.91270  98.24776  98.24776 
##      1081      1082      1083      1084      1085      1086      1087      1088 
##  88.16752  71.91270  88.16752  71.91270  88.16752  71.91270  70.00833  88.16752 
##      1089      1090      1091      1092      1093      1094      1095      1096 
##  71.91270  71.91270  98.24776  98.24776  88.16752  71.91270  71.91270  88.16752 
##      1097      1098      1099      1100      1101      1102      1103      1104 
##  71.91270  88.16752  71.91270  88.16752  98.24776  79.66708  70.00833  88.16752 
##      1105      1106      1107      1108      1109      1110      1111      1112 
##  98.24776  98.24776  90.39030  90.39030  88.16752  88.16752  90.39030  71.91270 
##      1113      1114      1115      1116      1117      1118      1119      1120 
##  88.16752  79.66708  79.66708  71.91270  90.39030  71.91270  79.66708  79.66708 
##      1121      1122      1123      1124      1125      1126      1127      1128 
##  71.91270  71.91270  88.16752  71.91270  71.91270  98.24776  98.24776  71.91270 
##      1129      1130      1131      1132      1133      1134      1135      1136 
##  71.91270  79.66708  79.66708  88.16752  71.91270  88.16752  88.16752  70.00833 
##      1137      1138      1139      1140      1141      1142      1143      1144 
##  88.16752  88.16752  88.16752  88.16752  88.16752  88.16752  88.16752  71.91270 
##      1145      1146      1147      1148      1149      1150      1151      1152 
##  71.91270  71.91270  71.91270  71.91270  71.91270  71.91270  79.66708  70.00833 
##      1153      1154      1155      1156      1157      1158      1159      1160 
##  70.00833  90.39030  90.39030  79.66708  79.66708  79.66708  70.00833  71.91270 
##      1161      1162      1163      1164      1165      1166      1167      1168 
##  71.91270  71.91270  71.91270  71.91270  71.91270  71.91270  88.16752  79.66708 
##      1169      1170      1171      1172      1173      1174      1175      1176 
##  71.91270  71.91270  98.24776  79.66708  79.66708  98.24776  79.66708  71.91270 
##      1177      1178      1179      1180      1181      1182      1183      1184 
##  71.91270  71.91270  79.66708  79.66708  79.66708  71.91270  71.91270  71.91270 
##      1185      1186      1187      1188      1189      1190      1191      1192 
##  71.91270  88.16752  98.24776  98.24776  71.91270  71.91270  79.66708  71.91270 
##      1193      1194      1195      1196      1197      1198      1199      1200 
##  79.66708  71.91270  88.16752  90.39030  90.39030  71.91270  71.91270  88.16752 
##      1201      1202      1203      1204      1205      1206      1207      1208 
##  88.16752  90.39030  71.91270  79.66708  71.91270  79.66708  79.66708  71.91270 
##      1209      1210      1211      1212      1213      1214      1215      1216 
##  71.91270  71.91270  71.91270  79.66708  70.00833  88.16752  98.24776  98.24776 
##      1217      1218      1219      1220      1221      1222      1223      1224 
##  71.91270  88.16752  71.91270  71.91270  79.66708  98.24776  98.24776  98.24776 
##      1225      1226      1227      1228      1229      1230      1231      1232 
##  79.66708  98.24776  71.91270  88.16752  88.16752  71.91270  88.16752  90.39030 
##      1233      1234      1235      1236      1237      1238      1239      1240 
##  71.91270  79.66708  98.24776  88.16752  79.66708  90.39030  90.39030  71.91270 
##      1241      1242      1243      1244      1245      1246      1247      1248 
##  71.91270  79.66708  98.24776  98.24776  88.16752  88.16752  88.16752  71.91270 
##      1249      1250      1251      1252      1253      1254      1255      1256 
##  71.91270  88.16752  88.16752  71.91270  79.66708  79.66708  98.24776  98.24776 
##      1257      1258      1259      1260      1261      1262      1263      1264 
##  98.24776  88.16752  98.24776  79.66708  71.91270  90.39030  90.39030  90.39030 
##      1265      1266      1267      1268      1269      1270      1271      1272 
##  71.91270  71.91270  71.91270  88.16752  88.16752  70.00833  70.00833  79.66708 
##      1273      1274      1275      1276      1277      1278      1279      1280 
##  79.66708  71.91270  71.91270  88.16752  71.91270  71.91270  71.91270  90.39030 
##      1281      1282      1283      1284      1285      1286      1287      1288 
##  90.39030  71.91270  98.24776  79.66708  79.66708  79.66708  79.66708  79.66708 
##      1289      1290      1291      1292      1293      1294      1295      1296 
##  79.66708  79.66708  98.24776  79.66708  79.66708  71.91270  79.66708  88.16752 
##      1297      1298      1299      1300      1301      1302      1303      1304 
##  71.91270  98.24776  98.24776  71.91270  88.16752  71.91270  79.66708  88.16752 
##      1305      1306      1307      1308      1309      1310      1311      1312 
##  79.66708  71.91270  90.39030  79.66708  79.66708  88.16752  88.16752  90.39030 
##      1313      1314      1315      1316      1317      1318      1319      1320 
##  90.39030  71.91270  88.16752  90.39030  90.39030  90.39030  71.91270  88.16752 
##      1321      1322      1323      1324      1325      1326      1327      1328 
##  71.91270  98.24776  88.16752  90.39030  71.91270  88.16752  88.16752  79.66708 
##      1329      1330      1331      1332      1333      1334      1335      1336 
##  98.24776  71.91270  71.91270  71.91270  71.91270  79.66708  79.66708  71.91270 
##      1337      1338      1339      1340      1341      1342      1343      1344 
##  71.91270  98.24776  71.91270  71.91270  71.91270  71.91270  98.24776  98.24776 
##      1345      1346      1347      1348      1349      1350      1351      1352 
##  88.16752  70.00833  71.91270  71.91270  71.91270  71.91270  88.16752  88.16752 
##      1353      1354      1355      1356      1357      1358      1359      1360 
##  88.16752  79.66708  79.66708  71.91270  79.66708  71.91270  90.39030  71.91270 
##      1361      1362      1363      1364      1365      1366      1367      1368 
##  79.66708  79.66708  71.91270  88.16752  98.24776  71.91270  88.16752  90.39030 
##      1369      1370      1371      1372      1373      1374      1375      1376 
##  90.39030  90.39030  90.39030  71.91270  88.16752  88.16752  88.16752  88.16752 
##      1377      1378      1379      1380      1381      1382      1383      1384 
##  71.91270  88.16752  71.91270  88.16752  71.91270  79.66708  79.66708  79.66708 
##      1385      1386      1387      1388      1389      1390      1391      1392 
##  90.39030  79.66708  98.24776  70.00833  71.91270  79.66708  98.24776  71.91270 
##      1393      1394      1395      1396      1397      1398      1399      1400 
##  98.24776  71.91270  88.16752  88.16752  71.91270  71.91270  79.66708  79.66708 
##      1401      1402      1403      1404      1405      1406      1407      1408 
##  88.16752  88.16752  88.16752  79.66708  71.91270  71.91270  71.91270  71.91270 
##      1409      1410      1411      1412      1413      1414      1415      1416 
##  88.16752  88.16752  98.24776  70.00833  98.24776  98.24776  71.91270  90.39030 
##      1417      1418      1419      1420      1421      1422      1423      1424 
##  98.24776  88.16752  88.16752  88.16752  71.91270  71.91270  71.91270  70.00833 
##      1425      1426      1427      1428      1429      1430      1431      1432 
##  88.16752  88.16752  71.91270  88.16752  88.16752  88.16752  98.24776  98.24776 
##      1433      1434      1435      1436      1437      1438      1439      1440 
##  79.66708  79.66708  79.66708  79.66708  71.91270  88.16752  71.91270  71.91270 
##      1441      1442      1443      1444      1445      1446      1447      1448 
##  71.91270  79.66708  98.24776  71.91270  71.91270  88.16752  88.16752  71.91270 
##      1449      1450      1451      1452      1453      1454      1455      1456 
##  79.66708  71.91270  88.16752  88.16752  79.66708  90.39030  90.39030  70.00833 
##      1457      1458      1459      1460      1461      1462      1463      1464 
##  90.39030  90.39030  90.39030  90.39030  79.66708  79.66708  71.91270  88.16752 
##      1465      1466      1467      1468      1469      1470      1471      1472 
##  71.91270  71.91270  79.66708  71.91270  98.24776  98.24776  98.24776  88.16752 
##      1473      1474      1475      1476      1477      1478      1479      1480 
##  90.39030  90.39030  71.91270  71.91270  71.91270  71.91270  79.66708  71.91270 
##      1481      1482      1483      1484      1485      1486      1487      1488 
##  88.16752  88.16752  98.24776  98.24776  88.16752  88.16752  88.16752  90.39030 
##      1489      1490      1491      1492      1493      1494      1495      1496 
##  98.24776  98.24776  98.24776  98.24776  71.91270  71.91270  71.91270  71.91270 
##      1497      1498      1499      1500      1501      1502      1503      1504 
##  71.91270  79.66708  79.66708  88.16752  88.16752  79.66708  79.66708  98.24776 
##      1505      1506      1507      1508      1509      1510      1511      1512 
##  90.39030  88.16752  88.16752  79.66708  79.66708  71.91270  90.39030  90.39030 
##      1513      1514      1515      1516      1517      1518      1519      1520 
##  71.91270  88.16752  71.91270  79.66708  71.91270  88.16752  71.91270  79.66708 
##      1521      1522      1523      1524      1525      1526      1527      1528 
##  79.66708  79.66708  71.91270  88.16752  88.16752  79.66708  71.91270  88.16752 
##      1529      1530      1531      1532      1533      1534      1535      1536 
##  71.91270  71.91270  71.91270  88.16752  88.16752  71.91270  71.91270  98.24776 
##      1537      1538      1539      1540      1541      1542      1543      1544 
##  79.66708  71.91270  79.66708  79.66708  88.16752  88.16752  88.16752  79.66708 
##      1545      1546      1547      1548      1549      1550      1551      1552 
##  88.16752  98.24776  71.91270  71.91270  79.66708  98.24776  98.24776  71.91270 
##      1553      1554      1555      1556      1557      1558      1559      1560 
##  98.24776  88.16752  79.66708  79.66708  88.16752  88.16752  88.16752  71.91270 
##      1561      1562      1563      1564      1565      1566      1567      1568 
##  79.66708  71.91270  71.91270  88.16752  88.16752  70.00833  71.91270  98.24776 
##      1569      1570      1571      1572      1573      1574      1575      1576 
##  71.91270  71.91270  88.16752  71.91270  98.24776  98.24776  71.91270  71.91270 
##      1577      1578      1579      1580      1581      1582      1583      1584 
##  88.16752  71.91270  98.24776  88.16752  79.66708  71.91270  71.91270  79.66708 
##      1585      1586      1587      1588      1589      1590      1591      1592 
##  79.66708  98.24776  71.91270  71.91270  88.16752  88.16752  88.16752  88.16752 
##      1593      1594      1595      1596      1597      1598      1599      1600 
##  88.16752  98.24776  79.66708  88.16752  98.24776  98.24776  71.91270  98.24776 
##      1601      1602      1603      1604      1605      1606      1607      1608 
##  88.16752  79.66708  79.66708  79.66708  79.66708  71.91270  71.91270  79.66708 
##      1609      1610      1611      1612      1613      1614      1615      1616 
##  79.66708  88.16752  71.91270  90.39030  90.39030  71.91270  88.16752  88.16752 
##      1617      1618      1619      1620      1621      1622      1623      1624 
##  88.16752  88.16752  98.24776  71.91270  88.16752  71.91270  71.91270  71.91270 
##      1625      1626      1627      1628      1629      1630      1631      1632 
##  71.91270  71.91270  88.16752  71.91270  71.91270  88.16752  71.91270  71.91270 
##      1633      1634      1635      1636      1637      1638      1639      1640 
##  71.91270  88.16752  70.00833  98.24776  79.66708  71.91270  71.91270  88.16752 
##      1641      1642      1643      1644      1645      1646      1647      1648 
##  71.91270  98.24776  88.16752  88.16752  98.24776  79.66708  79.66708  71.91270 
##      1649      1650      1651      1652      1653      1654      1655      1656 
##  71.91270  88.16752  98.24776  79.66708  88.16752  79.66708  79.66708  88.16752 
##      1657      1658      1659      1660      1661      1662      1663      1664 
##  70.00833  90.39030  71.91270  98.24776  98.24776  79.66708  71.91270  71.91270 
##      1665      1666      1667      1668      1669      1670      1671      1672 
##  71.91270  88.16752  88.16752  88.16752  90.39030  71.91270  71.91270  71.91270 
##      1673      1674      1675      1676      1677      1678      1679      1680 
##  71.91270  71.91270  71.91270  88.16752  88.16752  88.16752  88.16752  88.16752 
##      1681      1682      1683      1684      1685      1686      1687      1688 
##  71.91270  71.91270  98.24776  98.24776  79.66708  71.91270  71.91270  71.91270 
##      1689      1690      1691      1692      1693      1694      1695      1696 
##  90.39030  71.91270  79.66708  88.16752  71.91270  88.16752  88.16752  71.91270 
##      1697      1698      1699      1700      1701      1702      1703      1704 
##  70.00833  98.24776  88.16752  88.16752  88.16752  71.91270  79.66708  88.16752 
##      1705      1706      1707      1708      1709      1710      1711      1712 
##  88.16752  88.16752  90.39030  98.24776  90.39030  71.91270  71.91270  71.91270 
##      1713      1714      1715      1716      1717      1718      1719      1720 
##  98.24776  79.66708  88.16752  88.16752  88.16752  88.16752  88.16752  90.39030 
##      1721      1722      1723      1724      1725      1726      1727      1728 
##  71.91270  71.91270  98.24776  88.16752  71.91270  71.91270  88.16752  98.24776 
##      1729      1730      1731      1732      1733      1734      1735      1736 
##  71.91270  71.91270  71.91270  88.16752  88.16752  88.16752  88.16752  88.16752 
##      1737      1738      1739      1740      1741      1742      1743      1744 
##  88.16752  71.91270  71.91270  88.16752  98.24776  98.24776  70.00833  98.24776 
##      1745      1746      1747      1748      1749      1750      1751      1752 
##  98.24776  98.24776  98.24776  98.24776  88.16752  71.91270  71.91270  71.91270 
##      1753      1754      1755      1756      1757      1758      1759      1760 
##  71.91270  88.16752  98.24776  98.24776  90.39030  90.39030  71.91270  71.91270 
##      1761      1762      1763      1764      1765      1766      1767      1768 
##  71.91270  71.91270 133.65333 133.65333 133.65333  71.91270  88.16752  88.16752 
##      1769      1770      1771      1772      1773      1774      1775      1776 
##  79.66708  79.66708  79.66708  98.24776  98.24776  90.39030  90.39030  88.16752 
##      1777      1778      1779      1780      1781      1782      1783      1784 
##  79.66708  71.91270  71.91270  88.16752  88.16752  98.24776  71.91270  71.91270 
##      1785      1786      1787      1788      1789      1790      1791      1792 
##  71.91270  71.91270  71.91270  88.16752  98.24776  98.24776  88.16752  70.00833 
##      1793      1794      1795      1796      1797      1798      1799      1800 
##  71.91270  98.24776  79.66708  79.66708  98.24776  98.24776  98.24776  98.24776 
##      1801      1802      1803      1804      1805      1806      1807      1808 
##  71.91270  88.16752  88.16752  88.16752  88.16752  71.91270  71.91270  98.24776 
##      1809      1810      1811      1812      1813      1814      1815      1816 
##  98.24776  98.24776  71.91270  88.16752  88.16752  88.16752  88.16752  88.16752 
##      1817      1818      1819      1820      1821      1822      1823      1824 
##  71.91270  98.24776  88.16752  79.66708  88.16752  98.24776  98.24776  98.24776 
##      1825      1826      1827      1828      1829      1830      1831      1832 
##  71.91270  71.91270  71.91270  71.91270  79.66708  79.66708  88.16752  71.91270 
##      1833      1834      1835      1836      1837      1838      1839      1840 
##  98.24776  98.24776  98.24776  71.91270  88.16752  88.16752  71.91270  90.39030 
##      1841      1842      1843      1844      1845      1846      1847      1848 
##  98.24776  98.24776  71.91270  88.16752  71.91270  98.24776  98.24776  88.16752 
##      1849      1850      1851      1852      1853      1854      1855      1856 
##  88.16752  88.16752  88.16752  71.91270  71.91270  71.91270  71.91270  71.91270 
##      1857      1858      1859      1860      1861      1862      1863      1864 
##  71.91270  71.91270  71.91270  71.91270  88.16752  71.91270  71.91270  71.91270 
##      1865      1866      1867      1868      1869      1870      1871      1872 
##  71.91270  71.91270  71.91270  71.91270  88.16752  88.16752  71.91270  98.24776 
##      1873      1874      1875      1876      1877      1878      1879      1880 
##  71.91270  71.91270  88.16752  71.91270  71.91270  71.91270  71.91270  88.16752 
##      1881      1882      1883      1884      1885      1886      1887      1888 
##  88.16752  71.91270  88.16752  88.16752  71.91270  98.24776  98.24776  88.16752 
##      1889      1890      1891      1892      1893      1894      1895      1896 
##  88.16752  71.91270  71.91270  71.91270  71.91270  71.91270  71.91270  98.24776 
##      1897      1898      1899      1900      1901      1902      1903      1904 
##  98.24776  71.91270  71.91270  71.91270  71.91270  71.91270  71.91270  88.16752 
##      1905      1906      1907      1908      1909      1910      1911      1912 
##  88.16752  79.66708  90.39030  71.91270  88.16752  88.16752  71.91270  98.24776 
##      1913      1914      1915      1916      1917      1918      1919      1920 
##  71.91270  88.16752  79.66708  71.91270  71.91270  71.91270  71.91270  71.91270 
##      1921      1922      1923      1924      1925      1926      1927      1928 
##  79.66708  71.91270  70.00833  71.91270  88.16752  79.66708  98.24776  88.16752 
##      1929      1930      1931      1932      1933      1934      1935      1936 
##  88.16752  88.16752  71.91270  88.16752  79.66708  70.00833  88.16752  71.91270 
##      1937      1938      1939      1940      1941      1942      1943      1944 
##  71.91270  71.91270  71.91270  71.91270  88.16752  88.16752  88.16752  79.66708 
##      1945      1946      1947      1948      1949      1950      1951      1952 
##  88.16752  71.91270  71.91270  88.16752  98.24776  71.91270  71.91270  71.91270 
##      1953      1954      1955      1956      1957      1958      1959      1960 
##  71.91270  71.91270  71.91270  71.91270  71.91270  71.91270  98.24776  98.24776 
##      1961      1962      1963      1964      1965      1966      1967      1968 
##  79.66708  71.91270  98.24776  98.24776  79.66708  71.91270  79.66708  88.16752 
##      1969      1970      1971      1972      1973      1974      1975      1976 
##  88.16752  71.91270  88.16752  98.24776  88.16752  98.24776  88.16752  70.00833 
##      1977      1978      1979      1980      1981      1982      1983      1984 
##  88.16752  88.16752  71.91270  98.24776  98.24776  88.16752  90.39030  88.16752 
##      1985      1986      1987      1988      1989      1990      1991      1992 
##  71.91270  88.16752  88.16752  71.91270  88.16752  88.16752  88.16752  88.16752 
##      1993      1994      1995      1996      1997      1998      1999      2000 
##  90.39030  71.91270  71.91270  88.16752  79.66708  71.91270  71.91270  88.16752 
##      2001      2002      2003      2004      2005      2006      2007      2008 
##  88.16752  88.16752  88.16752  71.91270  71.91270  79.66708  79.66708  71.91270 
##      2009      2010      2011      2012      2013      2014      2015      2016 
##  90.39030  98.24776  98.24776  98.24776  88.16752  71.91270  71.91270  90.39030 
##      2017      2018      2019      2020      2021      2022      2023      2024 
##  88.16752  88.16752  71.91270  88.16752  71.91270  71.91270  98.24776  98.24776 
##      2025      2026      2027      2028      2029      2030      2031      2032 
##  88.16752  90.39030  88.16752  71.91270  88.16752  71.91270  90.39030  98.24776 
##      2033      2034      2035      2036      2037      2038      2039      2040 
##  88.16752  71.91270  79.66708  79.66708  71.91270  71.91270  71.91270  88.16752 
##      2041      2042      2043      2044      2045      2046      2047      2048 
##  71.91270  98.24776  88.16752  71.91270  88.16752  88.16752  90.39030  79.66708 
##      2049      2050      2051      2052      2053      2054      2055      2056 
##  79.66708  79.66708  71.91270  88.16752  88.16752  71.91270  88.16752  71.91270 
##      2057      2058      2059      2060      2061      2062      2063      2064 
##  71.91270  98.24776  71.91270  88.16752  88.16752  71.91270  88.16752  79.66708 
##      2065      2066      2067      2068      2069      2070      2071      2072 
##  71.91270  88.16752  88.16752  88.16752  98.24776  98.24776  98.24776  98.24776 
##      2073      2074      2075      2076      2077      2078      2079      2080 
##  88.16752  98.24776  71.91270  71.91270  71.91270  71.91270  71.91270  71.91270 
##      2081      2082      2083      2084      2085      2086      2087      2088 
##  71.91270  71.91270  71.91270  88.16752  88.16752  88.16752  98.24776  88.16752 
##      2089      2090      2091      2092      2093      2094      2095      2096 
##  90.39030  90.39030  79.66708  79.66708  71.91270  88.16752  88.16752  71.91270 
##      2097      2098      2099      2100      2101      2102      2103      2104 
##  71.91270  71.91270  88.16752  90.39030  70.00833  70.00833  88.16752  98.24776 
##      2105      2106      2107      2108      2109      2110      2111      2112 
##  71.91270  98.24776  88.16752  98.24776  71.91270  79.66708  71.91270  70.00833 
##      2113      2114      2115      2116      2117      2118      2119      2120 
##  98.24776  71.91270  71.91270  71.91270  71.91270  71.91270  70.00833  88.16752 
##      2121      2122      2123      2124      2125      2126      2127      2128 
##  88.16752  71.91270  98.24776  98.24776  90.39030  79.66708  98.24776  98.24776 
##      2129      2130      2131      2132      2133      2134      2135      2136 
##  88.16752  71.91270  88.16752  88.16752  88.16752  71.91270  88.16752  88.16752 
##      2137      2138      2139      2140      2141      2142      2143      2144 
##  88.16752  71.91270  71.91270  71.91270  88.16752  88.16752  88.16752  88.16752 
##      2145      2146      2147      2148      2149      2150      2151      2152 
##  79.66708  71.91270  98.24776  71.91270  79.66708  71.91270  71.91270  88.16752 
##      2153      2154      2155      2156      2157      2158      2159      2160 
##  90.39030  98.24776  98.24776  71.91270  71.91270  71.91270  71.91270  71.91270 
##      2161      2162      2163      2164      2165      2166      2167      2168 
##  88.16752  90.39030  71.91270  79.66708  79.66708  71.91270  79.66708  88.16752 
##      2169      2170      2171      2172      2173      2174      2175      2176 
##  90.39030  98.24776  88.16752  98.24776  98.24776  88.16752  71.91270  71.91270 
##      2177      2178      2179      2180      2181      2182      2183      2184 
##  79.66708  88.16752  79.66708  71.91270  79.66708  79.66708  79.66708  79.66708 
##      2185      2186      2187      2188      2189      2190      2191      2192 
##  79.66708  88.16752  90.39030  88.16752  98.24776  98.24776  71.91270  71.91270 
##      2193      2194      2195      2196      2197      2198      2199      2200 
##  88.16752  79.66708  71.91270  71.91270  71.91270  79.66708  79.66708  90.39030 
##      2201      2202      2203      2204      2205      2206      2207      2208 
##  71.91270  88.16752  88.16752  90.39030  79.66708  71.91270  71.91270  90.39030 
##      2209      2210      2211      2212      2213      2214      2215      2216 
##  88.16752  88.16752  88.16752  88.16752  71.91270  71.91270  71.91270  71.91270 
##      2217      2218      2219      2220      2221      2222      2223      2224 
##  71.91270  79.66708  79.66708  71.91270  71.91270  71.91270  71.91270  88.16752 
##      2225      2226      2227      2228      2229      2230      2231      2232 
##  71.91270  90.39030  79.66708  79.66708  79.66708  79.66708  79.66708  71.91270 
##      2233      2234      2235      2236      2237      2238      2239      2240 
##  71.91270  71.91270  98.24776  79.66708  98.24776  98.24776  98.24776  98.24776 
##      2241      2242      2243      2244      2245      2246      2247      2248 
##  88.16752  88.16752  71.91270  71.91270  71.91270  88.16752  88.16752  79.66708 
##      2249      2250      2251      2252      2253      2254      2255      2256 
##  90.39030  98.24776  88.16752  71.91270  90.39030  90.39030  71.91270  98.24776 
##      2257      2258      2259      2260      2261      2262      2263      2264 
##  90.39030  71.91270  71.91270  71.91270  71.91270  71.91270  88.16752  71.91270 
##      2265      2266      2267      2268      2269      2270      2271      2272 
##  71.91270  79.66708  79.66708  71.91270  71.91270  98.24776  88.16752  88.16752 
##      2273      2274      2275      2276      2277      2278      2279      2280 
##  88.16752  88.16752  88.16752  90.39030  90.39030  90.39030  79.66708  98.24776 
##      2281      2282      2283      2284      2285      2286      2287      2288 
##  88.16752  88.16752  79.66708  79.66708  98.24776  98.24776  88.16752  70.00833 
##      2289      2290      2291      2292      2293      2294      2295      2296 
##  70.00833  71.91270  90.39030  71.91270  88.16752  71.91270  79.66708  88.16752 
##      2297      2298      2299      2300      2301      2302      2303      2304 
##  88.16752  70.00833  79.66708  70.00833  79.66708  71.91270  88.16752  71.91270 
##      2305      2306      2307      2308      2309      2310      2311      2312 
##  71.91270  71.91270  90.39030  90.39030  88.16752  79.66708  88.16752  88.16752 
##      2313      2314      2315      2316      2317      2318      2319      2320 
##  98.24776  98.24776  98.24776  88.16752  71.91270  71.91270  71.91270  71.91270 
##      2321      2322      2323      2324      2325      2326      2327      2328 
##  90.39030  70.00833  98.24776  71.91270  71.91270  71.91270  88.16752  71.91270 
##      2329      2330      2331      2332      2333      2334      2335      2336 
##  71.91270  71.91270  79.66708  70.00833  71.91270  71.91270  98.24776  98.24776 
##      2337      2338      2339      2340      2341      2342      2343      2344 
##  98.24776  70.00833  90.39030  70.00833  90.39030  79.66708  71.91270  71.91270 
##      2345      2346      2347      2348      2349      2350      2351      2352 
##  79.66708  71.91270  79.66708  70.00833  79.66708  98.24776  98.24776  98.24776 
##      2353      2354      2355      2356      2357      2358      2359      2360 
##  79.66708  79.66708  71.91270  90.39030  90.39030  90.39030  98.24776  71.91270 
##      2361      2362      2363      2364      2365      2366      2367      2368 
##  98.24776  98.24776  71.91270  71.91270  71.91270  71.91270  71.91270  88.16752 
##      2369      2370      2371      2372      2373      2374      2375      2376 
##  71.91270  98.24776  98.24776  98.24776  98.24776  98.24776  98.24776  71.91270 
##      2377      2378      2379      2380      2381      2382      2383      2384 
##  71.91270  71.91270  79.66708  88.16752  71.91270  71.91270  71.91270  98.24776 
##      2385      2386      2387      2388      2389      2390      2391      2392 
##  79.66708  98.24776  98.24776  98.24776  98.24776  88.16752  90.39030  71.91270 
##      2393      2394      2395      2396      2397      2398      2399      2400 
##  71.91270  71.91270  98.24776  71.91270  71.91270  71.91270  71.91270  70.00833 
##      2401      2402      2403      2404      2405      2406      2407      2408 
##  98.24776  71.91270  71.91270  71.91270  88.16752  88.16752  90.39030  88.16752 
##      2409      2410      2411      2412      2413      2414      2415      2416 
##  88.16752  98.24776  88.16752  88.16752  71.91270  88.16752  88.16752  98.24776 
##      2417      2418      2419      2420      2421      2422      2423      2424 
##  71.91270  90.39030  79.66708  98.24776  98.24776  98.24776  88.16752  88.16752 
##      2425      2426      2427      2428      2429      2430      2431      2432 
##  90.39030  88.16752  70.00833  98.24776  90.39030  98.24776  71.91270  88.16752 
##      2433      2434      2435      2436      2437      2438      2439      2440 
##  88.16752  88.16752  88.16752  88.16752  88.16752  88.16752  88.16752  71.91270 
##      2441      2442      2443      2444      2445      2446      2447      2448 
##  71.91270  79.66708  71.91270  71.91270  71.91270  71.91270  88.16752  90.39030 
##      2449      2450      2451      2452      2453      2454      2455      2456 
##  79.66708  79.66708  90.39030  71.91270  70.00833  70.00833  88.16752  71.91270 
##      2457      2458      2459      2460      2461      2462      2463      2464 
##  71.91270  71.91270  71.91270  88.16752  88.16752  88.16752  71.91270  71.91270 
##      2465      2466      2467      2468      2469      2470      2471      2472 
##  71.91270  98.24776  71.91270  90.39030  98.24776  79.66708  88.16752  88.16752 
##      2473      2474      2475      2476      2477      2478      2479      2480 
##  98.24776  71.91270  90.39030  88.16752  88.16752  88.16752  88.16752  88.16752 
##      2481      2482      2483      2484      2485      2486      2487      2488 
##  71.91270  71.91270  70.00833  88.16752  71.91270 133.65333  79.66708  88.16752 
##      2489      2490      2491      2492      2493      2494      2495      2496 
##  71.91270  71.91270  71.91270  79.66708  71.91270  88.16752  71.91270  88.16752 
##      2497      2498      2499      2500      2501      2502      2503      2504 
##  71.91270  71.91270  71.91270  98.24776  79.66708  71.91270  98.24776  98.24776 
##      2505      2506      2507      2508      2509      2510      2511      2512 
##  98.24776  98.24776  79.66708  88.16752  88.16752  88.16752  88.16752  71.91270 
##      2513      2514      2515      2516      2517      2518      2519      2520 
##  98.24776  98.24776  98.24776  90.39030  98.24776  98.24776  70.00833  70.00833 
##      2521      2522      2523      2524      2525      2526      2527      2528 
##  79.66708  79.66708  79.66708  90.39030  88.16752  71.91270  71.91270  79.66708 
##      2529      2530      2531      2532      2533      2534      2535      2536 
##  71.91270  71.91270  98.24776  98.24776  88.16752  88.16752  71.91270  71.91270 
##      2537      2538      2539      2540      2541      2542      2543      2544 
##  79.66708  79.66708  90.39030  98.24776  98.24776  71.91270  71.91270  71.91270 
##      2545      2546      2547      2548      2549      2550      2551      2552 
##  71.91270  88.16752  79.66708  79.66708  79.66708  88.16752  88.16752  88.16752 
##      2553      2554      2555      2556      2557      2558      2559      2560 
##  71.91270  88.16752  90.39030  90.39030  71.91270  71.91270  71.91270  71.91270 
##      2561      2562      2563      2564      2565      2566      2567      2568 
##  98.24776  98.24776  98.24776  88.16752  98.24776  98.24776  71.91270  71.91270 
##      2569      2570      2571      2572      2573      2574      2575      2576 
##  88.16752  98.24776  71.91270  71.91270  71.91270  88.16752  88.16752  88.16752 
##      2577      2578      2579      2580      2581      2582      2583      2584 
##  71.91270  70.00833  88.16752  88.16752  88.16752  79.66708  71.91270  98.24776 
##      2585      2586      2587      2588      2589      2590      2591      2592 
##  71.91270  79.66708  88.16752  71.91270  71.91270  79.66708  79.66708  88.16752 
##      2593      2594      2595      2596      2597      2598      2599      2600 
##  71.91270  90.39030  90.39030  90.39030  71.91270  70.00833  88.16752  70.00833 
##      2601      2602      2603      2604      2605      2606      2607      2608 
##  70.00833  88.16752  90.39030  90.39030  90.39030  90.39030  88.16752  71.91270 
##      2609      2610      2611      2612      2613      2614      2615      2616 
##  71.91270  88.16752  70.00833  90.39030  90.39030  90.39030  88.16752  88.16752 
##      2617      2618      2619      2620      2621      2622      2623      2624 
##  79.66708  79.66708  79.66708  98.24776  98.24776  71.91270  88.16752  71.91270 
##      2625      2626      2627      2628      2629      2630      2631      2632 
##  71.91270  88.16752  90.39030  71.91270  70.00833  71.91270  71.91270  71.91270 
##      2633      2634      2635      2636      2637      2638      2639      2640 
##  79.66708  88.16752  88.16752  88.16752  88.16752  90.39030  71.91270  71.91270 
##      2641      2642      2643      2644      2645      2646      2647      2648 
##  79.66708  79.66708  98.24776  88.16752  71.91270  71.91270  71.91270  90.39030 
##      2649      2650      2651      2652      2653      2654      2655      2656 
##  98.24776  79.66708  79.66708  79.66708  79.66708  88.16752  71.91270  88.16752 
##      2657      2658      2659      2660      2661      2662      2663      2664 
##  88.16752  88.16752  88.16752  70.00833  79.66708  79.66708  88.16752  71.91270 
##      2665      2666      2667      2668      2669      2670      2671      2672 
##  79.66708  79.66708  88.16752  98.24776  88.16752  88.16752  71.91270  71.91270 
##      2673      2674      2675      2676      2677      2678      2679      2680 
##  71.91270  71.91270  71.91270  79.66708  79.66708  71.91270  79.66708  88.16752 
##      2681      2682      2683      2684      2685      2686      2687      2688 
##  90.39030  90.39030  90.39030  88.16752  88.16752  88.16752  71.91270  71.91270 
##      2689      2690      2691      2692      2693      2694      2695      2696 
##  71.91270  71.91270  71.91270  71.91270  98.24776  98.24776  79.66708  71.91270 
##      2697      2698      2699      2700      2701      2702      2703      2704 
##  90.39030  98.24776  98.24776  88.16752  88.16752  71.91270  71.91270  98.24776 
##      2705      2706      2707      2708      2709      2710      2711      2712 
##  98.24776  88.16752  88.16752  98.24776  71.91270  70.00833  70.00833  98.24776 
##      2713      2714      2715      2716      2717      2718      2719      2720 
##  88.16752  88.16752  98.24776  98.24776  71.91270  71.91270  88.16752  88.16752 
##      2721      2722      2723      2724      2725      2726      2727      2728 
##  79.66708  79.66708  79.66708  71.91270  98.24776  88.16752  79.66708  71.91270 
##      2729      2730      2731      2732      2733      2734      2735      2736 
##  71.91270  71.91270  88.16752  88.16752  71.91270  71.91270  88.16752  88.16752 
##      2737      2738      2739      2740      2741      2742      2743      2744 
##  88.16752  71.91270  88.16752  88.16752  90.39030  71.91270  71.91270  79.66708 
##      2745      2746      2747      2748      2749      2750      2751      2752 
##  79.66708  88.16752  98.24776  71.91270  71.91270  90.39030  71.91270  71.91270 
##      2753      2754      2755      2756      2757      2758      2759      2760 
##  88.16752  79.66708  79.66708  79.66708  79.66708  98.24776  71.91270  71.91270 
##      2761      2762      2763      2764      2765      2766      2767      2768 
##  71.91270  79.66708  98.24776  79.66708  88.16752  88.16752  79.66708  70.00833 
##      2769      2770      2771      2772      2773      2774      2775      2776 
##  70.00833  88.16752  88.16752  88.16752  71.91270  71.91270  79.66708  98.24776 
##      2777      2778      2779      2780      2781      2782      2783      2784 
##  98.24776  98.24776  98.24776  71.91270  71.91270  79.66708  79.66708  88.16752 
##      2785      2786      2787      2788      2789      2790      2791      2792 
##  71.91270  88.16752  88.16752  88.16752  88.16752  88.16752  71.91270  71.91270 
##      2793      2794      2795      2796      2797      2798      2799      2800 
##  71.91270  71.91270  79.66708  88.16752  88.16752  71.91270  88.16752  88.16752 
##      2801      2802      2803      2804      2805      2806      2807      2808 
##  88.16752  88.16752  70.00833  70.00833  88.16752  88.16752  88.16752  71.91270 
##      2809      2810      2811      2812      2813      2814      2815      2816 
##  71.91270  98.24776  90.39030  90.39030  79.66708  71.91270  88.16752  88.16752 
##      2817      2818      2819      2820      2821      2822      2823      2824 
##  88.16752  79.66708  88.16752 133.65333 133.65333  88.16752  79.66708  88.16752 
##      2825      2826      2827      2828      2829      2830      2831      2832 
##  70.00833  70.00833  88.16752  79.66708  71.91270  71.91270  88.16752  71.91270 
##      2833      2834      2835      2836      2837      2838      2839      2840 
##  88.16752  79.66708  98.24776  79.66708  88.16752  79.66708  88.16752  71.91270 
##      2841      2842      2843      2844      2845      2846      2847      2848 
##  71.91270  88.16752 133.65333 133.65333  71.91270  71.91270  88.16752  71.91270 
##      2849      2850      2851      2852      2853      2854      2855      2856 
##  71.91270  98.24776  98.24776  98.24776  79.66708  88.16752  71.91270  71.91270 
##      2857      2858      2859      2860      2861      2862      2863      2864 
##  71.91270  71.91270  90.39030  88.16752  88.16752  88.16752  71.91270  98.24776 
##      2865      2866      2867      2868      2869      2870      2871      2872 
##  71.91270  88.16752  71.91270  88.16752  88.16752  88.16752  88.16752  79.66708
MSE_dectree <- mean((dec_tree_pred - nhanes_test$Weight)^2)
MSE_dectree
## [1] 334.6264
rf_pred <- predict(nhanes_train_rf, nhanes_test)
rf_pred
##         1         2         3         4         5         6         7         8 
##  91.77570 103.45613  93.62301  85.90563  75.77411  75.77411  77.04329  87.65186 
##         9        10        11        12        13        14        15        16 
##  87.65186  87.65186  87.65186  78.56415  89.06767  77.79766  77.79766  73.13047 
##        17        18        19        20        21        22        23        24 
##  73.13047  63.76275  67.14757  72.54259  72.54259  79.75898  79.75898  79.75898 
##        25        26        27        28        29        30        31        32 
##  79.75898  69.50162  69.50162  69.17827  85.87352  96.73292  78.41879  84.59617 
##        33        34        35        36        37        38        39        40 
##  77.61602 105.57507 105.57507 105.57507  61.08209  63.03534  63.03534  80.82848 
##        41        42        43        44        45        46        47        48 
##  70.86806  92.26734  82.22403  69.01534  65.41198  63.06642  69.95330  72.10338 
##        49        50        51        52        53        54        55        56 
##  68.54365  83.89132  82.77043  77.88650  77.88650  77.88650  84.11842  89.68392 
##        57        58        59        60        61        62        63        64 
##  89.68392  79.70215  94.60670  89.79294  89.21816  91.50900  69.16661  79.11849 
##        65        66        67        68        69        70        71        72 
##  79.30947  77.31551  66.98751  97.50907  79.66145  83.13468  63.99225  80.22013 
##        73        74        75        76        77        78        79        80 
##  82.99590  85.74944  99.61668  95.02102  95.02102  92.17070  68.47831  93.45881 
##        81        82        83        84        85        86        87        88 
##  73.25566  81.91810  78.03569  78.03569  66.78961  66.78961  92.47397  61.62657 
##        89        90        91        92        93        94        95        96 
## 105.40778 105.40778 105.40778  95.07828  71.17714  95.92342  92.62682  82.93616 
##        97        98        99       100       101       102       103       104 
##  82.93616  81.23991  97.60295 109.73628  80.80462  74.35761  93.22760  86.33888 
##       105       106       107       108       109       110       111       112 
##  86.33888  83.51406  83.51406  94.86591  90.71755  90.71755 102.39048 105.50848 
##       113       114       115       116       117       118       119       120 
## 105.50848  56.64726  83.20883  99.33841  96.51548  93.93375  89.96079  89.96079 
##       121       122       123       124       125       126       127       128 
##  83.30225  70.57411  80.74548  79.18269  81.67836  67.51757  75.81560  73.15860 
##       129       130       131       132       133       134       135       136 
##  91.97556  82.98098  89.57518  99.67757  99.67757  72.37363  70.49524  76.41660 
##       137       138       139       140       141       142       143       144 
##  76.41660  81.87503  84.18685  94.19103  87.55960  66.82509  66.82509  82.45675 
##       145       146       147       148       149       150       151       152 
##  82.45675  72.46760 103.99181 103.99181  87.18550 100.40503  83.15928  77.65985 
##       153       154       155       156       157       158       159       160 
##  77.65985  69.83654  94.95909  81.31636  94.63318  76.63176  80.91135  72.87645 
##       161       162       163       164       165       166       167       168 
##  72.53575  80.63636  71.10724  84.36254  75.90619 107.95154  70.23042  78.35008 
##       169       170       171       172       173       174       175       176 
##  92.31673  74.82937  67.67393  93.53467  97.44652  89.15154  76.00787  76.00787 
##       177       178       179       180       181       182       183       184 
## 121.24879  79.27755  91.59814 101.92311  81.47467  82.14966  85.20189  73.94943 
##       185       186       187       188       189       190       191       192 
##  73.02841  85.59414  95.94805  95.94805  87.61374  72.24567  76.60954  83.76931 
##       193       194       195       196       197       198       199       200 
##  69.95780  77.85727  72.65206  72.65206  75.65994  76.51722  86.57745  75.38893 
##       201       202       203       204       205       206       207       208 
##  75.38893  85.84489 113.26945 109.13013  53.58816  93.51845  78.09623  94.71800 
##       209       210       211       212       213       214       215       216 
##  82.32187  82.32187  84.40740  94.31890  73.81548  84.01736  84.01736  62.77386 
##       217       218       219       220       221       222       223       224 
##  73.96883 109.68580 100.88213  67.11290  74.13041  68.69790  73.03763  90.98386 
##       225       226       227       228       229       230       231       232 
##  90.98386  72.73048  74.27147  86.96294  85.69015 100.96410  78.72012  75.63083 
##       233       234       235       236       237       238       239       240 
##  97.74539  77.89523 107.86483 107.86483  68.68618  99.55588  99.55588  99.55588 
##       241       242       243       244       245       246       247       248 
##  63.97149  78.41290  78.41290  75.46037  93.24671 104.54021  70.81884  81.24409 
##       249       250       251       252       253       254       255       256 
##  74.53400  74.53400  88.59492  81.26120  95.17560  95.17560  82.21856  75.69129 
##       257       258       259       260       261       262       263       264 
##  86.64049  96.55930  93.93664  89.60270  89.60270  82.43446  76.98210  60.72980 
##       265       266       267       268       269       270       271       272 
##  69.77257  92.72266  82.32799 110.68976  88.76996  88.76996  88.87627  90.96028 
##       273       274       275       276       277       278       279       280 
##  90.96028  71.64524  92.72126  92.72126  68.30062  71.86349  80.89418  95.07091 
##       281       282       283       284       285       286       287       288 
##  95.07091  77.60901  76.09627  73.71658  91.58715  91.58715  91.58715 110.83364 
##       289       290       291       292       293       294       295       296 
##  76.63976  72.01297  78.23241  78.23241  85.63836  82.98632  96.54271  75.23647 
##       297       298       299       300       301       302       303       304 
##  75.23647  63.62602  75.89002  75.59034 109.14203 106.17449  98.07833  98.07833 
##       305       306       307       308       309       310       311       312 
##  63.85281  78.38192  67.77875  71.19637  96.98038  82.35900  82.35900 100.49969 
##       313       314       315       316       317       318       319       320 
## 100.49969  97.79055  95.78845  93.61247  92.33424  88.93913  73.81035  98.34288 
##       321       322       323       324       325       326       327       328 
##  79.74618  76.71924  76.71924  83.67863  83.67863  88.62336  84.58299  84.58299 
##       329       330       331       332       333       334       335       336 
##  88.75453  88.75453  95.82800  67.33348  75.82696  78.44625  65.34721  71.63698 
##       337       338       339       340       341       342       343       344 
##  89.39088  89.39088  96.80284  84.70706  76.38678  77.20395  74.12549  97.97605 
##       345       346       347       348       349       350       351       352 
##  76.86270  90.18822  95.88937  83.47473  90.61002  90.61002  94.40730 106.76539 
##       353       354       355       356       357       358       359       360 
## 106.76539 106.76539  90.06732  90.06732  99.99185  99.99185  66.95937  97.34514 
##       361       362       363       364       365       366       367       368 
##  65.61609  88.94793  68.03285  91.21697  73.18177  94.25207  92.29820  92.29820 
##       369       370       371       372       373       374       375       376 
##  89.68819  89.68819  78.66045  71.12405  73.49358  71.96401  92.63111  92.63111 
##       377       378       379       380       381       382       383       384 
##  86.58044  74.80233  80.57450  94.72532  87.35589  95.57734  73.95544  85.09566 
##       385       386       387       388       389       390       391       392 
##  68.17626  86.53533  68.80297  68.80297  88.70871  68.17774  94.95348  89.88455 
##       393       394       395       396       397       398       399       400 
##  89.88455  90.26221  87.05709  73.01405  73.61790  76.29021  95.46080  74.07142 
##       401       402       403       404       405       406       407       408 
##  91.76551  70.05493  76.39459  76.39459  76.39459  73.48126  82.45472  82.50164 
##       409       410       411       412       413       414       415       416 
##  70.59044  89.30571  67.72381  95.95686  92.62643  71.95078  87.47895  73.35054 
##       417       418       419       420       421       422       423       424 
##  77.21677  77.21677  75.16910  83.07457  86.04097  87.92115  86.03081  75.36256 
##       425       426       427       428       429       430       431       432 
##  75.36256  76.72690  75.70432  86.78428  69.42436  74.10324  74.70610  84.60836 
##       433       434       435       436       437       438       439       440 
##  85.48794  85.48794 108.80834 108.80834  82.09463  80.06187  80.06187  85.01499 
##       441       442       443       444       445       446       447       448 
##  77.23528  92.53285  93.14895  77.77828  77.77828  77.77828  85.15936  94.84215 
##       449       450       451       452       453       454       455       456 
##  94.19894  71.60972  71.03741  84.23626  84.23626  68.77074  68.77074  76.78667 
##       457       458       459       460       461       462       463       464 
##  95.52562  54.90542  54.90542  87.79026  94.23152  94.23152  94.23152  74.66173 
##       465       466       467       468       469       470       471       472 
##  96.29439  78.92184  74.35497  74.35497  80.93445  69.66784  69.66784  81.11182 
##       473       474       475       476       477       478       479       480 
##  81.47381  68.14648  68.14648  68.14648  68.14648  69.58541  94.19845  85.56922 
##       481       482       483       484       485       486       487       488 
##  85.56922  65.32834  55.15860  55.15860  81.81567  90.30017  63.89086  63.89086 
##       489       490       491       492       493       494       495       496 
##  58.23662  61.99213  61.99213  74.78256  74.01755  75.91706 109.59134  97.93490 
##       497       498       499       500       501       502       503       504 
##  96.25879  96.25879 110.78247 110.78247  88.83545  63.80017  79.71351 106.82613 
##       505       506       507       508       509       510       511       512 
##  68.04571  69.00609  86.81666 100.52919 100.52919  82.95279  71.67661  76.80721 
##       513       514       515       516       517       518       519       520 
##  87.40415  75.13559  75.13559  79.42314  76.53864  65.21523  78.64531  78.44783 
##       521       522       523       524       525       526       527       528 
##  95.19078  75.48951  85.39768  72.41531  97.09451  77.59911 101.18477  70.74413 
##       529       530       531       532       533       534       535       536 
##  70.74413 103.51154  67.11316  76.69099  80.47602  68.64914  88.30586  61.99682 
##       537       538       539       540       541       542       543       544 
##  84.81989  84.81989  92.00297  72.27254  70.19012  70.19012  53.91620  82.22062 
##       545       546       547       548       549       550       551       552 
##  82.22062  89.80673  89.80673  92.11638  72.16155  76.01489  76.62617  79.81973 
##       553       554       555       556       557       558       559       560 
##  77.79232  94.27495  96.11448  89.10084  84.42601  85.81829  85.81829  87.65438 
##       561       562       563       564       565       566       567       568 
##  87.65438  92.13854  69.97362  80.86021  79.77449  83.96159  83.96159  83.96159 
##       569       570       571       572       573       574       575       576 
## 102.04798 102.04798  77.77645  98.58559  98.58559  57.02907  69.40022  69.40022 
##       577       578       579       580       581       582       583       584 
##  77.86067  68.93976  71.76763  81.19299  81.19299  81.19299  86.09765  81.99560 
##       585       586       587       588       589       590       591       592 
##  89.84582  75.59424  93.09400 115.05569  81.52790 105.16540 105.16540  72.00013 
##       593       594       595       596       597       598       599       600 
##  78.91709  77.44962  71.33584  84.60467  84.60467  69.48146  72.72504  91.00448 
##       601       602       603       604       605       606       607       608 
## 104.16627  77.92844  90.20707  60.74324  60.74324  73.42802  79.28234  79.28234 
##       609       610       611       612       613       614       615       616 
##  79.28234  81.32523 103.98527 103.98527  80.01357  95.66447  78.49423 100.10818 
##       617       618       619       620       621       622       623       624 
## 101.21432  71.96091  72.19663  71.54157  73.86247  97.55267  98.58890 147.50396 
##       625       626       627       628       629       630       631       632 
## 102.72661  92.76754  91.99519  81.57737  84.77866  93.51402 106.52179  90.86770 
##       633       634       635       636       637       638       639       640 
##  69.17883  69.17883  65.02666  74.74134  69.30763  69.30763  88.55952  78.88182 
##       641       642       643       644       645       646       647       648 
##  83.38591  84.47867  93.03670  68.52474  75.40134 106.67937  81.08427  79.36189 
##       649       650       651       652       653       654       655       656 
##  79.54891  79.54891  82.43292  82.37082  81.87503  81.87503  77.57744  56.21986 
##       657       658       659       660       661       662       663       664 
##  98.46630  73.47086  96.25195  79.03374  71.10812  80.10625 151.13794 151.13794 
##       665       666       667       668       669       670       671       672 
##  84.46179  84.46179  84.46179 103.07596  69.85221  66.63347  87.70512  87.70512 
##       673       674       675       676       677       678       679       680 
##  73.56843  74.46223  73.14461  98.52717  98.52717  75.23316  88.21609  91.54789 
##       681       682       683       684       685       686       687       688 
##  77.02395  69.20921  70.12944  70.86801  90.90531  68.26432  62.99334  87.56182 
##       689       690       691       692       693       694       695       696 
##  74.54042  70.42298 106.02254  96.67472  92.52111  91.03616  83.28194  83.18337 
##       697       698       699       700       701       702       703       704 
##  93.32601  67.14733  81.07524  92.91551  92.91551  70.80484  66.49020  87.61833 
##       705       706       707       708       709       710       711       712 
##  70.03826 107.74664  62.78660  62.78660  95.53841  61.33534  81.69442 102.49106 
##       713       714       715       716       717       718       719       720 
##  78.44045  74.69639  86.02143  92.97719  97.00815  77.43603  99.69034  74.22048 
##       721       722       723       724       725       726       727       728 
##  87.86173  74.97371  75.64746  70.78388  70.78388  72.19952  85.28080  82.05756 
##       729       730       731       732       733       734       735       736 
##  76.77791 105.35672 105.35672 105.35672  70.89448  79.06279  76.27777  76.27777 
##       737       738       739       740       741       742       743       744 
##  75.84644  78.95246  79.90924  74.02708  77.57720  66.36697  84.17343 112.06649 
##       745       746       747       748       749       750       751       752 
##  81.45766  81.45766  81.45766  75.12896  78.70600  67.87039  68.39208  74.84039 
##       753       754       755       756       757       758       759       760 
##  71.71833  80.95423  62.20616  70.52765  71.46057 106.82913  92.59902  81.72970 
##       761       762       763       764       765       766       767       768 
## 105.31633 105.31633  72.05590  75.65365  70.45723  54.95902  91.25496  71.66823 
##       769       770       771       772       773       774       775       776 
##  73.63801  73.63801  73.63801  73.63801  93.44675  93.44675  78.43367  86.93547 
##       777       778       779       780       781       782       783       784 
##  67.66267  92.99143  92.71138  92.71138  69.38518  94.84657  83.26765  78.15197 
##       785       786       787       788       789       790       791       792 
##  78.42200  71.84212  76.48250 100.57730 100.57730  68.78756  96.24340  96.24340 
##       793       794       795       796       797       798       799       800 
##  98.22013  98.22083  98.22083  98.22083  82.80836  82.80836  82.80836  80.61390 
##       801       802       803       804       805       806       807       808 
##  64.36573  64.36573  67.97031  82.48001  82.48001  76.71437  62.37272  69.70429 
##       809       810       811       812       813       814       815       816 
##  91.13652  69.41009  99.66299  99.66299  69.64510  88.38660  88.38660  77.02805 
##       817       818       819       820       821       822       823       824 
##  77.02805  94.36461  87.09791  88.84366  78.80180  78.80180  78.80180  75.47531 
##       825       826       827       828       829       830       831       832 
##  75.47531 100.41225 100.41225  97.62855  97.62855  88.23688  89.09520  89.95507 
##       833       834       835       836       837       838       839       840 
## 100.65272  79.41052  75.59720  69.89882  69.89882  79.40941 101.97084  79.64599 
##       841       842       843       844       845       846       847       848 
##  79.64599  79.64599  75.37380  74.40036  71.22014  85.56101 130.84790  88.49302 
##       849       850       851       852       853       854       855       856 
##  88.49302  97.07237 103.24337  76.63467  79.45805  79.45805  79.78691 115.53516 
##       857       858       859       860       861       862       863       864 
##  96.46050  96.46050  91.11561  91.11561  88.69781  65.44231  72.51250  70.69476 
##       865       866       867       868       869       870       871       872 
##  70.69476  70.69476  99.72478  83.04804  64.99525 101.17449 101.17449  62.91427 
##       873       874       875       876       877       878       879       880 
## 104.04301  91.88165  78.80718  90.08186  68.68055  98.82522  68.15644  68.15644 
##       881       882       883       884       885       886       887       888 
##  79.99700  68.91926  80.79697  85.02493  85.02493  85.02493  80.13390  80.99069 
##       889       890       891       892       893       894       895       896 
##  73.86490  67.48926  94.36355  94.09497  94.09497  94.09497  94.75236  89.65896 
##       897       898       899       900       901       902       903       904 
##  73.53177  73.53177  87.97784  74.11838  86.19129  86.19129  88.89889  77.00121 
##       905       906       907       908       909       910       911       912 
##  79.45747 103.06434  86.88379  86.88379  86.88379  77.49344  83.97456  77.39221 
##       913       914       915       916       917       918       919       920 
##  59.95473  74.70266  99.06273  99.06273 116.83435  72.60339  93.06451  66.93037 
##       921       922       923       924       925       926       927       928 
##  66.08363  78.15642  80.91329  70.77904  84.60795  85.24220 102.36769 108.52983 
##       929       930       931       932       933       934       935       936 
##  76.74107 105.08907  74.40240  76.06445  93.15584  84.77755  84.77755  70.65854 
##       937       938       939       940       941       942       943       944 
##  74.79237  74.79237  74.79237  84.58252  68.04647  68.04647  78.13252  84.26576 
##       945       946       947       948       949       950       951       952 
##  91.15835  80.27214  79.05607  74.61519  72.67713  80.82399  95.29095  79.38954 
##       953       954       955       956       957       958       959       960 
##  71.65838  60.55097  78.23653  89.46061  76.10598  93.36514  83.69898  79.01430 
##       961       962       963       964       965       966       967       968 
##  79.01430  81.14502  57.25139  88.73164  88.73164  71.39099  72.42490  72.42490 
##       969       970       971       972       973       974       975       976 
##  74.80105  82.92423  78.60344  80.57793  74.13079  69.04031  67.78690  81.01356 
##       977       978       979       980       981       982       983       984 
##  77.63377  62.51538  84.62980  96.67900  95.04993  64.29447  72.46078  79.86935 
##       985       986       987       988       989       990       991       992 
##  79.86935  79.86935  95.88582  97.48210  79.57204  68.61713  82.82114  65.38918 
##       993       994       995       996       997       998       999      1000 
##  79.41696  66.10937  66.10937  72.94923  73.71189  90.32549  77.87123  65.79610 
##      1001      1002      1003      1004      1005      1006      1007      1008 
##  80.98251  91.20595  96.86635  85.60852  85.60852  73.18619  68.62315  77.04097 
##      1009      1010      1011      1012      1013      1014      1015      1016 
##  77.04097  68.04923  77.21890 101.68235  68.41153  85.76802  77.82638  78.95954 
##      1017      1018      1019      1020      1021      1022      1023      1024 
##  78.95954  81.74693  68.75117  68.75117  75.84325  75.84325  76.85230  72.21510 
##      1025      1026      1027      1028      1029      1030      1031      1032 
##  71.57010  98.48386  69.59029  72.75254  70.16008  68.39947  84.37718  90.20806 
##      1033      1034      1035      1036      1037      1038      1039      1040 
##  75.88001  83.69671  91.95362  71.35546  71.35546  82.04322  88.97082  80.21052 
##      1041      1042      1043      1044      1045      1046      1047      1048 
##  80.21052  87.87715  87.87715  69.33188  82.01906  98.83290  86.21476 103.18732 
##      1049      1050      1051      1052      1053      1054      1055      1056 
##  95.63049  72.22313  88.61676  88.61676 101.87738  75.28544 102.02458  92.01900 
##      1057      1058      1059      1060      1061      1062      1063      1064 
##  91.83478  83.76077  71.37530  80.97216  87.66374  78.77345  78.77345  78.77345 
##      1065      1066      1067      1068      1069      1070      1071      1072 
##  89.28594  72.75112 100.33987 100.33987  75.50414  69.53588 100.07987 108.17565 
##      1073      1074      1075      1076      1077      1078      1079      1080 
##  92.38747  92.38747  71.61569  77.38210  70.86369  65.89462  95.81929  95.81929 
##      1081      1082      1083      1084      1085      1086      1087      1088 
##  95.44126  52.24363 100.41225  69.20703  99.11360  57.73886  78.07097  91.43047 
##      1089      1090      1091      1092      1093      1094      1095      1096 
##  53.64497  90.39684  93.90977  93.90977  84.57326  70.31773  68.38332  98.11786 
##      1097      1098      1099      1100      1101      1102      1103      1104 
##  72.68938  92.47100  76.68925  86.22445  99.02557  86.45874  70.82657 100.65316 
##      1105      1106      1107      1108      1109      1110      1111      1112 
## 105.12129 105.12129  89.81936  92.48782  83.97178  83.97178 104.36452  64.79492 
##      1113      1114      1115      1116      1117      1118      1119      1120 
##  92.56050  73.36406  74.79738  76.43451  89.53601  79.12567  76.56720  76.56720 
##      1121      1122      1123      1124      1125      1126      1127      1128 
##  81.58104  81.58104  87.89392  69.44042  69.44042  91.83536  83.10154  84.26152 
##      1129      1130      1131      1132      1133      1134      1135      1136 
##  70.47975  79.48071  82.13636  95.54874  74.26018  85.67685  85.67685  67.02066 
##      1137      1138      1139      1140      1141      1142      1143      1144 
##  97.85741  97.44845  88.15405  88.15405  96.50120  81.71774  81.71774  70.74591 
##      1145      1146      1147      1148      1149      1150      1151      1152 
##  70.74591  66.21422  67.66207  63.54199  72.43049  75.38275  95.12877  69.92911 
##      1153      1154      1155      1156      1157      1158      1159      1160 
##  69.92911  95.38597  95.38597  84.71911  84.71911  84.15115  67.36952  74.68405 
##      1161      1162      1163      1164      1165      1166      1167      1168 
##  78.71041  85.21620  76.21581  76.21581  79.50778  72.98535  80.02294  66.93108 
##      1169      1170      1171      1172      1173      1174      1175      1176 
##  76.64571  76.81924 119.47384  81.86893  81.86893  95.91028  83.07949  78.26472 
##      1177      1178      1179      1180      1181      1182      1183      1184 
##  72.90890  72.90890  67.31622  67.31622  67.31622  72.73095  72.73095  72.73095 
##      1185      1186      1187      1188      1189      1190      1191      1192 
##  74.38457 113.46328  98.56134  98.56134  84.84379  84.84379  82.81396  64.35216 
##      1193      1194      1195      1196      1197      1198      1199      1200 
##  86.47726  84.41646 103.48108  77.90947  77.90947  77.38378  64.17869 100.94605 
##      1201      1202      1203      1204      1205      1206      1207      1208 
##  89.99718  90.20092  66.18070  77.28544  74.12905  79.21415  69.98762  85.85075 
##      1209      1210      1211      1212      1213      1214      1215      1216 
##  79.92658  79.92658  65.47900  83.93273  68.83949  86.87593  96.41295  96.41295 
##      1217      1218      1219      1220      1221      1222      1223      1224 
##  84.74966 102.78995  69.73525  69.73525  75.86295 103.90443 103.90443  98.48319 
##      1225      1226      1227      1228      1229      1230      1231      1232 
##  76.06985  87.56863  63.85348  89.46093  80.23761  73.21522  87.78576  91.50592 
##      1233      1234      1235      1236      1237      1238      1239      1240 
##  84.94600  83.44396  95.71849  72.87146  78.02044  90.89756  90.89756  73.47357 
##      1241      1242      1243      1244      1245      1246      1247      1248 
##  73.47357  79.87081  95.21705 111.25377  80.37502  80.37502  80.10474  65.31383 
##      1249      1250      1251      1252      1253      1254      1255      1256 
##  65.31383  84.10447  84.10447  62.25859  66.82811  66.82811  95.27561  90.98279 
##      1257      1258      1259      1260      1261      1262      1263      1264 
##  93.35373  86.99794  88.15163  83.06505  83.42691  80.29346  80.29346  80.29346 
##      1265      1266      1267      1268      1269      1270      1271      1272 
##  80.71953  72.14544  69.33497  93.21450  93.21450  64.42432  68.80850  78.12805 
##      1273      1274      1275      1276      1277      1278      1279      1280 
##  92.52427  73.91929  80.51134  95.64243  61.55635  61.55635  73.38371  78.98495 
##      1281      1282      1283      1284      1285      1286      1287      1288 
##  78.98495  70.00873  92.97076  87.49015  75.44110  75.44110  75.44110  75.44110 
##      1289      1290      1291      1292      1293      1294      1295      1296 
##  77.23615  85.56765  96.23566  77.96929  77.96929  81.78823  89.13529  84.64368 
##      1297      1298      1299      1300      1301      1302      1303      1304 
##  64.38372  90.84625  90.84625  67.64368  91.59330  72.69747  83.49066  88.20283 
##      1305      1306      1307      1308      1309      1310      1311      1312 
##  79.41282  58.97538  76.89884  84.64539  72.32595  80.92841  97.24747  84.11724 
##      1313      1314      1315      1316      1317      1318      1319      1320 
##  84.11724  79.94380  73.05997  91.37187  91.37187  91.37187  70.91100  80.66633 
##      1321      1322      1323      1324      1325      1326      1327      1328 
##  64.52057  86.06759  87.27254 110.82388  63.64511  90.04629  90.04629  87.25246 
##      1329      1330      1331      1332      1333      1334      1335      1336 
## 105.59735  62.89433  62.89433  80.04918  80.04918  74.28823  74.28823  64.86308 
##      1337      1338      1339      1340      1341      1342      1343      1344 
##  64.86308  99.67341  82.71300  75.98524  68.12987  68.12987  91.74634 104.61856 
##      1345      1346      1347      1348      1349      1350      1351      1352 
## 110.74777  71.28497  71.70476  75.24949  75.24949  75.24949  90.91233 102.76181 
##      1353      1354      1355      1356      1357      1358      1359      1360 
##  84.98904  71.98495  71.98495  72.26944  76.22340  70.79710  84.91250  75.34755 
##      1361      1362      1363      1364      1365      1366      1367      1368 
##  80.31448  80.31448  67.16225  68.84100  96.33447  80.60228  76.68535  88.41944 
##      1369      1370      1371      1372      1373      1374      1375      1376 
##  88.41944 102.66593 102.66593  74.80471  87.72061 111.38702 111.38702 111.38702 
##      1377      1378      1379      1380      1381      1382      1383      1384 
##  75.52157  94.18308  66.57636  86.95394  69.98547  62.47910  77.53403  75.77146 
##      1385      1386      1387      1388      1389      1390      1391      1392 
##  84.43708  81.74333 107.86916  69.54768  74.25146  70.05212  77.52687  67.78295 
##      1393      1394      1395      1396      1397      1398      1399      1400 
##  94.81926  72.46580  86.88466  96.48547  72.13659  77.34549  65.59075  65.59075 
##      1401      1402      1403      1404      1405      1406      1407      1408 
##  82.06230  89.03486  89.03486  86.27870  73.69462  66.42314  66.42314  72.29633 
##      1409      1410      1411      1412      1413      1414      1415      1416 
##  82.08849  71.49885  93.20740  67.61458  94.35236  98.88369  57.59187  83.34631 
##      1417      1418      1419      1420      1421      1422      1423      1424 
##  83.14049  82.12976  82.44681  82.44681  86.14720  72.72033  70.90503  76.32156 
##      1425      1426      1427      1428      1429      1430      1431      1432 
##  90.51665  90.51665  70.54980  88.21417  88.02416  87.17779  96.64519  96.64519 
##      1433      1434      1435      1436      1437      1438      1439      1440 
##  80.79751  80.79751  80.79751  81.14639  53.29375  76.08491  75.34566  69.62599 
##      1441      1442      1443      1444      1445      1446      1447      1448 
##  69.62599  85.42851  99.18915  73.37472  70.60604  89.00210  89.00210  71.42454 
##      1449      1450      1451      1452      1453      1454      1455      1456 
##  83.34401  70.10202  79.13884  79.13884  77.34917  88.27033  88.27033  70.87010 
##      1457      1458      1459      1460      1461      1462      1463      1464 
##  81.92330  81.92330  81.92330  81.92330  77.92966  77.92966  74.76049  73.67480 
##      1465      1466      1467      1468      1469      1470      1471      1472 
##  70.78068  66.34965  84.24120  71.49833  95.67545  87.93021  87.93021  89.59614 
##      1473      1474      1475      1476      1477      1478      1479      1480 
##  86.29276  86.29276  64.71237  72.05928  82.92460  82.92460  75.10827  72.03597 
##      1481      1482      1483      1484      1485      1486      1487      1488 
##  89.03875 112.41262  88.64647  88.64647  84.64461  84.64461  84.64461 107.52113 
##      1489      1490      1491      1492      1493      1494      1495      1496 
##  85.99698  85.99698  85.99698  85.99698  67.57600  58.43822  73.49117  78.10181 
##      1497      1498      1499      1500      1501      1502      1503      1504 
##  78.10181  88.70886  88.70886  95.98107  95.98107 104.85227  82.96174  99.20194 
##      1505      1506      1507      1508      1509      1510      1511      1512 
##  78.85293  90.60806  90.60806  73.87908  75.35601  72.74558  77.44884  77.44884 
##      1513      1514      1515      1516      1517      1518      1519      1520 
##  67.72505  80.54107  80.17603  81.03432  67.96440  88.56007  52.12722  83.92631 
##      1521      1522      1523      1524      1525      1526      1527      1528 
##  83.92631  82.59874  65.28450  89.25626  89.25626  80.17380  82.75965  86.95573 
##      1529      1530      1531      1532      1533      1534      1535      1536 
##  65.71547  80.30488  67.80991  87.94317  87.94317  65.08037  66.93029 106.18611 
##      1537      1538      1539      1540      1541      1542      1543      1544 
##  74.39488  74.02671  72.02952  72.02952  91.00643  91.00643  91.00643  89.53295 
##      1545      1546      1547      1548      1549      1550      1551      1552 
##  88.39273  84.83120 110.86530  67.53592  75.55673  94.01725  94.01725  71.30578 
##      1553      1554      1555      1556      1557      1558      1559      1560 
##  86.01883  87.95095  85.02497  85.02497  94.66264  94.66264  72.04156  61.57482 
##      1561      1562      1563      1564      1565      1566      1567      1568 
##  83.01871  79.51870  79.51870  88.64195  87.35321  72.76893  72.20753  92.99772 
##      1569      1570      1571      1572      1573      1574      1575      1576 
##  59.97880  66.20928  82.17037  75.33463  88.14243 102.62733  78.67872  62.95763 
##      1577      1578      1579      1580      1581      1582      1583      1584 
##  88.66263  67.29924  87.12359  93.93644  76.04665  66.41993  65.86300  91.58397 
##      1585      1586      1587      1588      1589      1590      1591      1592 
##  91.58397  89.83891  74.85726  74.85726  89.55594  93.31073  93.31073  93.31073 
##      1593      1594      1595      1596      1597      1598      1599      1600 
##  93.31073  87.86912  85.88802  76.56125  85.11515  96.47122  64.34254  94.20762 
##      1601      1602      1603      1604      1605      1606      1607      1608 
##  77.32569  87.27993  87.27993  87.27993  87.75656  63.33144  76.00956  91.07223 
##      1609      1610      1611      1612      1613      1614      1615      1616 
##  73.91197  89.21868  63.42977  88.47580  88.47580  67.23899  69.64071  82.10546 
##      1617      1618      1619      1620      1621      1622      1623      1624 
##  82.10546  82.10546  96.62222  73.57896  95.63954  82.31046  82.31046  76.47968 
##      1625      1626      1627      1628      1629      1630      1631      1632 
##  71.83137  72.23915  80.99751  78.11489  78.11489 101.16959  59.31615  70.88699 
##      1633      1634      1635      1636      1637      1638      1639      1640 
##  70.88699  93.27620  77.65369  86.64346  81.95243  71.47723  61.40599  92.37994 
##      1641      1642      1643      1644      1645      1646      1647      1648 
##  65.49046 101.96045  89.19058  79.29437  99.37651  86.24404  86.24404  74.84154 
##      1649      1650      1651      1652      1653      1654      1655      1656 
##  74.84154 100.98115 100.82105  76.86770  86.86910  94.31489  94.31489  72.50999 
##      1657      1658      1659      1660      1661      1662      1663      1664 
##  66.24387  84.13807  60.05210  84.35240  84.35240  80.90187  69.28737  69.28737 
##      1665      1666      1667      1668      1669      1670      1671      1672 
##  69.28737  85.79993  85.79993  85.79993  90.31838  75.44187  75.44187  75.44187 
##      1673      1674      1675      1676      1677      1678      1679      1680 
##  66.59885  66.53119  66.53119  85.30073  85.30073  76.35339  76.35339  84.01188 
##      1681      1682      1683      1684      1685      1686      1687      1688 
##  76.21085  69.16555  98.17519  98.17519  78.89714  71.28468  71.60281  70.36272 
##      1689      1690      1691      1692      1693      1694      1695      1696 
##  87.06021  65.24391  86.88139  80.41000  73.52367  91.52225  99.52621  69.77977 
##      1697      1698      1699      1700      1701      1702      1703      1704 
##  72.00650 100.32484  80.43560  79.47017  79.47017  74.38165  84.86351  85.30387 
##      1705      1706      1707      1708      1709      1710      1711      1712 
##  85.30387  85.30387  87.92477 110.24460  84.49059  81.29993  81.29993  70.89762 
##      1713      1714      1715      1716      1717      1718      1719      1720 
##  99.49048  73.94191  79.94414  79.94414 103.83016 103.83016 103.83016  83.46859 
##      1721      1722      1723      1724      1725      1726      1727      1728 
##  80.44229  80.44229 100.61427  79.89774  78.53563  76.66444  96.23198 104.29515 
##      1729      1730      1731      1732      1733      1734      1735      1736 
##  75.43893  80.73471  80.73471  90.03096  96.96642  74.26288  74.26288  91.52632 
##      1737      1738      1739      1740      1741      1742      1743      1744 
##  96.04757  73.88406  74.56213  99.97304 100.32596 100.32596  70.12125 103.01188 
##      1745      1746      1747      1748      1749      1750      1751      1752 
## 103.01188 103.01188  99.59410  99.59410  86.60203  83.19480  71.03166  80.32715 
##      1753      1754      1755      1756      1757      1758      1759      1760 
##  71.42814  84.32367  84.57908  84.57908  88.09230  86.28522  68.90174  67.38359 
##      1761      1762      1763      1764      1765      1766      1767      1768 
##  88.80363  88.80363 133.51700 133.51700 133.51700  75.24926  90.21424  88.70701 
##      1769      1770      1771      1772      1773      1774      1775      1776 
##  84.65425  89.87287  89.87287 104.22913 104.22913  88.63740  88.63740  73.83047 
##      1777      1778      1779      1780      1781      1782      1783      1784 
##  78.03166  76.29685  76.29685  92.14163  92.14163  89.47203  85.83419  85.83419 
##      1785      1786      1787      1788      1789      1790      1791      1792 
##  85.83419  56.67124  56.67124  75.78831  93.82549  93.82549 106.03938  72.46067 
##      1793      1794      1795      1796      1797      1798      1799      1800 
##  63.32608  90.07872  81.21795  81.21795 101.62923  80.66128  80.66128  80.66128 
##      1801      1802      1803      1804      1805      1806      1807      1808 
##  68.01298  94.72670  94.72670  80.60713  91.47057  79.59582  79.59582  97.11581 
##      1809      1810      1811      1812      1813      1814      1815      1816 
##  97.11581  99.59890  66.45191  83.37576  83.37576  83.37576  94.04749  94.04749 
##      1817      1818      1819      1820      1821      1822      1823      1824 
##  73.79173  94.63058  90.85302  71.68469  91.46094  66.78650  66.78650  66.78650 
##      1825      1826      1827      1828      1829      1830      1831      1832 
##  93.23924  78.60157  76.25312  75.29914  70.36640  70.36640  89.02575  73.33699 
##      1833      1834      1835      1836      1837      1838      1839      1840 
##  92.29830  92.29830  92.29830  61.86161  70.38779  70.38779  64.06572  71.90252 
##      1841      1842      1843      1844      1845      1846      1847      1848 
##  95.40037  95.40037  77.27471  91.33441  71.09812 117.29531 117.29531  88.56815 
##      1849      1850      1851      1852      1853      1854      1855      1856 
##  79.73245  91.00769  91.00769  77.88436  77.88436  68.77959  79.87137  79.87137 
##      1857      1858      1859      1860      1861      1862      1863      1864 
##  63.37933  63.37933  63.37933  63.37933  95.68724  93.47137  81.72559  81.72559 
##      1865      1866      1867      1868      1869      1870      1871      1872 
##  74.77523  68.09170  78.32658  78.32658  76.20225  76.20225  72.00756  90.56585 
##      1873      1874      1875      1876      1877      1878      1879      1880 
##  77.02743  77.02743  92.62255  70.20381  77.36166  72.65577  76.42382  85.61099 
##      1881      1882      1883      1884      1885      1886      1887      1888 
##  85.61099  74.34358 107.23478  85.12947  74.96396  95.54439  90.74177 112.03208 
##      1889      1890      1891      1892      1893      1894      1895      1896 
##  93.56341  69.60885  72.77420  72.77420  72.77420  56.78243  56.78243 109.73180 
##      1897      1898      1899      1900      1901      1902      1903      1904 
##  94.87624  79.96086  79.96086  74.03768  74.03768  74.03768  74.03768  88.81431 
##      1905      1906      1907      1908      1909      1910      1911      1912 
##  88.81431  76.68287  81.48624  75.53474  77.37415  77.37415  72.65809  97.36070 
##      1913      1914      1915      1916      1917      1918      1919      1920 
##  73.00729  75.98234  78.63724  68.91632  68.91632  68.91632  70.76747  54.42787 
##      1921      1922      1923      1924      1925      1926      1927      1928 
##  85.62705  84.84035  72.14040  78.00329  75.73047  82.82218 106.01342  87.54623 
##      1929      1930      1931      1932      1933      1934      1935      1936 
##  87.54623  87.54623  64.12028  81.29947  80.65901  64.07151  97.35449  70.63302 
##      1937      1938      1939      1940      1941      1942      1943      1944 
##  89.55621  89.55621  86.82015  86.82015  88.31210  88.31210  88.31210  77.70478 
##      1945      1946      1947      1948      1949      1950      1951      1952 
##  87.09056  66.11325  66.11325  85.22744 103.54997  67.69669  67.69669  64.55439 
##      1953      1954      1955      1956      1957      1958      1959      1960 
##  64.55439  64.55439  63.94949  71.83853  67.56001  80.83852  94.30864  94.30864 
##      1961      1962      1963      1964      1965      1966      1967      1968 
##  79.80885  73.20245 108.00351  91.85453  80.40434  85.45202  89.31322  97.82808 
##      1969      1970      1971      1972      1973      1974      1975      1976 
##  97.82808  85.80402  75.23035  96.16249  87.44040  97.94573  87.56210  96.09105 
##      1977      1978      1979      1980      1981      1982      1983      1984 
##  93.53986  93.53986  71.39191  83.18838  83.18838  94.34508  90.09228  82.70713 
##      1985      1986      1987      1988      1989      1990      1991      1992 
##  74.89010  81.19353  81.19353  77.56005 105.19762 105.19762 105.19762 105.19762 
##      1993      1994      1995      1996      1997      1998      1999      2000 
##  78.50099  72.17988  81.53639  93.51505  93.18146  67.79708  67.79708  88.52730 
##      2001      2002      2003      2004      2005      2006      2007      2008 
##  88.52730  88.52730  88.52730  79.69481  81.61308  84.18739  79.05097  75.33963 
##      2009      2010      2011      2012      2013      2014      2015      2016 
## 100.80490 107.46687 133.24157 133.24157  81.76476  74.44431  74.44431  77.13794 
##      2017      2018      2019      2020      2021      2022      2023      2024 
##  79.19423  79.19423  74.86115  85.26193  66.79138  81.04152  99.57481  99.57481 
##      2025      2026      2027      2028      2029      2030      2031      2032 
## 105.61817  99.60243  91.02397  58.74939  75.44856  68.89781  88.53076  88.88348 
##      2033      2034      2035      2036      2037      2038      2039      2040 
##  85.24841  70.42679  89.13567  89.13567  70.07632  71.23543  71.23543  95.62052 
##      2041      2042      2043      2044      2045      2046      2047      2048 
##  70.09407 101.58026  95.64549  64.46862  80.20647  97.62849  91.18681  79.88012 
##      2049      2050      2051      2052      2053      2054      2055      2056 
##  91.58513  84.08213  71.10279  95.57537  95.57537  66.03618  79.13884  80.74787 
##      2057      2058      2059      2060      2061      2062      2063      2064 
##  80.74787 104.89874  62.27358  91.60966  91.60966  77.29727  89.19362  82.46691 
##      2065      2066      2067      2068      2069      2070      2071      2072 
##  72.64559  89.45018  89.45018  89.45018 105.30686 105.30686 105.30686 105.30686 
##      2073      2074      2075      2076      2077      2078      2079      2080 
##  86.59270  97.24477  75.56697  75.56697  71.48983  71.48983  71.48983  71.48983 
##      2081      2082      2083      2084      2085      2086      2087      2088 
##  82.46633  70.44433  68.38970  83.80426  83.80426  83.80426  96.21050  91.91422 
##      2089      2090      2091      2092      2093      2094      2095      2096 
## 103.01099 103.01099  88.87242  91.73918  62.20782  82.80336  82.80336  69.76360 
##      2097      2098      2099      2100      2101      2102      2103      2104 
##  75.19338  79.31465  93.50293 103.50421  72.84126  72.84126  97.38121  96.09549 
##      2105      2106      2107      2108      2109      2110      2111      2112 
##  72.38662  92.43067  84.05124 106.45116  72.67864  83.79651  74.03261  65.93152 
##      2113      2114      2115      2116      2117      2118      2119      2120 
##  89.74244  62.46611  71.25559  71.25559  71.25559  71.53789  65.05788 100.99964 
##      2121      2122      2123      2124      2125      2126      2127      2128 
## 132.55770  73.03554 104.87402 104.87402 100.60373  82.41758  87.41395 102.48832 
##      2129      2130      2131      2132      2133      2134      2135      2136 
##  92.59306  70.63638  98.84624  98.84624  98.84624  70.73605  76.38591  76.38591 
##      2137      2138      2139      2140      2141      2142      2143      2144 
## 121.25708  75.98373  75.87831  75.87831  71.55240  92.27358  97.04359  97.04359 
##      2145      2146      2147      2148      2149      2150      2151      2152 
##  93.97996  58.38350  95.90040  74.86121  73.29307  73.88970  73.88970  91.47701 
##      2153      2154      2155      2156      2157      2158      2159      2160 
##  93.08262  90.35487 103.14014  84.36835  79.49499  79.49499  79.49499  79.49499 
##      2161      2162      2163      2164      2165      2166      2167      2168 
##  91.84685  81.32652  81.14587  75.57856  75.57856  81.82369  73.55173  87.25632 
##      2169      2170      2171      2172      2173      2174      2175      2176 
##  89.85665  91.88803  87.64380  92.37213  83.72736  87.10121  70.67302  88.72009 
##      2177      2178      2179      2180      2181      2182      2183      2184 
##  74.87255  85.84498  74.58765  72.00962  77.92082  77.92082  77.92082  77.92082 
##      2185      2186      2187      2188      2189      2190      2191      2192 
##  76.07020  78.72026  91.04853  88.49180  94.13699  89.39381  66.46009  90.95880 
##      2193      2194      2195      2196      2197      2198      2199      2200 
##  87.46604  86.97193  75.71723  75.71723  65.05317  84.72656  84.72656  77.14444 
##      2201      2202      2203      2204      2205      2206      2207      2208 
##  65.88143  70.72940  85.42991  94.97713  74.07498  80.36633  63.56843  87.38739 
##      2209      2210      2211      2212      2213      2214      2215      2216 
##  91.32803  91.32803  91.32803  91.32803  76.54625  76.54625  71.82317  71.82317 
##      2217      2218      2219      2220      2221      2222      2223      2224 
##  66.99406  68.33666  68.33666  72.76821  81.07377  63.11822  68.13027  79.84861 
##      2225      2226      2227      2228      2229      2230      2231      2232 
##  75.68281 111.22281  84.19965  77.00570  82.18455  82.18455  75.98541  88.08999 
##      2233      2234      2235      2236      2237      2238      2239      2240 
##  65.94654  72.69530 105.66253  76.67267  83.08661  83.08661  99.50873  99.50873 
##      2241      2242      2243      2244      2245      2246      2247      2248 
##  77.66211  89.36548  73.70449  71.48603  71.48603  90.63726  84.58758  80.26877 
##      2249      2250      2251      2252      2253      2254      2255      2256 
##  93.53803  92.30975  84.33730  77.08074  78.28600  78.28600  62.13411  98.26366 
##      2257      2258      2259      2260      2261      2262      2263      2264 
##  83.81041  79.34412  80.22833  75.29820  79.67552  76.63576  82.26204  71.05622 
##      2265      2266      2267      2268      2269      2270      2271      2272 
##  71.05622  89.40335  89.40335  84.17290  84.17290  88.03572  85.86997 103.68568 
##      2273      2274      2275      2276      2277      2278      2279      2280 
## 103.68568 103.68568 103.68568  78.86893  78.86893  89.51492  76.24164 101.18263 
##      2281      2282      2283      2284      2285      2286      2287      2288 
##  86.77518  88.82919  80.10177  80.24672 104.83698 104.83698  92.25013  91.94693 
##      2289      2290      2291      2292      2293      2294      2295      2296 
##  91.94693  70.41381  92.62911  74.39103  78.85403  83.00354  75.36259  81.94623 
##      2297      2298      2299      2300      2301      2302      2303      2304 
##  81.94623  69.93879  75.05176  73.49720  78.34820  66.78460  90.61103  63.94419 
##      2305      2306      2307      2308      2309      2310      2311      2312 
##  63.94419  70.12368  90.66678  90.66678  81.68090  77.03090  81.88563  99.59169 
##      2313      2314      2315      2316      2317      2318      2319      2320 
##  95.50360  98.92322  98.92322  89.25558  65.18112  75.63867  70.45175  72.14560 
##      2321      2322      2323      2324      2325      2326      2327      2328 
##  91.87065  91.45081  99.06993  79.26081  79.26081  79.26081  90.18893  75.98040 
##      2329      2330      2331      2332      2333      2334      2335      2336 
##  82.67999  82.67999  76.75188  69.26318  85.05205  85.05205 102.80000 102.80000 
##      2337      2338      2339      2340      2341      2342      2343      2344 
## 102.80000  74.56098  80.13822  67.31661 104.37197  81.15952  69.16665  78.09192 
##      2345      2346      2347      2348      2349      2350      2351      2352 
##  79.62801  77.01935  75.38173  83.57111  70.00267 107.97894 107.97894 107.97894 
##      2353      2354      2355      2356      2357      2358      2359      2360 
##  94.85133  94.85133  73.93614 102.43478 102.43478 102.43478  96.34243  67.19738 
##      2361      2362      2363      2364      2365      2366      2367      2368 
## 100.52306 100.52306  67.39649  67.39649  67.39649  67.39649  75.76488  78.94035 
##      2369      2370      2371      2372      2373      2374      2375      2376 
##  65.77953  88.90918  88.90918  88.90918  88.90918  94.80023  94.80023  69.73763 
##      2377      2378      2379      2380      2381      2382      2383      2384 
##  69.73763  77.93393  90.11799  80.06430  80.91514  80.91514  80.91514 103.64426 
##      2385      2386      2387      2388      2389      2390      2391      2392 
##  80.45795  90.49031  93.63227  93.63227 103.26812  78.78815  92.10439  74.19497 
##      2393      2394      2395      2396      2397      2398      2399      2400 
##  74.19497  74.19497  93.62622  74.06798  66.79769  75.19008  65.06273  67.48096 
##      2401      2402      2403      2404      2405      2406      2407      2408 
##  88.62336  71.00904  66.01295  67.76237 101.35335 101.35335  79.21829 109.04607 
##      2409      2410      2411      2412      2413      2414      2415      2416 
## 109.04607  96.99392  90.15260  90.15260  67.15511  80.20942  80.20942  95.36222 
##      2417      2418      2419      2420      2421      2422      2423      2424 
##  86.47599  89.24729  60.41428  89.40232  89.40232  89.40232  84.27524  74.24805 
##      2425      2426      2427      2428      2429      2430      2431      2432 
##  78.95719  76.96637  68.46691  89.86701  86.13041  89.78585  54.85855  88.55459 
##      2433      2434      2435      2436      2437      2438      2439      2440 
##  88.55459  88.55459  71.31094  71.31094  99.42405  92.90527  92.90527  79.41816 
##      2441      2442      2443      2444      2445      2446      2447      2448 
##  63.67473  69.94048  79.02019  54.97592  68.92537  68.92537 104.29323  79.43112 
##      2449      2450      2451      2452      2453      2454      2455      2456 
##  77.04322  77.04322  82.12692  76.54613  65.42993  65.42993  86.96315  79.48452 
##      2457      2458      2459      2460      2461      2462      2463      2464 
##  69.27386  65.05176  65.05176  86.38338  86.38338  86.38338  70.09576  79.50714 
##      2465      2466      2467      2468      2469      2470      2471      2472 
##  77.04318 101.46460  70.03996  99.87175 100.80302  80.30931  88.06496  93.74660 
##      2473      2474      2475      2476      2477      2478      2479      2480 
## 105.53997  75.44138  93.82751  71.60184  71.60184  81.57827  81.57827  81.57827 
##      2481      2482      2483      2484      2485      2486      2487      2488 
##  83.20630  83.20630  71.28369  83.32414  86.28576 103.91992  84.47140  84.77296 
##      2489      2490      2491      2492      2493      2494      2495      2496 
##  71.56175  71.56175  71.56175  78.34021  74.92538  86.26398  90.15813  99.77635 
##      2497      2498      2499      2500      2501      2502      2503      2504 
##  71.88130  71.88130  71.88130  88.09407  84.51935  63.14260  84.73828  84.73828 
##      2505      2506      2507      2508      2509      2510      2511      2512 
##  84.73828  84.73828  78.84012  68.30914  91.24424 100.49349 100.49349  72.32319 
##      2513      2514      2515      2516      2517      2518      2519      2520 
## 103.96553 103.96553  97.88832  91.00268  94.68644  94.68644  69.63514  71.66786 
##      2521      2522      2523      2524      2525      2526      2527      2528 
##  76.23314  76.23314  78.14026  85.33726  89.39021  68.51290  77.00035  72.06540 
##      2529      2530      2531      2532      2533      2534      2535      2536 
##  80.63331  80.63331  91.91777  91.91777 105.51871 105.51871  74.64198  74.64198 
##      2537      2538      2539      2540      2541      2542      2543      2544 
##  74.20926  74.20926  93.65230  93.35180  85.16779  66.89305  66.89305  68.32174 
##      2545      2546      2547      2548      2549      2550      2551      2552 
##  88.66493  94.05555  90.37921  90.37921  90.37921  78.99326  78.99326  78.99326 
##      2553      2554      2555      2556      2557      2558      2559      2560 
##  77.51607  96.90054  79.80856 102.39086  66.38834  63.89367  67.17024  67.17024 
##      2561      2562      2563      2564      2565      2566      2567      2568 
## 100.94203  96.80271  96.80271  90.44393 100.37579 100.37579  69.61088  77.89185 
##      2569      2570      2571      2572      2573      2574      2575      2576 
##  90.95113  89.48310  72.81629  79.42461  79.42461  95.14742  79.57455  79.57455 
##      2577      2578      2579      2580      2581      2582      2583      2584 
##  79.71020  69.05999  82.21167  82.21167  90.81566  72.01548  71.48767  93.20423 
##      2585      2586      2587      2588      2589      2590      2591      2592 
##  78.71793  82.45821  82.33912 104.93852  71.20025  72.56278  87.40684  88.35912 
##      2593      2594      2595      2596      2597      2598      2599      2600 
##  66.01407 115.69037  75.05555  97.93590  75.58314  71.34187  87.82487  73.61371 
##      2601      2602      2603      2604      2605      2606      2607      2608 
##  71.68010  84.88179 117.80817  96.33543  96.33543  96.33543  85.33990  67.02834 
##      2609      2610      2611      2612      2613      2614      2615      2616 
##  68.55486  87.11161  78.32684 105.50015  84.32108  84.32108  88.55793  88.55793 
##      2617      2618      2619      2620      2621      2622      2623      2624 
##  77.35443  75.10141  75.10141  97.63469  97.63469  67.70143  85.49112  78.11243 
##      2625      2626      2627      2628      2629      2630      2631      2632 
##  78.11243  89.41262  88.34465  50.33581  62.36860  62.43898  62.43898  62.43898 
##      2633      2634      2635      2636      2637      2638      2639      2640 
##  79.58653 100.51008  87.92182  84.51422  84.51422  79.02874  67.32996  67.90040 
##      2641      2642      2643      2644      2645      2646      2647      2648 
##  69.22727  69.22727  92.67239  83.55028  62.20659  67.60102  66.90658  93.74572 
##      2649      2650      2651      2652      2653      2654      2655      2656 
##  98.16409  75.41963  75.41963  64.38105  64.38105  90.17723  64.71470  88.87573 
##      2657      2658      2659      2660      2661      2662      2663      2664 
##  88.87573  88.87573  81.56322  67.15807  88.66192  88.66192  94.35222  77.82888 
##      2665      2666      2667      2668      2669      2670      2671      2672 
##  78.79694  78.79694  84.93140 107.95844  87.24168  87.24168  72.26347  72.26347 
##      2673      2674      2675      2676      2677      2678      2679      2680 
##  70.23516  70.23516  70.23516  81.83149  81.83149  66.94408  76.35128  98.72282 
##      2681      2682      2683      2684      2685      2686      2687      2688 
##  81.50330  81.50330  81.50330  86.99597  86.99597  86.99597  69.36510  70.54127 
##      2689      2690      2691      2692      2693      2694      2695      2696 
##  71.31473  65.03328  65.03328  65.03328  99.65330  99.65330  83.64806  92.43872 
##      2697      2698      2699      2700      2701      2702      2703      2704 
##  84.86627  86.40772  86.40772  71.39694  82.11243  71.36641  66.63719 100.09603 
##      2705      2706      2707      2708      2709      2710      2711      2712 
## 100.09603  84.46112  84.46112  94.36079  80.64605  75.01664  75.01664 109.03332 
##      2713      2714      2715      2716      2717      2718      2719      2720 
##  85.15686  85.15686  91.91906  91.91906  79.57715  80.93062  78.79124  78.79124 
##      2721      2722      2723      2724      2725      2726      2727      2728 
##  82.35356  91.67456  71.99388  62.66917  89.38284  88.03070  78.43436  73.10202 
##      2729      2730      2731      2732      2733      2734      2735      2736 
##  73.10202  73.10202  86.49272  86.49272  76.03385  76.03385  91.13451  91.13451 
##      2737      2738      2739      2740      2741      2742      2743      2744 
##  91.13451  65.70413  95.77808  95.77808  74.07346  66.77414  74.73828  84.32457 
##      2745      2746      2747      2748      2749      2750      2751      2752 
##  84.32457  86.35792 108.06367  65.62533  65.62533  83.28675  71.84070  71.84070 
##      2753      2754      2755      2756      2757      2758      2759      2760 
##  73.98191  77.68739  76.02693  76.02693  76.02693 105.90073  68.91708  68.91708 
##      2761      2762      2763      2764      2765      2766      2767      2768 
##  68.91708  78.32805  95.03232  82.84341  83.77763  83.77763  83.66225  71.12729 
##      2769      2770      2771      2772      2773      2774      2775      2776 
##  71.12729  78.81318  78.81318  78.81318  69.91862  80.41099  72.90649 101.91593 
##      2777      2778      2779      2780      2781      2782      2783      2784 
## 101.91593 101.91593  87.19371  68.48726  68.48726  70.95866  70.95866  81.57817 
##      2785      2786      2787      2788      2789      2790      2791      2792 
##  83.02031  82.46254  82.46254  85.13017  85.13017  85.13017  62.86799  62.86799 
##      2793      2794      2795      2796      2797      2798      2799      2800 
##  62.86799  65.21090  71.77317  76.80671  82.55710  76.29225  79.65184  79.90412 
##      2801      2802      2803      2804      2805      2806      2807      2808 
##  86.05571 117.16152  69.39247  69.39247  77.51188  77.51188  92.68649  78.39073 
##      2809      2810      2811      2812      2813      2814      2815      2816 
##  78.39073 107.75923  71.50148  71.50148  72.23436  79.45495  89.45956  89.45956 
##      2817      2818      2819      2820      2821      2822      2823      2824 
##  89.45956  77.60257  87.18832 142.71541 142.71541  83.73118  87.22041  89.28180 
##      2825      2826      2827      2828      2829      2830      2831      2832 
##  69.28992  69.28992  79.54355  81.09107  71.75574  71.75574  93.08788  80.48150 
##      2833      2834      2835      2836      2837      2838      2839      2840 
##  93.29508  76.74687  99.53631  86.63945  84.17714  76.53505  99.74929  74.11358 
##      2841      2842      2843      2844      2845      2846      2847      2848 
##  74.50203  73.99713 109.84199 109.84199  72.58929  72.58929 105.87633  80.39125 
##      2849      2850      2851      2852      2853      2854      2855      2856 
##  73.03554  97.26242  97.26242 100.74519  76.05427  93.10093  63.14424  82.87431 
##      2857      2858      2859      2860      2861      2862      2863      2864 
##  74.65183  74.65183  83.51597  87.04368  86.12588  86.12588  66.13516  90.55139 
##      2865      2866      2867      2868      2869      2870      2871      2872 
##  73.66788  74.19275  78.00820  83.34789  83.34789  83.34789  89.41556  83.47968
MSE_rf <- mean((nhanes_test$Weight - rf_pred)^2)
MSE_rf
## [1] 262.9953
boost_pred <- predict(nhanes_train_boost, nhanes_test, n.trees = 200)
boost_pred
##    [1]  82.95018  90.49591  93.32893  86.11352  76.73711  76.73711  81.95109
##    [8]  87.57719  87.57719  87.57719  87.57719  79.90817  75.86963  74.12258
##   [15]  74.12258  74.98892  74.98892  62.85939  70.10751  76.54621  76.54621
##   [22]  83.51279  83.51279  83.51279  83.51279  68.87804  68.87804  79.99943
##   [29]  81.21890  90.44310  77.65354  77.67184  85.82173  92.83077  92.83077
##   [36]  92.83077  58.47097  70.71874  70.71874  82.82202  75.62011  90.81025
##   [43]  82.96919  61.52366  67.63359  75.89337  73.30768  72.08367  74.52774
##   [50]  82.59856  82.32943  83.55323  83.55323  83.55323  90.36601  95.26346
##   [57]  95.26346  86.72753  87.64513  90.23852  87.96861 100.30672  72.39679
##   [64]  76.04398  82.72838  72.46794  73.18931  95.17162  76.30361  74.26161
##   [71]  65.48938  84.66089  82.36428  96.27146  99.05802  95.56337  95.56337
##   [78]  94.21221  71.81919  95.69075  72.06178  75.29560  83.19203  83.19203
##   [85]  74.06006  74.06006  91.12843  68.83043  99.94270  99.94270  99.94270
##   [92]  96.32710  60.96273  76.93728  96.33151  81.71270  81.71270  82.37303
##   [99]  99.28494  98.25273  78.79849  78.85372  88.17950  86.87646  86.87646
##  [106]  95.70456  95.70456  90.62002  73.87468  73.87468  98.09464  97.26982
##  [113]  97.26982  67.84890  84.11727  97.58569  96.27851  91.67561  90.80660
##  [120]  90.80660  83.97894  81.95937  80.59706  86.42993  76.79489  70.35203
##  [127]  77.00400  74.27249  88.79271  80.84693  83.38911  90.02515  90.02515
##  [134]  69.64501  68.27171  81.79127  81.79127  78.90878  74.51669  96.14982
##  [141]  89.99208  67.57538  67.57538  81.83552  81.83552  76.11315  97.34996
##  [148]  97.34996  90.88286  94.88562  84.47806  88.64527  88.64527  69.87573
##  [155]  97.09946  89.48023  98.15365  74.78989  80.54171  75.95974  76.06465
##  [162]  80.49535  73.54306  74.73507  73.47654 101.54956  67.79097  75.25679
##  [169]  89.63755  75.92841  73.03961  90.15714  98.94495  91.64959  75.52275
##  [176]  75.52275 104.87466  81.44503  75.07799  82.01039  76.55074  80.17680
##  [183]  76.12041  68.67789  79.45542  87.85052  95.09198  95.09198  87.63474
##  [190]  68.85103  81.29341  78.47877  74.66137  75.36065  71.17910  71.17910
##  [197]  82.34617  80.07046  89.89824  72.69564  72.69564  86.08109 102.52407
##  [204]  94.58765  56.89796  94.11338  79.92342  89.70958  80.92210  80.92210
##  [211]  73.40415  97.81747  76.97645  87.61830  87.61830  73.35885  73.13061
##  [218] 101.90199 111.78266  75.50679  72.87497  73.91293  74.57682  87.12540
##  [225]  87.12540  80.14622  71.73110  82.13455  74.67960  99.35788  82.01311
##  [232]  73.18931  87.46391  74.48019  94.27128  94.27128  68.87833  86.89293
##  [239]  86.89293  86.89293  70.18014  69.68695  69.68695  85.98222  92.33156
##  [246] 101.62661  71.19452  81.80754  80.80684  80.80684  92.21992  81.99623
##  [253]  96.82004  96.82004  83.23119  73.13061  87.72125  96.85229  90.88819
##  [260]  91.26455  91.26455  88.66339  76.87269  64.89651  77.50427  94.14666
##  [267]  82.78330  85.95586  87.45924  87.45924  93.53662  84.00558  84.00558
##  [274]  67.85913  89.48023  89.48023  66.99080  74.61321  82.23980  90.16677
##  [281]  90.16677  76.03143  81.09330  71.12125  84.80574  84.80574  84.80574
##  [288] 113.05603  84.90759  72.47174  87.45614  87.45614  90.73909  76.81572
##  [295]  88.87474  75.88776  75.88776  70.17736  79.48282  72.02781  99.06014
##  [302]  99.46520  89.56482  89.56482  70.20196  75.65215  67.44004  71.76264
##  [309]  97.91403  77.18673  77.18673  98.49866  98.49866  94.54024  88.45385
##  [316]  81.89827  95.64422  93.96814  71.00940  87.44407  71.85412  73.90435
##  [323]  73.90435  86.68773  86.68773  94.87404  86.67144  86.67144  87.90758
##  [330]  87.90758  94.55343  79.31123  74.45508  78.99656  68.62610  74.83177
##  [337]  93.49280  93.49280  86.82243  88.45429  77.25192  71.10726  78.19405
##  [344]  96.74399  73.12333  78.77026  96.88794  85.85864  95.37244  95.37244
##  [351]  94.93405 101.48151 101.48151 101.48151  94.71291  94.71291  93.90973
##  [358]  93.90973  70.87396  94.13709  71.24018  84.44909  71.86920  85.22948
##  [365]  75.36644  89.79662  82.81187  82.81187  87.95268  87.95268  71.32071
##  [372]  74.95019  80.73177  75.39362  94.49365  94.49365  80.43597  79.86972
##  [379]  77.49273  83.60507  95.00150  92.31189  79.63236  78.40283  70.85168
##  [386]  84.02146  67.44316  67.44316  87.70306  68.77505  92.88570  83.94355
##  [393]  83.94355  95.55279  89.94256  76.61824  75.98919  82.57596  90.16677
##  [400]  82.71865  96.48634  75.78186  78.14549  78.14549  78.14549  70.87293
##  [407]  87.32734  88.69913  71.02024  94.45441  65.46111  92.88075  89.54192
##  [414]  70.10352  84.15575  74.98261  77.18143  77.18143  74.88823  75.17757
##  [421]  81.51353  95.65793  89.63083  74.13841  74.13841  80.48786  77.85587
##  [428]  90.38257  66.46074  71.73637  73.19284  74.09246  86.58374  86.58374
##  [435]  98.71586  98.71586  73.50053  78.49369  78.49369  81.00126  75.85284
##  [442]  94.28422  89.99463  76.58458  76.58458  76.58458  78.61400  98.21867
##  [449]  88.76590  71.43546  74.36468  72.65456  72.65456  73.56610  73.56610
##  [456]  74.26727  91.17642  68.24653  68.24653  91.12843  92.33379  92.33379
##  [463]  92.33379  77.30074  91.47752  79.54509  78.08760  78.08760  92.23653
##  [470]  73.58758  73.58758  70.54337  90.24163  69.41867  69.41867  69.41867
##  [477]  69.41867  67.38977  92.36604  95.32945  95.32945  68.95115  56.50936
##  [484]  56.50936  82.06709  95.96238  68.99139  68.99139  69.36100  68.13599
##  [491]  68.13599  75.41669  71.67083  72.27980 123.33363  90.44771  98.27869
##  [498]  98.27869  86.15963  86.15963  92.22599  74.52482  76.28544  97.58288
##  [505]  72.64788  61.39802  88.58864  89.86961  89.86961  90.02254  75.07799
##  [512]  84.95602  84.89177  70.53382  70.53382  73.74088  74.82987  75.75995
##  [519]  80.51212  79.09996  93.52541  79.06013  80.15338  74.97086  87.38513
##  [526]  77.86225  94.35261  68.16871  68.16871 100.19341  73.64123  78.37209
##  [533]  88.08065  71.65566  89.02267  63.64050  89.55638  89.55638  97.56478
##  [540]  72.76391  71.77025  71.77025  68.77340  85.18861  85.18861  92.77415
##  [547]  92.77415  97.55871  71.90835  80.38887  85.87713  86.06723  73.96023
##  [554]  87.90237  90.55014  83.40350  83.88497  85.53988  85.53988  89.00745
##  [561]  89.00745  93.91327  70.58699  89.52402  72.42236  92.63721  92.63721
##  [568]  92.63721  96.82117  96.82117  75.28451  91.19791  91.19791  57.33974
##  [575]  72.48959  72.48959  83.27123  72.66277  69.48998  80.96830  80.96830
##  [582]  80.96830  82.13775  75.80468  85.43604  72.59629  83.08446  97.67907
##  [589]  76.42639 113.23663 113.23663  70.48925  78.68339  80.89876  69.65122
##  [596]  80.70878  80.70878  65.48031  81.11543  99.36089 101.27960  83.53104
##  [603]  93.25746  70.98443  70.98443  71.86932  80.07913  80.07913  80.07913
##  [610]  81.81098  98.23332  98.23332  82.11178  80.21269  80.45145 111.04001
##  [617]  99.78471  74.27756  68.45483  70.96253  69.98801 104.56665 100.44723
##  [624] 144.09193  98.28721 103.47898  99.10067  70.87475  81.85310  94.29361
##  [631]  94.05460  92.38638  71.37055  71.37055  69.69244  78.49515  67.79097
##  [638]  67.79097  87.31814  78.48470  80.06467  84.02114  95.19953  72.77164
##  [645]  76.86890  94.41005  78.65878  77.85268  79.79967  79.79967  73.56445
##  [652]  81.78361  78.90878  78.90878  84.31393  67.95410  92.40102  74.52595
##  [659]  92.18895  82.83913  71.57514  75.51583 135.07194 135.07194  85.21557
##  [666]  85.21557  85.21557  93.12289  70.75724  70.54364  87.94393  87.94393
##  [673]  72.70939  76.12640  68.66082  87.39632  87.39632  72.40305  89.77751
##  [680]  89.56957  79.84947  73.50602  73.23345  75.05639  90.61793  69.71502
##  [687]  61.45665  92.02504  71.59300  71.44613 100.21637  94.49122  94.97171
##  [694]  89.22355  81.61007  83.97541  90.97040  66.92522  76.12871  81.12241
##  [701]  81.12241  75.81310  72.83411  86.02939  71.16195 113.52069  66.43550
##  [708]  66.43550  98.60214  66.48092  82.05499 101.58251  81.22660  74.86419
##  [715]  86.42221  94.07380  89.86961  75.04475  89.56200  77.29021  86.16085
##  [722]  77.28278  71.26929  70.10413  70.10413  75.07227  84.98624  79.44976
##  [729]  73.52325  99.82887  99.82887  99.82887  71.97300  80.48786  80.40172
##  [736]  80.40172  74.60525  81.89713  91.99795  76.56643  76.30711  69.96583
##  [743]  87.52129 102.25156  74.42767  74.42767  74.42767  72.05270  90.41549
##  [750]  68.10568  67.05698  85.64750  75.78086  79.79068  66.06213  69.87826
##  [757]  75.14964  94.21016  92.99280  82.08275  95.15863  95.15863  71.02023
##  [764]  74.45452  73.70595  56.85496  80.82367  74.65633  79.23172  79.23172
##  [771]  79.23172  79.23172  97.09659  97.09659  79.28851  87.54573  60.06051
##  [778]  91.66067  83.03368  83.03368  69.33581  97.59641  86.64976  81.79328
##  [785]  72.82519  72.39066  79.84410  99.77086  99.77086  71.72004  95.18013
##  [792]  95.18013  95.70461  91.13133  91.13133  91.13133  76.03648  76.03648
##  [799]  76.03648  83.40547  73.79826  73.79826  71.35211  80.55631  80.55631
##  [806]  80.98904  70.89376  65.44089  84.24497  70.93978 101.38770 101.38770
##  [813]  72.11473  86.81801  86.81801  74.67853  74.67853  93.57237  89.91187
##  [820]  84.56235  69.57317  69.57317  69.57317  79.79867  79.79867  91.00313
##  [827]  91.00313  94.67532  94.67532  93.33041  86.95168  91.06881  95.54315
##  [834]  78.36103  73.34267  71.37055  71.37055  81.27829  90.18841  75.41905
##  [841]  75.41905  75.41905  74.17053  76.63212  69.30523  88.87532 122.41637
##  [848]  87.77003  87.77003  97.14512 101.19441  82.87928  79.49494  79.49494
##  [855]  80.68910 100.53091  94.20459  94.20459  88.98551  88.98551  90.98834
##  [862]  59.70351  71.38811  73.22345  73.22345  73.22345  98.28831  85.14804
##  [869]  71.14401  90.27101  90.27101  67.77490  97.39294  90.21322  79.63456
##  [876]  84.86907  70.70196  98.12339  72.10352  72.10352  79.21773  70.84738
##  [883]  75.24040  81.35123  81.35123  81.35123  78.93721  91.71727  80.80392
##  [890]  70.81998  94.99262  94.09859  94.09859  94.09859  91.90119  85.07340
##  [897]  73.59961  73.59961  83.92184  73.11022  84.53774  84.53774  90.45576
##  [904]  74.97843  76.82459 101.15065  85.02071  85.02071  85.02071  78.33241
##  [911]  84.22938  71.51358  61.30033  73.16914 103.11195 103.11195 129.23090
##  [918]  71.51786  94.97396  73.35855  67.93590  82.25867  86.41149  71.76264
##  [925]  82.85259  86.07483  97.00938 101.85704  73.86925  99.27770  70.99283
##  [932]  72.74509  95.38915  83.65082  83.65082  72.54696  76.41243  76.41243
##  [939]  76.41243  82.60640  79.99943  79.99943  74.51177  87.34531  93.48163
##  [946]  81.63588  78.72815  75.31900  69.65122  74.59281  99.89636  78.76903
##  [953]  70.81018  58.39903  75.54438  93.27217  73.54299  96.25950  82.36979
##  [960]  81.97985  81.97985  89.69813  58.15982  83.39223  83.39223  73.96418
##  [967]  73.84214  73.84214  70.85773  83.78965  75.86580  78.58300  79.52185
##  [974]  77.73160  71.12397  74.37703  73.16527  68.10502  84.68948  90.17262
##  [981]  95.08408  71.43826  74.53619  96.28183  96.28183  96.28183  89.87484
##  [988]  88.40333  81.75738  70.86247  94.13239  67.50980  78.84077  62.86783
##  [995]  62.86783  70.28403  78.28806  80.74090  75.15385  63.92689  85.55745
## [1002]  97.01022  92.02339  82.27804  82.27804  74.82695  70.44955  86.18782
## [1009]  86.18782  67.88584  76.63042  88.14756  65.99896  88.76201  81.72443
## [1016]  82.00273  82.00273  81.20246  70.42296  70.42296  74.79031  74.79031
## [1023]  89.89834  72.03140  74.45657 100.12285  76.13479  74.27700  72.96698
## [1030]  71.99451  86.72774  95.40236  82.42168  75.09006  89.83716  72.47174
## [1037]  72.47174  73.38024  86.29621  79.21787  79.21787  83.23951  83.23951
## [1044]  75.93808  83.50438  94.47896  82.98444  97.61752  93.84508  73.74865
## [1051]  88.47322  88.47322  97.09420  88.81597 115.45373  94.14286  96.25013
## [1058]  89.60111  74.47690  79.99074  79.78595  91.98384  91.98384  91.98384
## [1065]  73.13160  73.32903  93.02908  93.02908  80.02822  71.36928  98.86158
## [1072] 102.63911  90.56894  90.56894  75.44035  79.49494  72.71289  65.84169
## [1079]  97.91980  97.91980  77.21159  61.20735  91.00313  73.65735  88.43003
## [1086]  68.43387  73.53761  90.62007  61.23750  78.48566  98.46625  98.46625
## [1093]  89.49406  69.23280  74.85102  92.58693  72.55356  93.61612  71.51215
## [1100]  83.09390  96.61750  81.18279  74.64366 102.23217 113.64599 113.64599
## [1107]  83.66967  88.10655  83.45454  83.45454  92.92511  71.30065  91.04748
## [1114]  81.09330  77.94215  75.18826  86.99288  75.65507  82.62868  82.62868
## [1121]  72.68366  72.68366  87.31706  75.51042  75.51042  91.29721  86.28688
## [1128]  77.02420  73.25180  78.76903  85.04914  95.23705  71.32787  86.91880
## [1135]  86.91880  71.00529  92.31482  89.46292  91.16008  91.16008  89.51398
## [1142]  90.25571  90.25571  72.34713  72.34713  66.52845  72.65428  59.13206
## [1149]  72.36078  78.02150  82.02054  68.59748  68.59748  88.27504  88.27504
## [1156]  85.22178  85.22178  84.83360  70.89057  76.35714  70.13930  73.38223
## [1163]  75.23375  75.23375  76.57540  73.30882  84.85651  83.35048  72.44609
## [1170]  73.34200 124.68900  81.77981  81.77981  98.98108  83.91310  71.00615
## [1177]  72.06282  72.06282  77.44046  77.44046  77.44046  75.00315  75.00315
## [1184]  75.00315  69.41862  97.09303  99.91020  99.91020  75.40603  75.40603
## [1191]  79.32740  66.98225  82.95014  82.41393  90.77352  93.17353  93.17353
## [1198]  73.32095  73.97973  95.99438  87.51833  91.11371  71.73403  80.06058
## [1205]  68.16617  82.94940  80.45700  71.54488  73.44078  73.44078  69.09197
## [1212]  80.95640  67.54731  86.72324  96.58382  96.58382  75.43655  95.68944
## [1219]  73.37428  73.37428  77.91001  92.63194  92.63194  95.52971  78.62492
## [1226]  95.36150  70.58047  90.73905  78.91922  76.52960  88.42299  89.86224
## [1233]  76.33188  79.91538 100.30249  78.40071  79.24732  86.85810  86.85810
## [1240]  76.03752  76.03752  79.92492  94.05084  95.67140  86.40055  86.40055
## [1247]  78.47157  70.22758  70.22758  87.67781  87.67781  64.32598  80.42061
## [1254]  80.42061  95.68351  97.79359  93.36792  85.90149  92.27441  82.89191
## [1261]  74.96587  84.01776  84.01776  84.01776  75.41669  71.40138  69.33581
## [1268]  89.68761  89.68761  71.40753  69.92609  81.36877  83.94553  77.80527
## [1275]  73.97851  91.28594  68.95115  68.95115  72.22026  81.41455  81.41455
## [1282]  72.34713  96.22820  80.26114  79.77984  79.77984  79.77984  79.77984
## [1289]  79.48282  84.07048  94.41310  80.64602  80.64602  74.17333  81.71798
## [1296]  82.32123  66.98225  99.37173  99.37173  74.26858  86.67846  69.49288
## [1303]  80.94921  91.20370  81.91588  71.60267  82.88310  84.83360  79.83163
## [1310]  89.78436  96.22342  84.75013  84.75013  73.24997  80.36641  85.55920
## [1317]  85.55920  85.55920  74.59084  86.80128  58.73679  97.49099  92.52116
## [1324] 105.66191  65.55304  89.98384  89.98384  82.12522  98.28063  72.42189
## [1331]  72.42189  73.24456  73.24456  75.75770  75.75770  73.77428  73.77428
## [1338]  99.36671  76.02057  73.10828  71.29012  71.29012  90.25428  94.61255
## [1345]  94.30481  70.42817  73.10965  74.27206  74.27206  74.27206  90.94874
## [1352]  92.07484  91.39769  80.23585  80.23585  72.88731  78.73226  72.50374
## [1359]  99.84144  70.99283  80.71288  80.71288  65.61226  79.34721  93.45853
## [1366]  75.41843  87.61830  87.97601  87.97601  88.57284  88.57284  71.36879
## [1373]  88.39080  91.21469  91.21469  91.21469  75.29180  87.64810  70.30503
## [1380]  85.88019  69.90450  80.34855  78.27231  79.84861  88.20112  81.63253
## [1387]  99.43444  68.15053  75.09046  79.51578  92.18867  68.59192  97.69386
## [1394]  71.68429  89.29777  89.92584  74.20844  74.06405  81.97985  81.97985
## [1401]  82.87737  85.04596  85.04596  80.83372  71.54625  70.66407  70.66407
## [1408]  72.48331  91.94158  71.81485  91.60079  73.16810 102.88113  96.88980
## [1415]  58.45361  83.83059  86.30890  86.22128  83.32925  83.32925  75.94007
## [1422]  75.94315  74.40871  70.56984  87.97493  87.97493  70.72771  89.11730
## [1429]  87.83943  87.68802 102.48330 102.48330  80.94831  80.94831  80.94831
## [1436]  78.45318  60.34376  78.16080  71.95544  74.01393  74.01393  80.60363
## [1443]  99.32560  76.81451  66.90834  89.56835  89.56835  69.90483  78.75882
## [1450]  71.30230  84.07514  84.07514  80.18958  86.09891  86.09891  72.18286
## [1457]  90.25888  90.25888  90.25888  90.25888  79.52800  79.52800  74.08825
## [1464]  81.93476  74.10779  70.86932  78.66206  71.79325 100.04669  96.40610
## [1471]  96.40610  90.79449  85.55542  85.55542  74.08572  71.72195  73.24456
## [1478]  73.24456  76.06864  71.37051  93.24857  93.28976  97.13222  97.13222
## [1485]  87.85493  87.85493  87.85493  90.47481  96.94704  96.94704  96.94704
## [1492]  96.94704  70.66757  60.16280  72.71809  72.22545  72.22545  80.70225
## [1499]  80.70225  91.84627  91.84627  82.04270  82.10303 102.81100  85.00100
## [1506]  89.01774  89.01774  75.85458  79.04337  74.50215  86.24994  86.24994
## [1513]  69.17133  87.08104  75.81169  78.49800  66.41091  96.32233  59.44919
## [1520]  84.11509  84.11509  82.16000  75.20360  85.10663  85.10663  80.96830
## [1527]  75.96914 100.58114  74.65606  77.30590  72.93017  91.07130  91.07130
## [1534]  66.39695  65.68875  99.74937  79.96438  73.19284  78.75362  78.75362
## [1541]  85.87414  85.87414  85.87414  80.82456  88.09345  92.14727  80.17517
## [1548]  70.41877  76.49578  93.18705  93.18705  73.92449  85.34612  90.82615
## [1555]  82.48880  82.48880  88.23781  88.23781  72.11757  70.60553  83.18793
## [1562]  78.97037  78.97037  86.72227  83.68425  67.36885  72.08804  96.17216
## [1569]  70.67466  63.01667  84.78569  75.22184 102.37155  96.62472  73.32768
## [1576]  62.00879  86.92004  71.20295 100.26770  91.04748  79.57908  70.18431
## [1583]  70.51198  82.13872  82.13872  92.18777  74.67853  74.67853  87.83943
## [1590]  92.98002  92.98002  92.98002  92.98002  96.27481  80.30070  80.64488
## [1597]  99.05637 100.59319  64.56501  94.69315  81.93476  81.06050  81.06050
## [1604]  81.06050  83.95421  73.54107  74.60343  83.31123  79.31773  90.79946
## [1611]  59.88197  85.26709  85.26709  72.06543  86.78285  85.60367  85.60367
## [1618]  85.60367  93.45853  70.38994  91.64365  73.87468  73.87468  79.61613
## [1625]  72.17304  68.77844  86.68399  77.14924  77.14924  95.73500  67.23303
## [1632]  73.70880  73.70880  90.01810  77.08117  88.42296  78.35105  73.11205
## [1639]  69.57246  88.72037  71.49106  96.80480  89.88362  85.64865  99.29228
## [1646]  82.04506  82.04506  75.40070  75.40070  95.73169  99.06092  81.61175
## [1653]  88.44150  82.42308  82.42308  80.14622  74.27423  88.82299  71.13538
## [1660]  92.67663  92.67663  83.85168  78.63364  78.63364  78.63364  90.23704
## [1667]  90.23704  90.23704  87.75417  74.49959  74.49959  74.49959  70.39434
## [1674]  72.62835  72.62835  86.93936  86.93936  89.86312  89.86312  91.52722
## [1681]  76.16547  75.18046  96.10106  96.10106  80.55210  71.62384  75.50690
## [1688]  73.18616  87.53307  63.08813  80.20862  84.88247  74.57608  86.19003
## [1695]  91.79685  73.89220  73.22476  97.55263  86.83459  85.94997  85.94997
## [1702]  71.96251  80.93230  76.20366  76.20366  76.20366  83.34204 101.18673
## [1709]  84.89818  76.54986  76.54986  72.24517 102.20920  79.64729  88.23125
## [1716]  88.23125  88.59494  88.59494  88.59494  88.49808  73.44131  73.44131
## [1723]  99.36671  85.49805  74.49604  75.22921  89.97548  96.24554  74.65644
## [1730]  73.34200  73.34200  87.46770  94.02265  77.87984  77.87984  92.31482
## [1737]  95.96341  73.41734  74.31454  93.69940  95.50747  95.50747  70.31383
## [1744]  95.19878  95.19878  95.19878  95.77599  95.77599  84.26634  72.91654
## [1751]  70.99283  75.35020  67.85646  85.33797  94.00821  94.00821  85.87757
## [1758]  86.46176  75.18046  75.16884  72.21292  72.21292 124.71046 124.71046
## [1765] 124.71046  74.52595  87.08513  93.53149  82.16842  80.66209  80.66209
## [1772]  94.65545  94.65545  86.27145  86.27145  73.66791  80.58399  74.26902
## [1779]  74.26902  83.39691  83.39691  91.67771  78.17610  78.17610  78.17610
## [1786]  59.78369  59.78369  77.91738  93.92697  93.92697  88.66778  73.30158
## [1793]  65.95287  88.63526  80.67219  80.67219  95.31817  93.94704  93.94704
## [1800]  93.94704  73.76463  86.26639  86.26639  85.80648  92.10066  74.73060
## [1807]  74.73060 100.63006 100.63006 109.13350  70.88986  85.44407  85.44407
## [1814]  85.44407  93.01750  93.01750  72.94700  96.38798  87.76502  80.55201
## [1821]  92.01403  86.47641  86.47641  86.47641  76.20521  74.13723  72.68197
## [1828]  78.09151  80.55945  80.55945  86.91648  75.74833  95.90216  95.90216
## [1835]  95.90216  60.83646  85.34020  85.34020  70.39470  82.21714  96.80116
## [1842]  96.80116  74.72408  88.42003  71.25878 113.43553 113.43553  87.03186
## [1849]  81.43286  88.53293  88.53293  72.87095  72.87095  71.30230  73.84682
## [1856]  73.84682  67.15023  67.15023  67.15023  67.15023  95.15024  71.33929
## [1863]  75.29560  75.29560  69.17133  70.82836  73.56017  73.56017  82.74725
## [1870]  82.74725  73.36284  94.68948  72.16132  72.16132  90.68896  72.60599
## [1877]  68.49896  69.30257  78.35859  84.57347  84.57347  71.37383  91.54148
## [1884]  88.85775  70.66839  95.81783  92.65453  94.24358  90.31879  71.12431
## [1891]  74.72497  74.72497  74.72497  68.83239  68.83239 113.12213  95.94435
## [1898]  70.95631  70.95631  72.82323  72.82323  72.82323  72.82323  86.73739
## [1905]  86.73739  77.63785  81.69793  74.96602  84.96566  84.96566  74.41545
## [1912]  94.91671  74.79789  80.15954  81.54148  75.54663  75.54663  75.54663
## [1919]  72.88634  59.70934  77.67184  76.69721  70.29573  76.30890  82.95702
## [1926]  78.75409  95.32796  85.02071  85.02071  85.02071  57.45309  85.71056
## [1933]  79.28544  73.54424  85.63312  76.46207  84.07156  84.07156  70.61968
## [1940]  70.61968  90.47517  90.47517  90.47517  80.78643  86.41640  72.55822
## [1947]  72.55822  76.83126  95.68786  69.02089  69.02089  64.50097  64.50097
## [1954]  64.50097  68.95420  74.44009  79.56276  79.68758  92.91233  92.91233
## [1961]  84.18850  76.23271 110.02972  91.71145  78.37002  80.22249  82.99446
## [1968]  94.25342  94.25342  73.60986  84.72257 111.01787  83.81487  94.22380
## [1975]  91.24400  85.54581  96.47080  96.47080  70.62241  93.71986  93.71986
## [1982]  87.19673  87.32973  86.93936  75.09532  86.65466  86.65466  72.69934
## [1989]  90.09753  90.09753  90.09753  90.09753  86.14631  75.43693  75.83224
## [1996]  90.57160  79.30597  73.01831  73.01831  89.11730  89.11730  89.11730
## [2003]  89.11730  73.43596  76.69980  80.03480  80.60475  68.85977  87.41119
## [2010] 101.61798 114.09556 114.09556  86.24369  72.46605  72.46605  82.87642
## [2017]  86.49873  86.49873  75.02607  82.00437  69.85663  76.69980  96.08867
## [2024]  96.08867  83.23365  88.63212  92.94581  57.89550  86.80128  72.29963
## [2031]  89.25572  94.16390  95.20397  70.87400  82.26692  82.26692  75.65476
## [2038]  69.98929  69.98929  96.27851  75.27502  97.77311  88.23809  75.98837
## [2045]  84.88247  91.46624  88.11540  78.77026  80.80736  80.33709  72.91290
## [2052]  93.33032  93.33032  72.97950  84.07514  70.96253  70.96253  99.99739
## [2059]  72.81234  91.41476  91.41476  72.28257  89.88163  79.04834  71.32090
## [2066]  94.07363  94.07363  94.07363 101.42542 101.42542 101.42542 101.42542
## [2073]  87.72787 101.68418  74.59950  74.59950  72.49982  72.49982  72.49982
## [2080]  72.49982  76.56280  67.46237  74.03001  84.68544  84.68544  84.68544
## [2087]  93.64860  89.63083  98.66649  98.66649  80.22806  79.88916  60.09914
## [2094]  85.45188  85.45188  71.43195  74.05564  74.46975  88.98524  86.55779
## [2101]  73.13322  73.13322  92.77415 100.28562  70.80586  95.18776  94.11011
## [2108] 111.34870  69.82632  85.32757  75.12371  71.84954  96.95280  70.30229
## [2115]  71.60195  71.60195  71.60195  74.86211  76.44398  96.37606  93.35025
## [2122]  73.13061  97.12323  97.12323  98.47888  79.17758  87.74275 100.28562
## [2129]  94.10442  69.92285  87.14821  87.14821  87.14821  74.19776  88.96087
## [2136]  88.96087  96.76247  70.31725  73.15152  73.15152  77.08350  89.12088
## [2143]  91.50514  91.50514  79.29565  57.99466  99.14120  76.07808  75.55006
## [2150]  76.15855  76.15855  95.28348  84.81253  88.91223  94.84977  72.52930
## [2157]  73.39634  73.39634  73.39634  73.39634  90.23636  87.31015  75.56185
## [2164]  77.88484  77.88484  72.96645  77.92900  78.74886  85.77998  95.18357
## [2171]  86.54516  95.36539  90.84895  87.04249  72.95717  72.50673  79.68086
## [2178]  89.71923  81.15495  74.32680  79.34999  79.34999  79.34999  79.34999
## [2185]  82.19506  88.80773  90.31849  88.59494  96.38960  92.98200  70.71996
## [2192]  72.98994  88.84140  81.77543  61.50224  61.50224  73.22900  81.61007
## [2199]  81.61007  83.40372  71.06169  77.87737  83.36582  85.41687  78.13448
## [2206]  73.22683  75.02625  86.45413  90.95297  90.95297  90.95297  90.95297
## [2213]  75.72474  75.72474  71.39134  71.39134  71.88627  76.64946  76.64946
## [2220]  72.77916  77.18384  66.61145  75.08931  83.84503  75.11657  88.13825
## [2227]  78.64274  80.62550  82.77627  82.77627  78.50236  71.15300  63.76714
## [2234]  73.45834 114.93648  81.36323  99.34729  99.34729  96.79799  96.79799
## [2241]  85.29666  82.21763  74.16898  74.62373  74.62373  96.75469  97.18184
## [2248]  81.71798  91.52821  96.32479  79.61769  74.04792  86.72753  86.72753
## [2255]  67.96329  90.28081  87.21823  76.28857  77.27880  73.13061  73.38223
## [2262]  74.40099  84.98343  72.33546  72.33546  80.92210  80.92210  75.43597
## [2269]  75.43597  94.55777  91.93161  93.17280  93.17280  93.17280  93.17280
## [2276]  88.81912  88.81912  85.55920  78.37635 102.67228  86.54460  86.61226
## [2283]  80.39232  79.10755 103.50325 103.50325  92.02724  91.81690  91.81690
## [2290]  75.57558  90.03248  75.27285  79.92064  74.00563  79.75914  80.99060
## [2297]  80.99060  73.58758  79.30717  75.74976  79.26596  72.04446  88.70448
## [2304]  65.75997  65.75997  68.90203  89.29462  89.29462  85.07915  78.45412
## [2311]  83.19958  96.58360  95.21845  97.11160  97.11160  94.21348  69.15887
## [2318]  76.50070  69.39797  72.64723  88.24567  75.72898  96.50624  75.28105
## [2325]  75.28105  75.28105  88.04873  75.07799  73.25881  73.25881  81.19511
## [2332]  70.04699  75.08554  75.08554  96.39190  96.39190  96.39190  69.95684
## [2339]  85.90852  71.56035  94.13033  79.79208  68.90406  75.02212  80.18805
## [2346]  74.16593  78.72617  69.12933  78.69930 110.47621 110.47621 110.47621
## [2353]  82.13872  82.13872  70.01393  95.65052  95.65052  95.65052  98.34218
## [2360]  68.41764  95.86602  95.86602  67.70767  67.70767  67.70767  67.70767
## [2367]  71.48033  83.19354  73.67858  97.20399  97.20399  97.20399  97.20399
## [2374]  95.62124  95.62124  72.35443  72.35443  76.75993  80.17448  84.66563
## [2381]  72.97940  72.97940  72.97940 100.70570  80.71288  91.46437  94.62668
## [2388]  94.62668  97.77055  82.54522  87.15133  74.50087  74.50087  74.50087
## [2395]  94.71172  74.66345  64.99564  75.92024  73.64123  69.35306  94.87404
## [2402]  73.41935  71.65617  70.87786  89.17966  89.17966  86.19082  85.18817
## [2409]  85.18817  94.85838  94.25664  94.25664  72.89834  85.84887  85.84887
## [2416] 108.25450  76.95546  86.50810  77.62005 100.61137 100.61137 100.61137
## [2423]  83.82448  84.73950  83.13705  78.13732  67.78175  89.17215  86.65974
## [2430]  96.91507  56.50936  87.69852  87.69852  87.69852  78.12961  78.12961
## [2437]  95.38576  89.27331  89.27331  75.91074  66.76090  79.83163  69.47591
## [2444]  60.56516  75.85817  75.85817  87.84341  82.72442  78.02497  78.02497
## [2451]  82.45272  76.33281  70.61895  70.61895  77.16777  77.25109  70.90964
## [2458]  65.68875  65.68875  88.68021  88.68021  88.68021  71.06801  77.57793
## [2465]  76.25111 101.35090  59.68961  85.82622  96.86104  83.23308  88.94250
## [2472]  89.67233 113.36674  73.52297  90.03452  79.25928  79.25928  89.57293
## [2479]  89.57293  89.57293  74.89341  74.89341  70.45695  83.15509  79.73849
## [2486] 119.08327  80.86425  89.28234  74.72017  74.72017  74.72017  79.53669
## [2493]  75.92024  89.89635  72.98350  93.92530  73.20225  73.20225  73.20225
## [2500]  97.76487  83.13117  64.58095  88.44805  88.44805  88.44805  88.44805
## [2507]  78.73263  82.45864  89.22083  94.38076  94.38076  74.18629 100.91133
## [2514] 100.91133  90.76124  87.65190  93.11951  93.11951  74.55119  70.51201
## [2521]  80.38887  80.38887  79.69787  86.86945  85.29859  72.01004  79.38296
## [2528]  76.89271  73.97302  73.97302  93.65415  93.65415  97.44929  97.44929
## [2535]  76.31112  76.31112  77.04979  77.04979  88.95287  97.18987  89.68119
## [2542]  73.44432  73.44432  75.53031  78.26635  89.00908  82.49481  82.49481
## [2549]  82.49481  87.19052  87.19052  87.19052  73.53098  94.27819  77.59264
## [2556]  84.83743  70.75331  69.86388  75.44035  75.44035 101.97430  99.94224
## [2563]  99.94224  87.60092 104.32864 104.32864  70.41570  78.24813  89.69919
## [2570]  97.52322  74.52362  75.78536  75.78536  92.87395  89.65735  89.65735
## [2577]  73.84538  71.94247  88.83761  88.83761  93.75466  77.88118  76.48887
## [2584]  95.69075  76.77704  78.57761  87.20875  76.38200  73.74210  79.68962
## [2591]  84.01630  91.87376  68.52399 108.63715  84.74911  90.51267  74.24963
## [2598]  68.17738  91.85412  74.61321  66.36453  87.90182 102.56197  89.14593
## [2605]  89.14593  89.14593  85.03370  76.70623  64.58934  87.31238  70.99755
## [2612]  92.75366  82.07302  82.07302  79.34743  79.34743  78.61990  78.47524
## [2619]  78.47524  98.51707  98.51707  71.01104  87.27641  72.36089  72.36089
## [2626]  89.01958  86.26832  56.58681  71.68953  74.02171  74.02171  74.02171
## [2633]  80.49741  92.73947  91.87132  87.72209  87.72209  82.22354  72.01041
## [2640]  70.99321  79.51578  79.51578  94.02702  87.61830  69.21019  71.17910
## [2647]  73.79826  88.23533  95.81701  81.00126  81.00126  79.99877  79.99877
## [2654]  97.92113  66.66103  82.51239  82.51239  82.51239  86.63388  70.82485
## [2661]  80.29993  80.29993  88.85856  79.24527  78.64856  78.64856  88.91795
## [2668] 121.69718  81.11575  81.11575  70.85934  70.85934  73.74779  73.74779
## [2675]  73.74779  77.91648  77.91648  65.43660  79.25673  91.49963  82.23158
## [2682]  82.23158  82.23158  93.18109  93.18109  93.18109  67.55560  75.81310
## [2689]  73.44466  72.62835  72.62835  72.62835  95.16591  95.16591  78.40283
## [2696]  73.22250  85.15678  93.48499  93.48499  75.83727  85.01824  76.08792
## [2703]  72.98486  95.35444  95.35444  93.95745  93.95745 100.96054  72.72582
## [2710]  75.71195  75.71195  99.29980  89.87728  89.87728 100.24573 100.24573
## [2717]  73.81364  75.39759  88.03771  88.03771  79.27437  81.56252  80.91828
## [2724]  72.96830  97.23257  84.38602  78.45461  74.31477  74.31477  74.31477
## [2731]  90.56488  90.56488  69.57907  69.57907  94.21405  94.21405  94.21405
## [2738]  70.20018  95.77056  95.77056  87.73448  73.91999  74.84920  81.71798
## [2745]  81.71798  90.49579  95.63409  71.08082  71.08082  84.78400  72.00434
## [2752]  72.00434  85.63945  80.17214  78.12407  78.12407  78.12407 100.51053
## [2759]  73.65735  73.65735  73.65735  82.47371  95.47345  80.43597  88.55957
## [2766]  88.55957  79.79867  70.17372  70.17372  85.88236  85.88236  85.88236
## [2773]  75.88639  76.69025  80.87449  97.89540  97.89540  97.89540  93.64503
## [2780]  75.08931  75.08931  79.61685  79.61685  82.36124  70.41801  87.49764
## [2787]  87.49764  88.24214  88.24214  88.24214  66.31151  66.31151  66.31151
## [2794]  74.91070  78.49369  80.97690  94.24837  75.93193  77.77967  91.64205
## [2801]  87.08367  92.75912  72.69932  72.69932  85.58066  85.58066  88.33508
## [2808]  72.59328  72.59328 101.83085  86.34149  86.34149  77.38849  76.69643
## [2815]  86.88552  86.88552  86.88552  80.40172  84.03921 144.03608 144.03608
## [2822]  87.12683  78.63137  89.65352  83.40307  83.40307  88.92123  79.93644
## [2829]  72.24715  72.24715  87.66207  76.18773  89.57768  81.97985  99.99884
## [2836]  80.92210  80.74072  79.09436  91.44155  73.78425  70.33347  71.99567
## [2843] 126.76493 126.76493  76.32960  76.32960  91.74369  74.70030  73.13061
## [2850]  93.17401  93.17401 100.90249  77.25732  87.96096  71.02566  75.28034
## [2857]  70.77552  70.77552  86.24994  90.17660  87.14410  87.14410  69.08629
## [2864]  95.47201  72.03347  85.51409  74.72017  86.35655  86.35655  86.35655
## [2871]  86.67144  83.36962
MSE_boost <- mean((nhanes_test$Weight - boost_pred)^2)
MSE_boost
## [1] 315.6755
MSE_reg
## [1] 332.8215
MSE_dectree
## [1] 334.6264
MSE_rf
## [1] 262.9953

Based on the lowest MSE, the Random Forest Model seems to be the best at predicting weight based on all other factors.

Part 3: Clustering

  1. Use R to compute the mean of each variable in the nhanes_train csv file.
summary(nhanes_train)
##       Age            Weight           Height          Pulse       
##  Min.   :16.00   Min.   : 39.30   Min.   :139.9   Min.   : 40.00  
##  1st Qu.:30.00   1st Qu.: 67.50   1st Qu.:162.2   1st Qu.: 64.00  
##  Median :44.00   Median : 79.40   Median :169.7   Median : 72.00  
##  Mean   :45.15   Mean   : 82.63   Mean   :169.5   Mean   : 72.32  
##  3rd Qu.:58.00   3rd Qu.: 94.65   3rd Qu.:176.7   3rd Qu.: 80.00  
##  Max.   :80.00   Max.   :223.00   Max.   :199.9   Max.   :122.00
  1. Perform k-means clustering on the data in the nhanes_train csv file. Create 4 distinct clusters.
library(fpc)
nhanes_fit <- kmeans(nhanes_train[1:4], 4)
nhanes_fit
## K-means clustering with 4 clusters of sizes 821, 716, 487, 847
## 
## Cluster means:
##        Age    Weight   Height    Pulse
## 1 36.82095  88.26090 174.1502 71.74178
## 2 30.04888  63.92165 165.1246 75.13966
## 3 48.06571 117.06982 176.2801 75.34292
## 4 64.30224  73.19764 164.9505 68.76033
## 
## Clustering vector:
##    [1] 4 3 2 1 3 4 1 1 1 4 2 2 1 3 3 1 2 2 2 4 1 2 4 1 4 4 4 3 2 1 1 4 2 3 2 1 4
##   [38] 4 1 1 1 4 4 1 1 4 2 4 1 4 4 4 2 3 2 4 3 4 4 4 1 2 2 2 4 2 3 1 1 2 4 4 1 4
##   [75] 3 2 2 1 2 1 4 1 3 2 3 2 2 4 4 1 2 4 2 3 3 4 1 2 2 2 4 4 4 2 2 3 4 1 4 2 2
##  [112] 2 1 3 4 2 4 1 4 2 2 4 4 4 4 1 1 3 3 1 1 1 4 3 4 2 2 3 3 4 4 4 4 4 1 3 4 1
##  [149] 2 4 1 2 1 2 4 4 1 2 1 1 1 2 3 1 3 2 2 1 2 4 1 1 1 2 1 1 2 1 2 4 1 2 1 2 2
##  [186] 4 3 4 1 2 4 1 3 1 4 1 4 2 2 4 1 4 1 1 3 4 3 4 4 2 1 1 3 3 1 3 4 2 2 3 1 2
##  [223] 2 3 1 1 2 3 4 4 2 1 3 4 1 3 3 4 4 1 2 2 1 4 4 3 2 4 4 4 2 1 4 1 2 3 4 1 4
##  [260] 1 4 3 3 4 1 4 3 3 4 2 1 2 1 3 2 1 1 3 1 4 4 4 4 4 4 3 1 2 1 2 1 3 3 2 2 2
##  [297] 4 3 3 2 1 3 2 2 1 3 4 1 2 4 4 2 2 1 2 4 2 1 4 2 3 3 1 1 1 2 3 4 2 2 2 4 1
##  [334] 2 4 4 4 2 2 3 4 1 1 4 1 4 2 2 1 4 3 4 3 2 3 2 3 2 3 1 4 4 2 1 1 2 4 2 4 2
##  [371] 4 2 1 2 1 2 4 1 2 4 1 4 1 1 4 2 1 2 3 2 4 4 4 2 4 3 1 1 2 1 1 1 2 1 4 1 4
##  [408] 4 3 2 1 1 4 1 4 3 4 4 2 4 4 4 4 1 1 2 4 3 4 1 3 2 2 2 1 2 2 3 1 2 4 2 1 1
##  [445] 2 4 2 1 2 3 4 1 4 4 1 4 3 4 2 2 1 1 1 3 3 1 1 4 1 4 1 4 1 3 1 1 3 1 3 1 2
##  [482] 1 4 2 2 4 3 4 1 1 1 2 1 2 4 2 1 1 4 2 4 3 3 1 3 1 1 1 2 4 4 1 4 2 4 4 1 3
##  [519] 1 2 2 2 1 1 4 4 2 3 2 1 4 4 4 4 1 3 1 1 2 4 3 3 4 1 2 1 3 2 1 2 4 1 1 4 1
##  [556] 3 4 2 3 4 1 1 4 4 1 1 2 4 4 4 3 2 4 3 2 1 3 2 4 1 2 2 3 1 4 2 2 4 3 3 4 2
##  [593] 1 1 4 1 4 4 4 2 2 1 2 4 4 2 4 3 2 1 4 2 1 4 4 1 2 1 4 2 2 1 2 1 1 1 3 1 4
##  [630] 4 4 1 4 1 3 4 4 3 3 1 4 3 4 2 2 3 1 1 4 1 2 3 4 2 4 1 1 2 1 4 1 2 2 2 2 4
##  [667] 1 1 2 2 2 2 3 4 3 2 4 1 3 1 3 1 1 3 3 2 2 2 4 1 4 3 1 1 4 4 2 3 4 1 3 1 2
##  [704] 3 3 3 4 4 4 4 2 2 4 4 2 2 2 2 1 4 4 4 4 1 2 2 1 4 3 4 3 3 2 1 2 4 4 1 3 1
##  [741] 2 4 3 2 2 4 2 2 4 1 2 1 1 4 4 4 4 4 1 1 2 1 1 4 2 1 2 1 2 4 1 3 3 3 2 1 3
##  [778] 1 4 1 2 1 4 4 1 4 1 3 2 2 3 2 2 4 1 4 4 1 4 3 2 1 4 1 4 2 1 4 4 2 2 3 1 3
##  [815] 3 1 3 1 2 1 4 2 1 2 1 1 4 3 1 4 4 3 4 1 2 4 4 2 1 1 1 1 2 4 1 4 2 1 1 4 2
##  [852] 3 4 1 2 1 2 1 1 2 4 3 4 2 2 4 2 4 2 4 4 3 3 1 4 1 4 4 1 2 1 4 3 4 1 1 1 1
##  [889] 3 4 1 1 3 4 2 1 3 4 1 3 4 3 4 1 1 4 4 2 4 1 1 2 1 1 1 1 2 1 2 4 2 1 3 1 2
##  [926] 2 3 4 4 2 2 1 4 2 3 4 1 1 4 4 4 1 1 4 1 4 1 2 3 1 2 2 4 4 4 1 3 1 4 1 2 2
##  [963] 2 3 2 2 2 3 1 1 4 1 4 2 1 3 2 1 3 3 2 3 4 3 1 4 2 4 2 4 2 1 2 3 2 4 3 1 3
## [1000] 4 2 1 4 3 4 1 2 3 4 1 3 2 2 4 1 1 1 1 4 2 1 3 3 4 1 4 2 3 2 3 4 2 2 3 3 2
## [1037] 3 1 2 4 3 2 2 1 2 4 3 2 4 2 2 2 2 4 3 4 1 1 1 1 1 2 1 4 4 4 2 2 2 4 1 2 2
## [1074] 1 3 4 1 3 4 4 4 3 3 2 1 3 4 2 2 2 2 4 4 3 3 1 2 1 1 2 1 4 1 4 4 1 2 3 1 1
## [1111] 1 2 4 1 3 4 3 3 2 4 3 3 3 1 1 4 2 1 1 4 4 1 2 1 2 2 1 4 3 2 3 1 1 2 4 2 1
## [1148] 4 2 4 4 4 2 2 2 4 4 1 1 3 4 2 2 1 2 3 3 2 4 1 1 3 3 4 4 3 1 3 4 2 3 2 2 4
## [1185] 4 2 4 1 3 3 1 4 1 1 3 3 4 1 1 4 1 4 4 2 1 2 1 4 2 2 3 1 1 1 1 4 1 4 4 3 1
## [1222] 1 1 2 4 4 2 4 2 2 4 3 2 2 3 4 2 3 1 1 1 4 4 2 3 3 2 3 4 4 2 2 2 4 4 2 3 3
## [1259] 3 4 4 4 1 4 2 2 2 4 4 1 4 1 1 2 1 1 4 1 1 4 4 4 4 4 2 1 4 1 2 2 2 2 2 2 2
## [1296] 2 3 1 1 3 1 3 1 4 4 4 4 1 4 4 3 2 3 1 4 1 3 2 4 4 3 1 2 1 2 4 1 4 4 3 3 3
## [1333] 4 4 2 1 3 4 4 3 4 4 4 3 1 1 4 2 3 2 1 2 4 4 1 4 3 1 2 1 4 4 4 3 4 1 4 2 1
## [1370] 1 1 4 2 4 4 1 2 4 2 3 1 2 4 4 4 4 4 2 2 4 1 4 1 1 3 2 4 1 4 4 4 1 4 2 3 2
## [1407] 4 3 1 4 3 1 4 3 1 3 2 1 4 4 2 3 1 4 3 1 1 4 4 4 4 3 4 3 3 2 2 1 4 4 4 2 1
## [1444] 3 1 2 2 4 4 4 3 4 4 2 3 1 2 2 4 1 1 1 4 2 3 2 2 1 2 2 2 2 1 4 3 1 2 2 1 4
## [1481] 4 4 3 3 2 3 1 4 1 2 2 4 3 1 2 2 1 4 3 2 4 4 3 1 4 4 4 3 1 2 4 2 1 1 4 2 4
## [1518] 3 1 4 4 2 4 3 3 4 4 4 2 4 3 1 2 1 1 1 2 4 1 1 4 1 3 2 2 3 2 4 4 1 1 1 2 1
## [1555] 3 4 4 2 1 4 3 4 4 4 2 2 4 4 1 3 1 2 3 3 2 1 4 1 1 3 4 2 3 1 1 2 1 4 2 1 4
## [1592] 4 1 2 1 2 4 2 3 1 4 1 4 4 4 1 4 4 4 1 1 1 3 3 1 4 3 3 4 1 2 1 1 4 1 1 3 4
## [1629] 1 4 1 4 1 2 2 2 1 3 4 2 1 1 4 2 1 1 4 4 1 4 1 2 1 4 3 1 1 2 4 1 1 4 3 4 1
## [1666] 4 4 1 2 1 3 2 2 2 3 4 1 2 3 3 1 2 2 1 2 1 4 4 2 1 3 4 4 4 2 3 3 2 3 3 1 1
## [1703] 3 2 4 4 1 3 2 2 2 1 3 4 4 4 3 4 3 1 1 4 3 4 3 2 1 1 2 1 4 3 4 2 4 2 1 2 3
## [1740] 1 3 3 2 2 4 1 1 4 1 1 1 4 3 4 2 1 1 1 2 4 2 4 4 2 3 1 3 1 2 2 1 4 2 2 2 2
## [1777] 4 3 4 3 4 1 2 1 1 4 1 2 1 4 1 4 1 1 1 2 3 2 4 1 2 4 4 4 4 2 4 3 4 4 4 3 1
## [1814] 4 2 1 1 2 2 1 4 2 2 4 3 4 1 4 4 4 4 4 1 4 1 2 2 4 1 4 3 1 3 1 2 4 2 2 1 2
## [1851] 3 1 4 4 1 4 4 4 4 2 1 3 4 4 1 4 1 2 1 2 1 4 4 3 4 1 2 4 4 4 2 2 1 4 1 1 1
## [1888] 1 2 2 1 4 1 3 2 4 3 4 3 1 1 4 1 4 4 1 2 2 1 3 2 3 2 3 4 1 4 2 4 3 2 1 2 3
## [1925] 1 1 3 4 3 1 4 3 3 4 4 2 4 3 1 1 2 2 3 1 3 2 3 2 3 3 4 4 2 1 1 1 2 4 4 4 1
## [1962] 4 1 2 4 1 2 4 4 4 2 2 2 1 1 4 4 2 4 3 2 1 1 1 4 3 2 2 4 4 2 4 2 1 1 3 1 2
## [1999] 2 1 2 2 4 3 1 1 3 3 1 1 1 4 3 4 2 1 4 1 2 2 1 2 4 1 4 3 3 1 3 2 2 3 1 3 2
## [2036] 4 4 2 1 1 4 1 1 1 1 2 3 3 2 2 1 2 1 3 2 2 3 3 2 2 3 4 4 2 1 3 2 1 3 1 1 3
## [2073] 2 2 1 2 3 3 4 3 2 4 4 2 1 3 3 3 2 4 4 1 2 1 2 3 1 4 3 1 3 1 4 4 1 4 2 1 1
## [2110] 4 2 1 1 2 4 2 1 3 3 2 3 2 2 1 2 1 3 4 4 1 2 4 1 4 2 1 1 1 2 2 4 2 4 2 4 2
## [2147] 2 3 2 1 3 4 3 1 2 2 1 4 4 1 2 3 3 4 1 1 4 4 3 1 1 2 3 3 2 3 4 4 3 4 4 4 1
## [2184] 1 1 1 2 4 4 3 3 2 1 1 4 3 1 2 4 2 4 3 3 1 2 4 4 1 4 3 2 3 1 1 3 1 3 2 2 3
## [2221] 3 2 4 3 2 2 3 2 3 1 1 1 1 2 1 1 3 4 1 1 4 4 3 3 2 4 4 2 2 2 4 4 2 2 1 4 1
## [2258] 2 3 2 2 3 4 4 1 4 3 3 4 2 3 3 2 4 1 1 2 1 1 2 4 2 1 3 1 2 3 2 3 1 3 4 3 1
## [2295] 1 2 4 1 2 4 4 2 4 3 1 1 2 4 1 2 2 4 2 2 2 4 2 3 1 3 4 4 2 1 4 4 1 3 4 2 4
## [2332] 3 1 4 3 1 4 4 4 3 2 2 4 4 1 1 2 1 2 1 4 2 2 1 4 4 4 1 4 1 4 4 3 2 4 2 4 4
## [2369] 3 2 1 1 4 1 3 3 3 1 4 1 2 4 3 4 1 3 4 4 4 2 2 2 1 1 3 3 1 4 4 4 1 1 2 4 2
## [2406] 2 2 2 1 4 2 1 4 2 1 1 1 1 4 1 1 1 1 2 2 2 4 2 3 3 3 3 2 4 2 2 1 1 1 2 4 2
## [2443] 4 1 4 1 4 4 1 2 2 4 1 3 1 4 2 4 4 2 2 3 1 2 2 1 3 1 1 1 2 2 3 3 2 4 1 2 1
## [2480] 1 1 3 2 1 1 1 2 1 3 2 3 2 1 4 4 3 1 4 1 4 2 3 1 3 2 1 2 1 2 3 2 1 4 1 3 4
## [2517] 4 4 1 4 4 4 2 3 1 4 4 2 2 1 1 2 4 3 3 2 1 2 1 3 4 2 1 4 2 4 1 1 1 1 2 4 2
## [2554] 4 4 4 2 1 4 2 3 2 4 2 2 3 3 2 3 1 3 3 3 2 1 4 2 4 1 1 4 1 3 1 4 4 3 3 3 2
## [2591] 4 4 1 4 4 3 4 1 1 4 1 4 1 1 2 2 4 4 1 4 1 1 3 4 2 1 1 1 2 2 4 1 4 1 4 1 1
## [2628] 1 4 3 4 3 1 2 1 4 1 2 4 1 2 4 4 1 4 3 4 2 3 4 1 2 1 1 1 3 2 4 1 4 4 4 2 2
## [2665] 2 3 4 1 3 3 1 2 4 2 4 2 2 3 1 1 3 4 1 4 4 1 2 4 2 4 4 1 3 1 3 4 3 2 2 2 4
## [2702] 1 3 2 4 4 4 3 4 1 4 4 1 1 3 1 1 2 4 2 1 4 4 4 4 4 3 2 1 2 4 3 3 2 1 4 4 3
## [2739] 1 4 1 1 2 3 1 3 1 3 1 3 3 3 4 1 4 1 2 1 2 4 4 4 4 2 2 2 4 4 4 3 1 4 1 3 2
## [2776] 4 2 2 1 1 4 1 1 1 2 4 1 1 1 4 4 2 4 3 4 3 4 4 1 2 4 1 2 2 4 3 3 1 4 1 1 3
## [2813] 2 2 1 4 4 2 2 2 4 1 1 4 2 1 3 3 1 1 4 2 3 1 2 4 1 1 4 1 1 4 4 3 4 1 1 1 1
## [2850] 1 3 4 3 4 3 3 4 1 4 4 2 2 2 3 2 4 4 2 2 4 3
## 
## Within cluster sum of squares by cluster:
## [1] 317006.3 262863.8 365425.0 370405.2
##  (between_SS / total_SS =  54.2 %)
## 
## Available components:
## 
## [1] "cluster"      "centers"      "totss"        "withinss"     "tot.withinss"
## [6] "betweenss"    "size"         "iter"         "ifault"
  1. Use R to display the mean of each variable in each cluster, and compare these means with those that you obtained in the previous question.
summary(nhanes_train)
##       Age            Weight           Height          Pulse       
##  Min.   :16.00   Min.   : 39.30   Min.   :139.9   Min.   : 40.00  
##  1st Qu.:30.00   1st Qu.: 67.50   1st Qu.:162.2   1st Qu.: 64.00  
##  Median :44.00   Median : 79.40   Median :169.7   Median : 72.00  
##  Mean   :45.15   Mean   : 82.63   Mean   :169.5   Mean   : 72.32  
##  3rd Qu.:58.00   3rd Qu.: 94.65   3rd Qu.:176.7   3rd Qu.: 80.00  
##  Max.   :80.00   Max.   :223.00   Max.   :199.9   Max.   :122.00
nhanes_fit
## K-means clustering with 4 clusters of sizes 821, 716, 487, 847
## 
## Cluster means:
##        Age    Weight   Height    Pulse
## 1 36.82095  88.26090 174.1502 71.74178
## 2 30.04888  63.92165 165.1246 75.13966
## 3 48.06571 117.06982 176.2801 75.34292
## 4 64.30224  73.19764 164.9505 68.76033
## 
## Clustering vector:
##    [1] 4 3 2 1 3 4 1 1 1 4 2 2 1 3 3 1 2 2 2 4 1 2 4 1 4 4 4 3 2 1 1 4 2 3 2 1 4
##   [38] 4 1 1 1 4 4 1 1 4 2 4 1 4 4 4 2 3 2 4 3 4 4 4 1 2 2 2 4 2 3 1 1 2 4 4 1 4
##   [75] 3 2 2 1 2 1 4 1 3 2 3 2 2 4 4 1 2 4 2 3 3 4 1 2 2 2 4 4 4 2 2 3 4 1 4 2 2
##  [112] 2 1 3 4 2 4 1 4 2 2 4 4 4 4 1 1 3 3 1 1 1 4 3 4 2 2 3 3 4 4 4 4 4 1 3 4 1
##  [149] 2 4 1 2 1 2 4 4 1 2 1 1 1 2 3 1 3 2 2 1 2 4 1 1 1 2 1 1 2 1 2 4 1 2 1 2 2
##  [186] 4 3 4 1 2 4 1 3 1 4 1 4 2 2 4 1 4 1 1 3 4 3 4 4 2 1 1 3 3 1 3 4 2 2 3 1 2
##  [223] 2 3 1 1 2 3 4 4 2 1 3 4 1 3 3 4 4 1 2 2 1 4 4 3 2 4 4 4 2 1 4 1 2 3 4 1 4
##  [260] 1 4 3 3 4 1 4 3 3 4 2 1 2 1 3 2 1 1 3 1 4 4 4 4 4 4 3 1 2 1 2 1 3 3 2 2 2
##  [297] 4 3 3 2 1 3 2 2 1 3 4 1 2 4 4 2 2 1 2 4 2 1 4 2 3 3 1 1 1 2 3 4 2 2 2 4 1
##  [334] 2 4 4 4 2 2 3 4 1 1 4 1 4 2 2 1 4 3 4 3 2 3 2 3 2 3 1 4 4 2 1 1 2 4 2 4 2
##  [371] 4 2 1 2 1 2 4 1 2 4 1 4 1 1 4 2 1 2 3 2 4 4 4 2 4 3 1 1 2 1 1 1 2 1 4 1 4
##  [408] 4 3 2 1 1 4 1 4 3 4 4 2 4 4 4 4 1 1 2 4 3 4 1 3 2 2 2 1 2 2 3 1 2 4 2 1 1
##  [445] 2 4 2 1 2 3 4 1 4 4 1 4 3 4 2 2 1 1 1 3 3 1 1 4 1 4 1 4 1 3 1 1 3 1 3 1 2
##  [482] 1 4 2 2 4 3 4 1 1 1 2 1 2 4 2 1 1 4 2 4 3 3 1 3 1 1 1 2 4 4 1 4 2 4 4 1 3
##  [519] 1 2 2 2 1 1 4 4 2 3 2 1 4 4 4 4 1 3 1 1 2 4 3 3 4 1 2 1 3 2 1 2 4 1 1 4 1
##  [556] 3 4 2 3 4 1 1 4 4 1 1 2 4 4 4 3 2 4 3 2 1 3 2 4 1 2 2 3 1 4 2 2 4 3 3 4 2
##  [593] 1 1 4 1 4 4 4 2 2 1 2 4 4 2 4 3 2 1 4 2 1 4 4 1 2 1 4 2 2 1 2 1 1 1 3 1 4
##  [630] 4 4 1 4 1 3 4 4 3 3 1 4 3 4 2 2 3 1 1 4 1 2 3 4 2 4 1 1 2 1 4 1 2 2 2 2 4
##  [667] 1 1 2 2 2 2 3 4 3 2 4 1 3 1 3 1 1 3 3 2 2 2 4 1 4 3 1 1 4 4 2 3 4 1 3 1 2
##  [704] 3 3 3 4 4 4 4 2 2 4 4 2 2 2 2 1 4 4 4 4 1 2 2 1 4 3 4 3 3 2 1 2 4 4 1 3 1
##  [741] 2 4 3 2 2 4 2 2 4 1 2 1 1 4 4 4 4 4 1 1 2 1 1 4 2 1 2 1 2 4 1 3 3 3 2 1 3
##  [778] 1 4 1 2 1 4 4 1 4 1 3 2 2 3 2 2 4 1 4 4 1 4 3 2 1 4 1 4 2 1 4 4 2 2 3 1 3
##  [815] 3 1 3 1 2 1 4 2 1 2 1 1 4 3 1 4 4 3 4 1 2 4 4 2 1 1 1 1 2 4 1 4 2 1 1 4 2
##  [852] 3 4 1 2 1 2 1 1 2 4 3 4 2 2 4 2 4 2 4 4 3 3 1 4 1 4 4 1 2 1 4 3 4 1 1 1 1
##  [889] 3 4 1 1 3 4 2 1 3 4 1 3 4 3 4 1 1 4 4 2 4 1 1 2 1 1 1 1 2 1 2 4 2 1 3 1 2
##  [926] 2 3 4 4 2 2 1 4 2 3 4 1 1 4 4 4 1 1 4 1 4 1 2 3 1 2 2 4 4 4 1 3 1 4 1 2 2
##  [963] 2 3 2 2 2 3 1 1 4 1 4 2 1 3 2 1 3 3 2 3 4 3 1 4 2 4 2 4 2 1 2 3 2 4 3 1 3
## [1000] 4 2 1 4 3 4 1 2 3 4 1 3 2 2 4 1 1 1 1 4 2 1 3 3 4 1 4 2 3 2 3 4 2 2 3 3 2
## [1037] 3 1 2 4 3 2 2 1 2 4 3 2 4 2 2 2 2 4 3 4 1 1 1 1 1 2 1 4 4 4 2 2 2 4 1 2 2
## [1074] 1 3 4 1 3 4 4 4 3 3 2 1 3 4 2 2 2 2 4 4 3 3 1 2 1 1 2 1 4 1 4 4 1 2 3 1 1
## [1111] 1 2 4 1 3 4 3 3 2 4 3 3 3 1 1 4 2 1 1 4 4 1 2 1 2 2 1 4 3 2 3 1 1 2 4 2 1
## [1148] 4 2 4 4 4 2 2 2 4 4 1 1 3 4 2 2 1 2 3 3 2 4 1 1 3 3 4 4 3 1 3 4 2 3 2 2 4
## [1185] 4 2 4 1 3 3 1 4 1 1 3 3 4 1 1 4 1 4 4 2 1 2 1 4 2 2 3 1 1 1 1 4 1 4 4 3 1
## [1222] 1 1 2 4 4 2 4 2 2 4 3 2 2 3 4 2 3 1 1 1 4 4 2 3 3 2 3 4 4 2 2 2 4 4 2 3 3
## [1259] 3 4 4 4 1 4 2 2 2 4 4 1 4 1 1 2 1 1 4 1 1 4 4 4 4 4 2 1 4 1 2 2 2 2 2 2 2
## [1296] 2 3 1 1 3 1 3 1 4 4 4 4 1 4 4 3 2 3 1 4 1 3 2 4 4 3 1 2 1 2 4 1 4 4 3 3 3
## [1333] 4 4 2 1 3 4 4 3 4 4 4 3 1 1 4 2 3 2 1 2 4 4 1 4 3 1 2 1 4 4 4 3 4 1 4 2 1
## [1370] 1 1 4 2 4 4 1 2 4 2 3 1 2 4 4 4 4 4 2 2 4 1 4 1 1 3 2 4 1 4 4 4 1 4 2 3 2
## [1407] 4 3 1 4 3 1 4 3 1 3 2 1 4 4 2 3 1 4 3 1 1 4 4 4 4 3 4 3 3 2 2 1 4 4 4 2 1
## [1444] 3 1 2 2 4 4 4 3 4 4 2 3 1 2 2 4 1 1 1 4 2 3 2 2 1 2 2 2 2 1 4 3 1 2 2 1 4
## [1481] 4 4 3 3 2 3 1 4 1 2 2 4 3 1 2 2 1 4 3 2 4 4 3 1 4 4 4 3 1 2 4 2 1 1 4 2 4
## [1518] 3 1 4 4 2 4 3 3 4 4 4 2 4 3 1 2 1 1 1 2 4 1 1 4 1 3 2 2 3 2 4 4 1 1 1 2 1
## [1555] 3 4 4 2 1 4 3 4 4 4 2 2 4 4 1 3 1 2 3 3 2 1 4 1 1 3 4 2 3 1 1 2 1 4 2 1 4
## [1592] 4 1 2 1 2 4 2 3 1 4 1 4 4 4 1 4 4 4 1 1 1 3 3 1 4 3 3 4 1 2 1 1 4 1 1 3 4
## [1629] 1 4 1 4 1 2 2 2 1 3 4 2 1 1 4 2 1 1 4 4 1 4 1 2 1 4 3 1 1 2 4 1 1 4 3 4 1
## [1666] 4 4 1 2 1 3 2 2 2 3 4 1 2 3 3 1 2 2 1 2 1 4 4 2 1 3 4 4 4 2 3 3 2 3 3 1 1
## [1703] 3 2 4 4 1 3 2 2 2 1 3 4 4 4 3 4 3 1 1 4 3 4 3 2 1 1 2 1 4 3 4 2 4 2 1 2 3
## [1740] 1 3 3 2 2 4 1 1 4 1 1 1 4 3 4 2 1 1 1 2 4 2 4 4 2 3 1 3 1 2 2 1 4 2 2 2 2
## [1777] 4 3 4 3 4 1 2 1 1 4 1 2 1 4 1 4 1 1 1 2 3 2 4 1 2 4 4 4 4 2 4 3 4 4 4 3 1
## [1814] 4 2 1 1 2 2 1 4 2 2 4 3 4 1 4 4 4 4 4 1 4 1 2 2 4 1 4 3 1 3 1 2 4 2 2 1 2
## [1851] 3 1 4 4 1 4 4 4 4 2 1 3 4 4 1 4 1 2 1 2 1 4 4 3 4 1 2 4 4 4 2 2 1 4 1 1 1
## [1888] 1 2 2 1 4 1 3 2 4 3 4 3 1 1 4 1 4 4 1 2 2 1 3 2 3 2 3 4 1 4 2 4 3 2 1 2 3
## [1925] 1 1 3 4 3 1 4 3 3 4 4 2 4 3 1 1 2 2 3 1 3 2 3 2 3 3 4 4 2 1 1 1 2 4 4 4 1
## [1962] 4 1 2 4 1 2 4 4 4 2 2 2 1 1 4 4 2 4 3 2 1 1 1 4 3 2 2 4 4 2 4 2 1 1 3 1 2
## [1999] 2 1 2 2 4 3 1 1 3 3 1 1 1 4 3 4 2 1 4 1 2 2 1 2 4 1 4 3 3 1 3 2 2 3 1 3 2
## [2036] 4 4 2 1 1 4 1 1 1 1 2 3 3 2 2 1 2 1 3 2 2 3 3 2 2 3 4 4 2 1 3 2 1 3 1 1 3
## [2073] 2 2 1 2 3 3 4 3 2 4 4 2 1 3 3 3 2 4 4 1 2 1 2 3 1 4 3 1 3 1 4 4 1 4 2 1 1
## [2110] 4 2 1 1 2 4 2 1 3 3 2 3 2 2 1 2 1 3 4 4 1 2 4 1 4 2 1 1 1 2 2 4 2 4 2 4 2
## [2147] 2 3 2 1 3 4 3 1 2 2 1 4 4 1 2 3 3 4 1 1 4 4 3 1 1 2 3 3 2 3 4 4 3 4 4 4 1
## [2184] 1 1 1 2 4 4 3 3 2 1 1 4 3 1 2 4 2 4 3 3 1 2 4 4 1 4 3 2 3 1 1 3 1 3 2 2 3
## [2221] 3 2 4 3 2 2 3 2 3 1 1 1 1 2 1 1 3 4 1 1 4 4 3 3 2 4 4 2 2 2 4 4 2 2 1 4 1
## [2258] 2 3 2 2 3 4 4 1 4 3 3 4 2 3 3 2 4 1 1 2 1 1 2 4 2 1 3 1 2 3 2 3 1 3 4 3 1
## [2295] 1 2 4 1 2 4 4 2 4 3 1 1 2 4 1 2 2 4 2 2 2 4 2 3 1 3 4 4 2 1 4 4 1 3 4 2 4
## [2332] 3 1 4 3 1 4 4 4 3 2 2 4 4 1 1 2 1 2 1 4 2 2 1 4 4 4 1 4 1 4 4 3 2 4 2 4 4
## [2369] 3 2 1 1 4 1 3 3 3 1 4 1 2 4 3 4 1 3 4 4 4 2 2 2 1 1 3 3 1 4 4 4 1 1 2 4 2
## [2406] 2 2 2 1 4 2 1 4 2 1 1 1 1 4 1 1 1 1 2 2 2 4 2 3 3 3 3 2 4 2 2 1 1 1 2 4 2
## [2443] 4 1 4 1 4 4 1 2 2 4 1 3 1 4 2 4 4 2 2 3 1 2 2 1 3 1 1 1 2 2 3 3 2 4 1 2 1
## [2480] 1 1 3 2 1 1 1 2 1 3 2 3 2 1 4 4 3 1 4 1 4 2 3 1 3 2 1 2 1 2 3 2 1 4 1 3 4
## [2517] 4 4 1 4 4 4 2 3 1 4 4 2 2 1 1 2 4 3 3 2 1 2 1 3 4 2 1 4 2 4 1 1 1 1 2 4 2
## [2554] 4 4 4 2 1 4 2 3 2 4 2 2 3 3 2 3 1 3 3 3 2 1 4 2 4 1 1 4 1 3 1 4 4 3 3 3 2
## [2591] 4 4 1 4 4 3 4 1 1 4 1 4 1 1 2 2 4 4 1 4 1 1 3 4 2 1 1 1 2 2 4 1 4 1 4 1 1
## [2628] 1 4 3 4 3 1 2 1 4 1 2 4 1 2 4 4 1 4 3 4 2 3 4 1 2 1 1 1 3 2 4 1 4 4 4 2 2
## [2665] 2 3 4 1 3 3 1 2 4 2 4 2 2 3 1 1 3 4 1 4 4 1 2 4 2 4 4 1 3 1 3 4 3 2 2 2 4
## [2702] 1 3 2 4 4 4 3 4 1 4 4 1 1 3 1 1 2 4 2 1 4 4 4 4 4 3 2 1 2 4 3 3 2 1 4 4 3
## [2739] 1 4 1 1 2 3 1 3 1 3 1 3 3 3 4 1 4 1 2 1 2 4 4 4 4 2 2 2 4 4 4 3 1 4 1 3 2
## [2776] 4 2 2 1 1 4 1 1 1 2 4 1 1 1 4 4 2 4 3 4 3 4 4 1 2 4 1 2 2 4 3 3 1 4 1 1 3
## [2813] 2 2 1 4 4 2 2 2 4 1 1 4 2 1 3 3 1 1 4 2 3 1 2 4 1 1 4 1 1 4 4 3 4 1 1 1 1
## [2850] 1 3 4 3 4 3 3 4 1 4 4 2 2 2 3 2 4 4 2 2 4 3
## 
## Within cluster sum of squares by cluster:
## [1] 317006.3 262863.8 365425.0 370405.2
##  (between_SS / total_SS =  54.2 %)
## 
## Available components:
## 
## [1] "cluster"      "centers"      "totss"        "withinss"     "tot.withinss"
## [6] "betweenss"    "size"         "iter"         "ifault"

The means of the total table versus the kmeans are clearly related; clusters 2 and 3 seem to be the closest.

  1. Determine which cluster the data in row 2000 was placed in.
nhanes_fit$cluster[2000]
## [1] 1