Exercise 2

##Libraries that will be needed/used

library(funModeling) 
## Loading required package: Hmisc
## Loading required package: lattice
## Loading required package: survival
## Loading required package: Formula
## Loading required package: ggplot2
## 
## Attaching package: 'Hmisc'
## The following objects are masked from 'package:base':
## 
##     format.pval, units
## funModeling v.1.9.4 :)
## Examples and tutorials at livebook.datascienceheroes.com
##  / Now in Spanish: librovivodecienciadedatos.ai
library(tidyverse) 
## ── Attaching packages ─────────────────────────────────────── tidyverse 1.3.1 ──
## ✓ tibble  3.1.6     ✓ dplyr   1.0.8
## ✓ tidyr   1.2.0     ✓ stringr 1.4.0
## ✓ readr   2.1.2     ✓ forcats 0.5.1
## ✓ purrr   0.3.4
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## x dplyr::filter()    masks stats::filter()
## x dplyr::lag()       masks stats::lag()
## x dplyr::src()       masks Hmisc::src()
## x dplyr::summarize() masks Hmisc::summarize()
library(Hmisc)

Explaination : Those library are used for explorartory data analysis

Importing the dataset.

library (readr)
mydata <- read_csv("bike_buyers.csv")
## Rows: 1000 Columns: 13
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (8): Marital Status, Gender, Education, Occupation, Home Owner, Commute ...
## dbl (5): ID, Income, Children, Cars, Age
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
mydata
## # A tibble: 1,000 × 13
##       ID `Marital Status` Gender Income Children Education           Occupation 
##    <dbl> <chr>            <chr>   <dbl>    <dbl> <chr>               <chr>      
##  1 12496 Married          Female  40000        1 Bachelors           Skilled Ma…
##  2 24107 Married          Male    30000        3 Partial College     Clerical   
##  3 14177 Married          Male    80000        5 Partial College     Profession…
##  4 24381 Single           <NA>    70000        0 Bachelors           Profession…
##  5 25597 Single           Male    30000        0 Bachelors           Clerical   
##  6 13507 Married          Female  10000        2 Partial College     Manual     
##  7 27974 Single           Male   160000        2 High School         Management 
##  8 19364 Married          Male    40000        1 Bachelors           Skilled Ma…
##  9 22155 <NA>             Male    20000        2 Partial High School Clerical   
## 10 19280 Married          Male       NA        2 Partial College     Manual     
## # … with 990 more rows, and 6 more variables: `Home Owner` <chr>, Cars <dbl>,
## #   `Commute Distance` <chr>, Region <chr>, Age <dbl>, `Purchased Bike` <chr>

Explaination : The function used above is to import and show us the dataset that has been given.

The dim() function

dim(mydata)
## [1] 1000   13

Explaination: The dim() function is used to see the data’s dimension.

str() function

str(mydata)
## spec_tbl_df [1,000 × 13] (S3: spec_tbl_df/tbl_df/tbl/data.frame)
##  $ ID              : num [1:1000] 12496 24107 14177 24381 25597 ...
##  $ Marital Status  : chr [1:1000] "Married" "Married" "Married" "Single" ...
##  $ Gender          : chr [1:1000] "Female" "Male" "Male" NA ...
##  $ Income          : num [1:1000] 40000 30000 80000 70000 30000 10000 160000 40000 20000 NA ...
##  $ Children        : num [1:1000] 1 3 5 0 0 2 2 1 2 2 ...
##  $ Education       : chr [1:1000] "Bachelors" "Partial College" "Partial College" "Bachelors" ...
##  $ Occupation      : chr [1:1000] "Skilled Manual" "Clerical" "Professional" "Professional" ...
##  $ Home Owner      : chr [1:1000] "Yes" "Yes" "No" "Yes" ...
##  $ Cars            : num [1:1000] 0 1 2 1 0 0 4 0 2 1 ...
##  $ Commute Distance: chr [1:1000] "0-1 Miles" "0-1 Miles" "2-5 Miles" "5-10 Miles" ...
##  $ Region          : chr [1:1000] "Europe" "Europe" "Europe" "Pacific" ...
##  $ Age             : num [1:1000] 42 43 60 41 36 50 33 43 58 NA ...
##  $ Purchased Bike  : chr [1:1000] "No" "No" "No" "Yes" ...
##  - attr(*, "spec")=
##   .. cols(
##   ..   ID = col_double(),
##   ..   `Marital Status` = col_character(),
##   ..   Gender = col_character(),
##   ..   Income = col_double(),
##   ..   Children = col_double(),
##   ..   Education = col_character(),
##   ..   Occupation = col_character(),
##   ..   `Home Owner` = col_character(),
##   ..   Cars = col_double(),
##   ..   `Commute Distance` = col_character(),
##   ..   Region = col_character(),
##   ..   Age = col_double(),
##   ..   `Purchased Bike` = col_character()
##   .. )
##  - attr(*, "problems")=<externalptr>

Explaination : This function allows us to see the string type of the dataset, and each variable has it’s own string.

describe() function using Hmisc library

library(Hmisc)
describe(mydata)
## mydata 
## 
##  13  Variables      1000  Observations
## --------------------------------------------------------------------------------
## ID 
##        n  missing distinct     Info     Mean      Gmd      .05      .10 
##     1000        0     1000        1    19966     6176    11781    12627 
##      .25      .50      .75      .90      .95 
##    15291    19744    24471    27544    28413 
## 
## lowest : 11000 11047 11061 11090 11116, highest: 29337 29355 29380 29424 29447
## --------------------------------------------------------------------------------
## Marital Status 
##        n  missing distinct 
##      993        7        2 
##                           
## Value      Married  Single
## Frequency      535     458
## Proportion   0.539   0.461
## --------------------------------------------------------------------------------
## Gender 
##        n  missing distinct 
##      989       11        2 
##                         
## Value      Female   Male
## Frequency     489    500
## Proportion  0.494  0.506
## --------------------------------------------------------------------------------
## Income 
##        n  missing distinct     Info     Mean      Gmd      .05      .10 
##      994        6       16    0.986    56268    34273    10000    20000 
##      .25      .50      .75      .90      .95 
##    30000    60000    70000   100000   120000 
## 
## lowest :  10000  20000  30000  40000  50000, highest: 120000 130000 150000 160000 170000
##                                                                          
## Value       10000  20000  30000  40000  50000  60000  70000  80000  90000
## Frequency      73     74    134    153     40    165    123     90     38
## Proportion  0.073  0.074  0.135  0.154  0.040  0.166  0.124  0.091  0.038
##                                                            
## Value      100000 110000 120000 130000 150000 160000 170000
## Frequency      29     16     17     32      4      3      3
## Proportion  0.029  0.016  0.017  0.032  0.004  0.003  0.003
## --------------------------------------------------------------------------------
## Children 
##        n  missing distinct     Info     Mean      Gmd 
##      992        8        6     0.96     1.91    1.827 
## 
## lowest : 0 1 2 3 4, highest: 1 2 3 4 5
##                                               
## Value          0     1     2     3     4     5
## Frequency    274   169   209   133   126    81
## Proportion 0.276 0.170 0.211 0.134 0.127 0.082
## --------------------------------------------------------------------------------
## Education 
##        n  missing distinct 
##     1000        0        5 
## 
## lowest : Bachelors           Graduate Degree     High School         Partial College     Partial High School
## highest: Bachelors           Graduate Degree     High School         Partial College     Partial High School
##                                                                       
## Value                Bachelors     Graduate Degree         High School
## Frequency                  306                 174                 179
## Proportion               0.306               0.174               0.179
##                                                   
## Value          Partial College Partial High School
## Frequency                  265                  76
## Proportion               0.265               0.076
## --------------------------------------------------------------------------------
## Occupation 
##        n  missing distinct 
##     1000        0        5 
## 
## lowest : Clerical       Management     Manual         Professional   Skilled Manual
## highest: Clerical       Management     Manual         Professional   Skilled Manual
##                                                                       
## Value            Clerical     Management         Manual   Professional
## Frequency             177            173            119            276
## Proportion          0.177          0.173          0.119          0.276
##                          
## Value      Skilled Manual
## Frequency             255
## Proportion          0.255
## --------------------------------------------------------------------------------
## Home Owner 
##        n  missing distinct 
##      996        4        2 
##                       
## Value         No   Yes
## Frequency    314   682
## Proportion 0.315 0.685
## --------------------------------------------------------------------------------
## Cars 
##        n  missing distinct     Info     Mean      Gmd 
##      991        9        5    0.925    1.455    1.226 
## 
## lowest : 0 1 2 3 4, highest: 0 1 2 3 4
##                                         
## Value          0     1     2     3     4
## Frequency    238   267   342    85    59
## Proportion 0.240 0.269 0.345 0.086 0.060
## --------------------------------------------------------------------------------
## Commute Distance 
##        n  missing distinct 
##     1000        0        5 
## 
## lowest : 0-1 Miles  1-2 Miles  10+ Miles  2-5 Miles  5-10 Miles
## highest: 0-1 Miles  1-2 Miles  10+ Miles  2-5 Miles  5-10 Miles
##                                                                  
## Value       0-1 Miles  1-2 Miles  10+ Miles  2-5 Miles 5-10 Miles
## Frequency         366        169        111        162        192
## Proportion      0.366      0.169      0.111      0.162      0.192
## --------------------------------------------------------------------------------
## Region 
##        n  missing distinct 
##     1000        0        3 
##                                                     
## Value             Europe North America       Pacific
## Frequency            300           508           192
## Proportion         0.300         0.508         0.192
## --------------------------------------------------------------------------------
## Age 
##        n  missing distinct     Info     Mean      Gmd      .05      .10 
##      992        8       53    0.999    44.18    12.85    28.00    30.00 
##      .25      .50      .75      .90      .95 
##    35.00    43.00    52.00    60.90    65.45 
## 
## lowest : 25 26 27 28 29, highest: 73 74 78 80 89
## --------------------------------------------------------------------------------
## Purchased Bike 
##        n  missing distinct 
##     1000        0        2 
##                       
## Value         No   Yes
## Frequency    519   481
## Proportion 0.519 0.481
## --------------------------------------------------------------------------------

status() function

status(mydata)
##                          variable q_zeros p_zeros q_na  p_na q_inf p_inf
## ID                             ID       0   0.000    0 0.000     0     0
## Marital Status     Marital Status       0   0.000    7 0.007     0     0
## Gender                     Gender       0   0.000   11 0.011     0     0
## Income                     Income       0   0.000    6 0.006     0     0
## Children                 Children     274   0.274    8 0.008     0     0
## Education               Education       0   0.000    0 0.000     0     0
## Occupation             Occupation       0   0.000    0 0.000     0     0
## Home Owner             Home Owner       0   0.000    4 0.004     0     0
## Cars                         Cars     238   0.238    9 0.009     0     0
## Commute Distance Commute Distance       0   0.000    0 0.000     0     0
## Region                     Region       0   0.000    0 0.000     0     0
## Age                           Age       0   0.000    8 0.008     0     0
## Purchased Bike     Purchased Bike       0   0.000    0 0.000     0     0
##                       type unique
## ID                 numeric   1000
## Marital Status   character      2
## Gender           character      2
## Income             numeric     16
## Children           numeric      6
## Education        character      5
## Occupation       character      5
## Home Owner       character      2
## Cars               numeric      5
## Commute Distance character      5
## Region           character      3
## Age                numeric     53
## Purchased Bike   character      2

Explaination : This function will show the data types inside the dataset, including missing values in the dataset. By using status I can tell that : - There are 1000 unique intergers in the ID Variable - The variable Children and Cars has the most zeros out of all - The Gender variable has 11 missing interger values.

freq(mydata)
## Warning: `guides(<scale> = FALSE)` is deprecated. Please use `guides(<scale> =
## "none")` instead.
##   Marital.Status frequency percentage cumulative_perc
## 1        Married       535       53.5            53.5
## 2         Single       458       45.8            99.3
## 3           <NA>         7        0.7           100.0
## Warning: `guides(<scale> = FALSE)` is deprecated. Please use `guides(<scale> =
## "none")` instead.

##   Gender frequency percentage cumulative_perc
## 1   Male       500       50.0            50.0
## 2 Female       489       48.9            98.9
## 3   <NA>        11        1.1           100.0
## Warning: `guides(<scale> = FALSE)` is deprecated. Please use `guides(<scale> =
## "none")` instead.

##             Education frequency percentage cumulative_perc
## 1           Bachelors       306       30.6            30.6
## 2     Partial College       265       26.5            57.1
## 3         High School       179       17.9            75.0
## 4     Graduate Degree       174       17.4            92.4
## 5 Partial High School        76        7.6           100.0
## Warning: `guides(<scale> = FALSE)` is deprecated. Please use `guides(<scale> =
## "none")` instead.

##       Occupation frequency percentage cumulative_perc
## 1   Professional       276       27.6            27.6
## 2 Skilled Manual       255       25.5            53.1
## 3       Clerical       177       17.7            70.8
## 4     Management       173       17.3            88.1
## 5         Manual       119       11.9           100.0
## Warning: `guides(<scale> = FALSE)` is deprecated. Please use `guides(<scale> =
## "none")` instead.

##   Home.Owner frequency percentage cumulative_perc
## 1        Yes       682       68.2            68.2
## 2         No       314       31.4            99.6
## 3       <NA>         4        0.4           100.0
## Warning: `guides(<scale> = FALSE)` is deprecated. Please use `guides(<scale> =
## "none")` instead.

##   Commute.Distance frequency percentage cumulative_perc
## 1        0-1 Miles       366       36.6            36.6
## 2       5-10 Miles       192       19.2            55.8
## 3        1-2 Miles       169       16.9            72.7
## 4        2-5 Miles       162       16.2            88.9
## 5        10+ Miles       111       11.1           100.0
## Warning: `guides(<scale> = FALSE)` is deprecated. Please use `guides(<scale> =
## "none")` instead.

##          Region frequency percentage cumulative_perc
## 1 North America       508       50.8            50.8
## 2        Europe       300       30.0            80.8
## 3       Pacific       192       19.2           100.0
## Warning: `guides(<scale> = FALSE)` is deprecated. Please use `guides(<scale> =
## "none")` instead.

##   Purchased.Bike frequency percentage cumulative_perc
## 1             No       519       51.9            51.9
## 2            Yes       481       48.1           100.0
## [1] "Variables processed: Marital.Status, Gender, Education, Occupation, Home.Owner, Commute.Distance, Region, Purchased.Bike"

Explaination : This function shows us the percentage or frequency of each variables, including the dataframes too. Some of the data that i’ve read and found is : - The frequency of Marital Status are mostly Married - The most gender that is shown in the data is Male - The most education that is being recorded in the data are Bachelors.

The plot_num() Function

plot_num(mydata)
## Warning: `guides(<scale> = FALSE)` is deprecated. Please use `guides(<scale> =
## "none")` instead.

## qqPlot() Function

library(car)
## Loading required package: carData
## 
## Attaching package: 'car'
## The following object is masked from 'package:dplyr':
## 
##     recode
## The following object is masked from 'package:purrr':
## 
##     some
qqPlot(mydata$Income)

## [1] 13 44
outlierIndex <- which(mydata$Income > 100)
rownames(mydata)[outlierIndex]
##   [1] "1"    "2"    "3"    "4"    "5"    "6"    "7"    "8"    "9"    "11"  
##  [11] "12"   "13"   "14"   "15"   "16"   "17"   "18"   "19"   "20"   "21"  
##  [21] "22"   "23"   "24"   "25"   "26"   "27"   "28"   "29"   "30"   "31"  
##  [31] "32"   "33"   "34"   "35"   "36"   "37"   "38"   "39"   "40"   "41"  
##  [41] "42"   "43"   "44"   "45"   "46"   "47"   "48"   "49"   "50"   "51"  
##  [51] "52"   "53"   "54"   "55"   "56"   "57"   "58"   "59"   "60"   "61"  
##  [61] "62"   "63"   "64"   "65"   "66"   "67"   "68"   "69"   "70"   "71"  
##  [71] "72"   "73"   "74"   "75"   "76"   "77"   "78"   "79"   "80"   "81"  
##  [81] "82"   "83"   "84"   "85"   "86"   "87"   "88"   "89"   "90"   "91"  
##  [91] "92"   "93"   "94"   "95"   "96"   "97"   "98"   "99"   "100"  "101" 
## [101] "102"  "103"  "104"  "105"  "106"  "107"  "108"  "109"  "110"  "112" 
## [111] "113"  "114"  "115"  "116"  "117"  "118"  "119"  "120"  "121"  "122" 
## [121] "123"  "124"  "125"  "126"  "127"  "128"  "129"  "130"  "131"  "132" 
## [131] "133"  "134"  "135"  "136"  "137"  "138"  "139"  "140"  "141"  "142" 
## [141] "143"  "144"  "145"  "146"  "147"  "148"  "149"  "150"  "151"  "152" 
## [151] "153"  "154"  "155"  "156"  "157"  "158"  "159"  "160"  "161"  "162" 
## [161] "163"  "164"  "165"  "166"  "167"  "168"  "169"  "170"  "171"  "172" 
## [171] "173"  "174"  "175"  "176"  "177"  "178"  "179"  "180"  "181"  "182" 
## [181] "183"  "184"  "185"  "186"  "187"  "188"  "189"  "190"  "191"  "193" 
## [191] "194"  "195"  "196"  "197"  "198"  "199"  "200"  "201"  "202"  "203" 
## [201] "204"  "205"  "206"  "207"  "208"  "209"  "210"  "211"  "212"  "213" 
## [211] "214"  "215"  "216"  "217"  "218"  "219"  "220"  "221"  "222"  "223" 
## [221] "224"  "225"  "226"  "227"  "228"  "229"  "230"  "231"  "232"  "233" 
## [231] "234"  "235"  "236"  "237"  "238"  "239"  "240"  "241"  "242"  "243" 
## [241] "244"  "245"  "246"  "247"  "248"  "249"  "250"  "251"  "252"  "253" 
## [251] "254"  "255"  "256"  "257"  "258"  "259"  "260"  "261"  "262"  "263" 
## [261] "264"  "265"  "266"  "267"  "268"  "269"  "270"  "271"  "272"  "273" 
## [271] "274"  "275"  "276"  "277"  "278"  "279"  "280"  "281"  "282"  "283" 
## [281] "284"  "285"  "286"  "287"  "288"  "289"  "290"  "291"  "292"  "293" 
## [291] "294"  "295"  "296"  "297"  "298"  "299"  "300"  "301"  "303"  "304" 
## [301] "305"  "306"  "307"  "308"  "309"  "310"  "311"  "312"  "313"  "314" 
## [311] "315"  "316"  "317"  "318"  "319"  "320"  "321"  "322"  "323"  "324" 
## [321] "325"  "326"  "327"  "328"  "329"  "330"  "331"  "332"  "333"  "334" 
## [331] "335"  "336"  "337"  "338"  "339"  "340"  "341"  "342"  "343"  "344" 
## [341] "345"  "346"  "347"  "348"  "349"  "350"  "351"  "352"  "353"  "354" 
## [351] "355"  "356"  "357"  "358"  "359"  "360"  "361"  "362"  "363"  "364" 
## [361] "365"  "366"  "367"  "368"  "369"  "370"  "371"  "372"  "373"  "374" 
## [371] "375"  "376"  "377"  "378"  "379"  "380"  "381"  "382"  "383"  "384" 
## [381] "385"  "386"  "387"  "388"  "389"  "390"  "391"  "392"  "393"  "394" 
## [391] "395"  "396"  "397"  "398"  "399"  "400"  "401"  "402"  "403"  "404" 
## [401] "405"  "406"  "407"  "408"  "409"  "410"  "411"  "412"  "413"  "414" 
## [411] "415"  "416"  "417"  "418"  "419"  "420"  "421"  "422"  "423"  "424" 
## [421] "425"  "426"  "427"  "428"  "429"  "430"  "431"  "432"  "433"  "434" 
## [431] "435"  "436"  "437"  "438"  "439"  "440"  "441"  "443"  "444"  "445" 
## [441] "446"  "447"  "448"  "449"  "450"  "451"  "452"  "453"  "454"  "455" 
## [451] "456"  "457"  "458"  "459"  "460"  "461"  "462"  "463"  "464"  "465" 
## [461] "466"  "467"  "468"  "469"  "470"  "471"  "472"  "473"  "474"  "475" 
## [471] "476"  "477"  "478"  "479"  "480"  "481"  "482"  "483"  "484"  "485" 
## [481] "486"  "487"  "488"  "489"  "490"  "491"  "492"  "493"  "494"  "495" 
## [491] "496"  "497"  "498"  "499"  "500"  "501"  "502"  "503"  "504"  "505" 
## [501] "506"  "507"  "508"  "509"  "511"  "512"  "513"  "514"  "515"  "516" 
## [511] "517"  "518"  "519"  "520"  "521"  "522"  "523"  "524"  "525"  "526" 
## [521] "527"  "528"  "529"  "530"  "531"  "532"  "533"  "534"  "535"  "536" 
## [531] "537"  "538"  "539"  "540"  "541"  "542"  "543"  "544"  "545"  "546" 
## [541] "547"  "548"  "549"  "550"  "551"  "552"  "553"  "554"  "555"  "556" 
## [551] "557"  "558"  "559"  "560"  "561"  "562"  "563"  "564"  "565"  "566" 
## [561] "567"  "568"  "569"  "570"  "571"  "572"  "573"  "574"  "575"  "576" 
## [571] "577"  "578"  "579"  "580"  "581"  "582"  "583"  "584"  "585"  "586" 
## [581] "587"  "588"  "589"  "590"  "591"  "592"  "593"  "594"  "595"  "596" 
## [591] "597"  "598"  "599"  "600"  "601"  "602"  "603"  "604"  "605"  "606" 
## [601] "607"  "608"  "609"  "610"  "611"  "612"  "613"  "614"  "615"  "616" 
## [611] "617"  "618"  "619"  "620"  "621"  "622"  "623"  "624"  "625"  "626" 
## [621] "627"  "628"  "629"  "630"  "631"  "632"  "633"  "634"  "635"  "636" 
## [631] "637"  "638"  "639"  "640"  "641"  "642"  "643"  "644"  "645"  "646" 
## [641] "647"  "648"  "649"  "650"  "651"  "652"  "653"  "654"  "655"  "656" 
## [651] "657"  "658"  "659"  "660"  "661"  "662"  "663"  "664"  "665"  "666" 
## [661] "667"  "668"  "669"  "670"  "671"  "672"  "673"  "674"  "675"  "676" 
## [671] "677"  "678"  "679"  "680"  "681"  "682"  "683"  "684"  "685"  "686" 
## [681] "687"  "688"  "689"  "690"  "691"  "692"  "693"  "694"  "695"  "696" 
## [691] "697"  "698"  "699"  "700"  "701"  "702"  "703"  "704"  "705"  "706" 
## [701] "707"  "708"  "709"  "710"  "711"  "712"  "713"  "714"  "715"  "716" 
## [711] "717"  "718"  "719"  "720"  "721"  "722"  "723"  "724"  "725"  "726" 
## [721] "727"  "728"  "729"  "730"  "731"  "732"  "733"  "734"  "735"  "736" 
## [731] "737"  "738"  "739"  "740"  "741"  "742"  "743"  "744"  "745"  "746" 
## [741] "747"  "748"  "749"  "750"  "751"  "752"  "753"  "754"  "755"  "756" 
## [751] "757"  "758"  "759"  "760"  "761"  "762"  "763"  "764"  "765"  "766" 
## [761] "767"  "768"  "769"  "770"  "771"  "772"  "773"  "774"  "775"  "776" 
## [771] "777"  "778"  "779"  "780"  "781"  "782"  "783"  "784"  "785"  "786" 
## [781] "787"  "788"  "789"  "790"  "791"  "792"  "793"  "794"  "795"  "796" 
## [791] "797"  "798"  "799"  "800"  "801"  "802"  "803"  "804"  "805"  "806" 
## [801] "807"  "808"  "809"  "810"  "811"  "812"  "813"  "814"  "815"  "816" 
## [811] "817"  "818"  "819"  "820"  "821"  "822"  "823"  "824"  "825"  "826" 
## [821] "827"  "828"  "829"  "830"  "831"  "832"  "833"  "834"  "835"  "836" 
## [831] "837"  "838"  "839"  "840"  "841"  "842"  "843"  "844"  "845"  "846" 
## [841] "847"  "848"  "849"  "850"  "851"  "852"  "853"  "854"  "855"  "856" 
## [851] "857"  "858"  "859"  "860"  "861"  "862"  "863"  "864"  "865"  "866" 
## [861] "867"  "868"  "869"  "870"  "871"  "872"  "873"  "874"  "875"  "876" 
## [871] "877"  "878"  "879"  "880"  "881"  "882"  "883"  "884"  "885"  "886" 
## [881] "887"  "888"  "889"  "890"  "891"  "892"  "893"  "894"  "895"  "896" 
## [891] "897"  "898"  "899"  "900"  "901"  "902"  "903"  "904"  "905"  "906" 
## [901] "907"  "908"  "909"  "910"  "911"  "912"  "913"  "914"  "915"  "916" 
## [911] "917"  "918"  "919"  "920"  "921"  "922"  "923"  "924"  "925"  "926" 
## [921] "927"  "928"  "929"  "930"  "931"  "932"  "933"  "934"  "935"  "936" 
## [931] "937"  "938"  "939"  "940"  "941"  "942"  "943"  "944"  "945"  "946" 
## [941] "947"  "948"  "949"  "950"  "951"  "952"  "953"  "954"  "955"  "956" 
## [951] "957"  "958"  "959"  "960"  "961"  "962"  "963"  "964"  "965"  "966" 
## [961] "967"  "968"  "969"  "970"  "971"  "972"  "973"  "974"  "975"  "976" 
## [971] "977"  "978"  "979"  "980"  "981"  "982"  "983"  "984"  "985"  "986" 
## [981] "987"  "988"  "989"  "990"  "991"  "992"  "993"  "994"  "995"  "996" 
## [991] "997"  "998"  "999"  "1000"