Introduction

In this tutorial, we will try to understand some fundamental control structures used in statistical programming. In the beginning, we will separately analyze different control structures.

Part 1: If-Else Statements

General Construction:

if (CONDITION) {
    ACTION
}
if (CONDITION) {
    ACTION 1
} else {
    ACTION 2
}
ifelse(CONDITION,ACTION1,ACTION2)

Chunk 1: Illustration of If

Question: What does the following code do?

x = 3
if(x > 0){
  print(log(x))
}

x = -3
if(x > 0){
  print(log(x))
}

Chunk 2: Illustration of If-Else

x = 3
if(x > 0){
  print(log(x))
} else{
  message("Unable to Take Logarithm")
}

x = -3
if(x > 0){
  print(log(x))
} else {
  message("Unable to Take Logarithm")
}

Excercise 1

Write code that takes numbers a and b as input and prints ‘a is greater than b’ if a>b, otherwise prints ‘a is not greater than b’.

a = 10
b = 8
if(a > b){
  print('a is greater than b')
} else{
  print('a is not greater than b')
}
## [1] "a is greater than b"

Chunk 3: Potential Problem of If-Else Statements

Question: The following code will fail when x equals to what?

x = 10
if(x > 0){
  print(log(x))
}

if(x > 0){
  print(log(x))
} else{
  message("Unable to Take Logarithm")
}

Chunk 4: Fixing Potential Problem in Chunk 3

Question: What do you think we can do to get rid of the problem?

x=BLANK
if(is.numeric(x)){
  if(x > 0){
    print(log(x))
  } else{
    message("Unable to Take Logarithm")
  }
} else{
  message("Please Input Numbers")
}

Excercise 2

Redo Excercise 1 but check the data types before doing the comparison. Hint: && (and) and || (or) can be used to combine multiple logical expressions. Please don’t use & and | in an if statement: these are vectorized operations.

a = '10'
b = 8
if (is.numeric(a) && is.numeric(b)){
  if (a>b){
    print('a is greater than b')
  } else {
    print('a is not greater than b')
  }
} else {
  message("Please Input Numbers")
}
## Please Input Numbers

Chunk 5: Vectorized Version with ifelse()

Question: What’s the difference between if esle and ifelse?

x=c(-1,3,200)
#print(log(x))

y1 =  if(x > 0){
        log(x)
      } else{
        NA
      }
print(y1)
y2 = ifelse(x>0,log(x),NA)
print(y2)

Chunk 6: Nested ifelse() Statements

x=rnorm(1000,mean=0,sd=1)
y=ifelse(abs(x)<1,"Within 1 SD",ifelse(abs(x)>2,"Far Far Away","Between 1 and 2 SD"))
y.fct=factor(y,levels=c("Within 1 SD","Between 1 and 2 SD","Far Far Away"))
ggplot() +
  geom_bar(aes(x=y.fct),fill="lightskyblue1") +
  theme_minimal()

Excercise 3

Please use ifelse() function to create a new column WageLevel with lwage column of the Wages dataset from Ecdat.

  • If the lwage is greater than \(7.0\), the corresponding value in the final vector is High Wage.
  • If lwage is lower than \(6.4\), the value is Low Wage.
  • For all the other cases, the values are Normal.
Wages %>%
  mutate(WageLevel=ifelse(lwage>7.0, "High Wage",ifelse(lwage<6.4,"Low","Normal")))
##      exp wks bluecol ind south smsa married    sex union ed black   lwage
## 1      3  32      no   0   yes   no     yes   male    no  9    no 5.56068
## 2      4  43      no   0   yes   no     yes   male    no  9    no 5.72031
## 3      5  40      no   0   yes   no     yes   male    no  9    no 5.99645
## 4      6  39      no   0   yes   no     yes   male    no  9    no 5.99645
## 5      7  42      no   1   yes   no     yes   male    no  9    no 6.06146
## 6      8  35      no   1   yes   no     yes   male    no  9    no 6.17379
## 7      9  32      no   1   yes   no     yes   male    no  9    no 6.24417
## 8     30  34     yes   0    no   no     yes   male    no 11    no 6.16331
## 9     31  27     yes   0    no   no     yes   male    no 11    no 6.21461
## 10    32  33     yes   1    no   no     yes   male   yes 11    no 6.26340
## 11    33  30     yes   1    no   no     yes   male    no 11    no 6.54391
## 12    34  30     yes   1    no   no     yes   male    no 11    no 6.69703
## 13    35  37     yes   1    no   no     yes   male    no 11    no 6.79122
## 14    36  30     yes   1    no   no     yes   male    no 11    no 6.81564
## 15     6  50     yes   1    no   no     yes   male   yes 12    no 5.65249
## 16     7  51     yes   1    no   no     yes   male   yes 12    no 6.43615
## 17     8  50     yes   1    no   no     yes   male   yes 12    no 6.54822
## 18     9  52     yes   1    no   no     yes   male   yes 12    no 6.60259
## 19    10  52     yes   1    no   no     yes   male   yes 12    no 6.69580
## 20    11  52     yes   1    no   no      no   male   yes 12    no 6.77878
## 21    12  46     yes   1    no   no      no   male   yes 12    no 6.86066
## 22    31  52     yes   0    no  yes      no female    no 10   yes 6.15698
## 23    32  46     yes   0    no  yes      no female    no 10   yes 6.23832
## 24    33  46     yes   0    no  yes      no female    no 10   yes 6.30079
## 25    34  49     yes   0    no  yes      no female    no 10   yes 6.35957
## 26    35  44     yes   0    no  yes      no female    no 10   yes 6.46925
## 27    36  52     yes   0    no  yes      no female    no 10   yes 6.56244
## 28    37  46     yes   0    no  yes      no female    no 10   yes 6.62141
## 29    10  50     yes   0    no   no     yes   male   yes 16    no 6.43775
## 30    11  46     yes   0    no   no     yes   male   yes 16    no 6.62007
## 31    12  40     yes   0    no   no     yes   male   yes 16    no 6.63332
## 32    13  50      no   0    no   no     yes   male    no 16    no 6.98286
## 33    14  47     yes   0    no  yes     yes   male    no 16    no 7.04752
## 34    15  47      no   0    no   no     yes   male    no 16    no 7.31322
## 35    16  49      no   0    no   no     yes   male    no 16    no 7.29574
## 36    26  44     yes   1    no  yes     yes   male    no 12    no 6.90575
## 37    27  47     yes   1    no  yes     yes   male    no 12    no 6.90575
## 38    28  47     yes   1    no  yes     yes   male    no 12    no 6.90776
## 39    29  47     yes   1    no  yes     yes   male    no 12    no 7.00307
## 40    30  44     yes   1    no  yes     yes   male    no 12    no 7.06902
## 41    31  45     yes   1    no  yes     yes   male    no 12    no 7.52023
## 42    32  47     yes   1    no  yes     yes   male    no 12    no 7.33889
## 43    15  46     yes   0    no   no     yes   male   yes 12    no 6.13340
## 44    16  48     yes   0    no   no     yes   male   yes 12    no 6.17379
## 45    17  49     yes   0    no   no     yes   male   yes 12    no 6.21261
## 46    18  46     yes   0    no   no     yes   male   yes 12    no 6.31355
## 47    19  47     yes   0    no   no     yes   male   yes 12    no 6.37502
## 48    20  47     yes   0    no   no     yes   male   yes 12    no 6.44572
## 49    21  48     yes   0    no   no     yes   male   yes 12    no 6.52209
## 50    23  51     yes   1   yes   no     yes   male   yes 10    no 6.33150
## 51    24  50     yes   1   yes   no     yes   male   yes 10    no 6.40357
## 52    25  50     yes   1   yes   no     yes   male   yes 10    no 6.54391
## 53    26  50     yes   1   yes   no     yes   male   yes 10    no 6.56244
## 54    27  44     yes   1    no  yes     yes   male   yes 10    no 6.59167
## 55    28  51     yes   1    no  yes     yes   male   yes 10    no 6.81783
## 56    29  51     yes   1    no  yes     yes   male   yes 10    no 6.89163
## 57     3  50      no   0   yes  yes     yes   male    no 16    no 6.55108
## 58     4  48      no   0   yes  yes     yes   male    no 16    no 6.55108
## 59     5  50      no   0   yes  yes     yes   male    no 16    no 6.80239
## 60     6  48      no   0   yes  yes     yes   male    no 16    no 6.90776
## 61     7  48      no   0   yes  yes     yes   male    no 16    no 7.09008
## 62     8  44      no   0   yes  yes     yes   male    no 16    no 7.17012
## 63     9  48      no   0   yes  yes     yes   male    no 16    no 7.20786
## 64     3  49      no   0   yes  yes     yes   male    no 16    no 6.39693
## 65     4  47      no   0   yes  yes     yes   male    no 16    no 6.43775
## 66     5  46      no   0   yes  yes     yes   male    no 16    no 6.43775
## 67     6  44      no   0   yes  yes     yes   male    no 16    no 6.43775
## 68     7  43      no   0   yes  yes     yes   male    no 16    no 6.52209
## 69     8  34      no   0   yes  yes     yes   male    no 16    no 6.61338
## 70     9  40      no   0   yes  yes     yes   male    no 16    no 6.73934
## 71    24  47     yes   0    no  yes      no   male   yes 12    no 6.65801
## 72    25  48     yes   0    no  yes      no   male   yes 12    no 6.72623
## 73    26  45     yes   0    no  yes      no   male   yes 12    no 6.80239
## 74    27  45     yes   0    no  yes     yes   male   yes 12    no 6.90776
## 75    28  47     yes   0    no  yes     yes   male   yes 12    no 7.03966
## 76    29  17     yes   0    no  yes     yes   male   yes 12    no 7.12769
## 77    30  47     yes   0    no  yes     yes   male   yes 12    no 7.24423
## 78    21  47     yes   0   yes  yes     yes   male   yes 12    no 6.55108
## 79    22  46     yes   0   yes  yes     yes   male   yes 12    no 6.62936
## 80    23  47     yes   0   yes  yes     yes   male   yes 12    no 6.72263
## 81    24  47     yes   0   yes  yes     yes   male   yes 12    no 6.73340
## 82    25  47     yes   0   yes  yes     yes   male   yes 12    no 6.72263
## 83    26  47     yes   0   yes  yes     yes   male   yes 12    no 6.95177
## 84    27  46     yes   0   yes  yes     yes   male   yes 12    no 7.05272
## 85    26  48     yes   0   yes  yes     yes   male    no 12    no 6.90575
## 86    27  48     yes   0   yes  yes     yes   male    no 12    no 6.90073
## 87    28  50     yes   0   yes  yes     yes   male    no 12    no 7.17012
## 88    29  48     yes   0   yes  yes     yes   male    no 12    no 7.26543
## 89    30  48     yes   0   yes  yes     yes   male    no 12    no 7.25912
## 90    31  46      no   0   yes  yes     yes   male    no 12    no 7.25488
## 91    32  46     yes   0   yes  yes     yes   male    no 12    no 7.40001
## 92    15  45      no   0   yes  yes     yes   male    no 17    no 6.80239
## 93    16  45      no   0   yes  yes     yes   male    no 17    no 6.80239
## 94    17  45      no   0   yes  yes     yes   male    no 17    no 6.92560
## 95    18  44      no   0   yes  yes     yes   male    no 17    no 7.00307
## 96    19  44      no   0   yes  yes     yes   male    no 17    no 7.13090
## 97    20  44      no   0   yes  yes     yes   male    no 17    no 7.12448
## 98    21  44      no   0   yes  yes     yes   male    no 17    no 7.12287
## 99     9  50      no   0    no   no      no female    no 14    no 5.94017
## 100   10  46      no   0    no   no      no female    no 14    no 5.86079
## 101   11  48      no   0    no   no      no female    no 14    no 5.99894
## 102   12  46      no   0    no   no      no female    no 14    no 6.08450
## 103   13  48      no   0    no   no      no female    no 14    no 6.39526
## 104   14  41      no   0    no   no      no female    no 14    no 6.47697
## 105   15  48      no   0    no   no      no female    no 14    no 6.47697
## 106   16  50     yes   0   yes  yes      no female    no 12   yes 5.97889
## 107   17  50     yes   0   yes  yes      no female    no 12   yes 5.78383
## 108   18  48     yes   0   yes  yes      no female    no 12   yes 5.85793
## 109   19  48     yes   0   yes  yes      no female    no 12   yes 5.95324
## 110   20  50     yes   0   yes  yes      no female    no 12   yes 6.14633
## 111   21  50     yes   0   yes  yes      no female    no 12   yes 6.17587
## 112   22  49     yes   0   yes  yes      no female    no 12   yes 6.38856
## 113   16  49      no   1    no   no     yes   male    no 14    no 6.62007
## 114   17  48      no   1    no   no     yes   male    no 14    no 6.49224
## 115   18  49      no   1    no   no     yes   male    no 14    no 6.77992
## 116   19  50      no   1    no   no     yes   male    no 14    no 6.74524
## 117   20  51      no   1    no   no     yes   male    no 14    no 7.09008
## 118   21  46      no   1    no   no     yes   male    no 14    no 7.13090
## 119   22  47      no   1    no   no     yes   male    no 14    no 7.13090
## 120   25  47      no   1   yes  yes     yes   male    no 16    no 6.90575
## 121   26  46      no   1   yes  yes     yes   male    no 16    no 6.90575
## 122   27  47      no   1   yes  yes     yes   male    no 16    no 7.60090
## 123   28  47      no   1   yes  yes     yes   male    no 16    no 7.64969
## 124   29  47      no   1   yes  yes     yes   male    no 16    no 7.71869
## 125   30  48      no   1   yes  yes     yes   male    no 16    no 7.78322
## 126   31  47      no   1   yes  yes     yes   male    no 16    no 7.80384
## 127   40  37     yes   1    no  yes     yes   male   yes 12    no 6.38688
## 128   41  49     yes   1    no  yes     yes   male   yes 12    no 6.47389
## 129   42  50     yes   1    no  yes     yes   male   yes 12    no 6.54247
## 130   43  47     yes   1    no  yes     yes   male   yes 12    no 6.67582
## 131   44  47     yes   1    no  yes     yes   male   yes 12    no 6.74170
## 132   45  25     yes   1    no  yes     yes   male   yes 12    no 6.83195
## 133   46  40     yes   1    no  yes     yes   male   yes 12    no 6.93634
## 134   25  50      no   0    no   no     yes   male    no 16    no 6.78333
## 135   26  49      no   1    no   no     yes   male    no 16    no 6.85751
## 136   27  49      no   1    no   no     yes   male    no 16    no 6.98472
## 137   28  48      no   1    no   no     yes   male    no 16    no 7.05790
## 138   29  48      no   1    no   no     yes   male    no 16    no 7.20564
## 139   30  49      no   1    no   no     yes   male    no 16    no 7.10988
## 140   31  48      no   1    no   no     yes   male    no 16    no 7.26683
## 141   28  42     yes   1   yes   no     yes   male   yes  4    no 6.05912
## 142   29  46     yes   1   yes   no     yes   male   yes  4    no 6.05209
## 143   30  49     yes   1   yes   no     yes   male   yes  4    no 5.99146
## 144   31  49     yes   1   yes   no     yes   male   yes  4    no 6.21461
## 145   32  48     yes   0   yes   no     yes   male   yes  4    no 6.32436
## 146   33  45     yes   0   yes   no     yes   male   yes  4    no 6.44254
## 147   34  42     yes   1   yes   no     yes   male   yes  4    no 6.44254
## 148   20  46      no   0    no   no     yes   male    no 14    no 6.59987
## 149   21  45      no   0    no   no     yes   male    no 14    no 6.59987
## 150   22  44      no   0    no   no     yes   male    no 14    no 6.68461
## 151   23  46      no   0    no   no     yes   male    no 14    no 6.72743
## 152   24  47      no   0    no   no     yes   male    no 14    no 6.88244
## 153   25  51      no   1    no   no     yes   male    no 14    no 6.95655
## 154   26  47      no   0    no   no     yes   male    no 14    no 7.04752
## 155   11  50      no   0    no  yes     yes   male    no 16    no 6.90575
## 156   12  50      no   0    no  yes     yes   male    no 16    no 6.90575
## 157   13  51      no   0    no  yes     yes   male    no 16    no 7.49554
## 158   14  50      no   0    no  yes     yes   male    no 16    no 7.66153
## 159   15  48      no   0    no  yes     yes   male    no 16    no 7.86327
## 160   16  47      no   0    no  yes     yes   male    no 16    no 8.03916
## 161   17  50      no   0    no  yes     yes   male    no 16    no 7.89357
## 162    5  30      no   0    no   no      no female    no 12    no 5.43808
## 163    6  51      no   0    no   no      no female    no 12    no 5.52146
## 164    7  51     yes   0    no   no      no female    no 12    no 5.57973
## 165    8  52     yes   0    no   no      no female    no 12    no 5.66988
## 166    9  49     yes   0    no   no      no female    no 12    no 5.73657
## 167   10  51     yes   0    no   no      no female   yes 12    no 5.84354
## 168   11  50     yes   0    no   no      no female    no 12    no 5.85793
## 169    8  37      no   0    no  yes     yes   male   yes 17    no 6.52942
## 170    9  39      no   0    no  yes     yes   male   yes 17    no 6.57925
## 171   10  40      no   0    no  yes     yes   male   yes 17    no 6.71538
## 172   11  38      no   0    no  yes     yes   male   yes 17    no 6.68461
## 173   12  38      no   0    no  yes     yes   male   yes 17    no 6.79122
## 174   13  39      no   0    no  yes     yes   male   yes 17    no 6.97541
## 175   14  41      no   0    no  yes     yes   male   yes 17    no 6.90776
## 176   14  48      no   1   yes  yes     yes   male    no 15    no 6.47697
## 177   15  47     yes   1   yes  yes     yes   male    no 15    no 6.55108
## 178   16  49      no   1   yes  yes     yes   male    no 15    no 6.86693
## 179   17  48      no   1   yes  yes     yes   male    no 15    no 6.85646
## 180   18  47      no   1   yes  yes     yes   male    no 15    no 7.27932
## 181   19  47      no   1   yes  yes     yes   male    no 15    no 7.54961
## 182   20  48      no   1   yes  yes     yes   male    no 15    no 7.36708
## 183    8  50      no   0    no  yes      no   male    no 16    no 6.01616
## 184    9  52      no   0    no  yes      no   male    no 16    no 6.90575
## 185   10  48      no   0    no   no      no   male    no 16    no 7.04752
## 186   11  50      no   0    no   no      no   male    no 16    no 7.26193
## 187   12  50      no   0    no   no      no   male    no 16    no 7.09008
## 188   13  45      no   0    no   no      no   male    no 16    no 6.96319
## 189   14  23      no   0    no   no      no   male    no 16    no 7.31322
## 190   26  50     yes   0    no  yes     yes   male    no 12    no 6.73340
## 191   27  50     yes   0    no  yes     yes   male    no 12    no 6.69703
## 192   28  50     yes   0    no  yes     yes   male    no 12    no 6.68461
## 193   29  50     yes   0    no  yes     yes   male    no 12    no 6.74524
## 194   30  50     yes   0    no  yes     yes   male    no 12    no 6.73102
## 195   31  49     yes   0    no  yes     yes   male    no 12    no 6.80239
## 196   32  49     yes   0    no  yes     yes   male    no 12    no 6.74524
## 197   31  49      no   0    no  yes     yes   male    no 14    no 6.90575
## 198   32  49      no   0    no  yes     yes   male    no 14    no 6.90575
## 199   33  49      no   0    no  yes     yes   male    no 14    no 7.06219
## 200   34  49      no   0    no  yes     yes   male    no 14    no 7.57558
## 201   35  50      no   0    no  yes     yes   male    no 14    no 7.67322
## 202   36  49      no   0    no  yes     yes   male    no 14    no 7.47307
## 203   37  49      no   0    no  yes     yes   male    no 14    no 7.56008
## 204   17  47      no   0   yes  yes      no female    no 12    no 6.19644
## 205   18  47      no   0   yes  yes      no female    no 12    no 6.29895
## 206   19  48      no   0   yes  yes      no female    no 12    no 6.33150
## 207   20  49      no   0   yes  yes      no female    no 12    no 6.36303
## 208   21  49      no   0   yes  yes      no female    no 12    no 6.48158
## 209   22  45      no   0   yes  yes      no female    no 12    no 6.57786
## 210   23  49      no   0   yes  yes      no female    no 12    no 6.64379
## 211   22  48      no   1    no  yes     yes   male    no 17    no 6.90575
## 212   23  48      no   1    no  yes     yes   male    no 17    no 6.90575
## 213   24  48      no   1    no  yes     yes   male    no 17    no 7.31322
## 214   25  47      no   1    no  yes     yes   male    no 17    no 7.24423
## 215   26  43      no   1    no  yes     yes   male    no 17    no 7.48437
## 216   27  47      no   0    no  yes     yes   male    no 17    no 7.54961
## 217   28  45      no   1    no  yes     yes   male    no 17    no 7.61332
## 218   30  50      no   1    no  yes     yes   male    no 16    no 6.90575
## 219   31  49      no   1    no  yes     yes   male    no 16    no 6.90575
## 220   32  49      no   1    no  yes     yes   male    no 16    no 7.46737
## 221   33  48      no   1    no  yes     yes   male    no 16    no 7.40853
## 222   34  49      no   1    no  yes     yes   male    no 16    no 7.60589
## 223   35  47      no   1    no  yes     yes   male    no 16    no 8.04879
## 224   36  47      no   1    no  yes     yes   male    no 16    no 7.74066
## 225   14  51      no   0    no  yes     yes   male    no 16    no 6.90575
## 226   15  47      no   0    no  yes     yes   male    no 16    no 6.90575
## 227   16  51      no   0    no  yes     yes   male    no 16    no 7.17012
## 228   17  47      no   0    no  yes     yes   male    no 16    no 7.27932
## 229   18  48      no   0    no  yes     yes   male    no 16    no 7.24065
## 230   19  50      no   0    no  yes     yes   male    no 16    no 7.37776
## 231   20  49      no   0    no  yes     yes   male    no 16    no 7.46737
## 232   45  48     yes   0   yes   no     yes   male    no  8    no 5.75890
## 233   46  48     yes   0   yes   no     yes   male    no  8    no 5.86079
## 234   47  48     yes   0   yes   no     yes   male    no  8    no 5.82305
## 235   48  49     yes   0   yes   no     yes   male    no  8    no 5.94803
## 236   49  50     yes   0   yes   no     yes   male    no  8    no 6.24804
## 237   50  48     yes   0   yes   no     yes   male    no  8    no 6.20658
## 238   51  46     yes   0   yes   no     yes   male    no  8    no 5.98394
## 239    8  30     yes   0    no  yes     yes   male   yes 13   yes 6.51471
## 240    9  49     yes   1    no  yes     yes   male   yes 13   yes 6.61070
## 241   10  48     yes   1    no  yes     yes   male   yes 13   yes 6.39693
## 242   11  49     yes   1    no  yes     yes   male   yes 13   yes 6.75227
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## 1602  21  42      no   0    no  yes      no female    no 17    no 6.90776
## 1603  22  42      no   1    no  yes      no female   yes 17    no 6.90776
## 1604   2  50     yes   0    no   no     yes   male   yes 12    no 5.91350
## 1605   3  50     yes   0    no   no     yes   male   yes 12    no 6.24028
## 1606   4  50     yes   0    no   no     yes   male   yes 12    no 6.36303
## 1607   5  50     yes   0    no   no     yes   male   yes 12    no 6.55108
## 1608   6  50     yes   0    no   no     yes   male   yes 12    no 6.71538
## 1609   7  50     yes   0    no   no     yes   male   yes 12    no 6.80239
## 1610   8  50     yes   0    no   no     yes   male   yes 12    no 6.90776
## 1611  23  49      no   1    no  yes     yes   male    no 16    no 6.90575
## 1612  24  48      no   1    no  yes     yes   male    no 16    no 6.90575
## 1613  25  49      no   1    no  yes     yes   male    no 16    no 7.64969
## 1614  26  48      no   1    no  yes     yes   male    no 16    no 7.88231
## 1615  27  49      no   1    no  yes     yes   male    no 16    no 7.82405
## 1616  28  48      no   1    no  yes     yes   male    no 16    no 7.97247
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## 1619  28  49      no   0    no   no     yes   male    no 17    no 6.90575
## 1620  29  49      no   0    no   no     yes   male    no 17    no 6.95655
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## 1628  33  50     yes   1    no  yes     yes   male   yes 10    no 6.90776
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## 1640  19  48     yes   1   yes   no     yes   male    no  7    no 5.95324
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## 1644  23  40     yes   1   yes   no     yes   male    no  7    no 6.17379
## 1645  24  49     yes   1   yes   no     yes   male    no  7    no 6.17379
## 1646   7  48      no   1    no   no     yes   male    no 17    no 6.90575
## 1647   8  49      no   1    no   no     yes   male    no 17    no 6.90575
## 1648   9  49      no   1    no   no     yes   male    no 17    no 7.18917
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## 1651  12  48      no   1    no  yes     yes   male    no 17    no 7.37776
## 1652  13  48      no   1    no  yes     yes   male    no 17    no 7.48717
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## 1658  11  40      no   0    no   no     yes   male    no 16    no 6.57925
## 1659  12  36      no   0    no   no     yes   male    no 16    no 6.59304
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## 1668  28  47      no   0    no  yes     yes   male    no 16    no 6.90575
## 1669  29  47      no   0    no  yes     yes   male    no 16    no 7.82405
## 1670  30  47      no   0    no  yes     yes   male    no 16    no 7.90101
## 1671  31  47      no   0    no  yes     yes   male    no 16    no 7.67322
## 1672  32  47      no   0    no   no     yes   male    no 16    no 8.00637
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## 1674  34  49     yes   1    no  yes     yes   male   yes 12    no 6.90575
## 1675  35  49     yes   1    no  yes     yes   male   yes 12    no 6.90575
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## 1680  40  48     yes   0    no  yes     yes   male   yes 12    no 7.55747
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## 1687  21  38     yes   0    no  yes     yes   male   yes 10    no 6.76964
## 1688   7  47     yes   0    no  yes      no female   yes 10    no 5.75257
## 1689   8  45     yes   0    no  yes      no female   yes 10    no 5.75257
## 1690   9  46     yes   0    no  yes      no female   yes 10    no 5.88053
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## 1692  11  48     yes   0    no  yes      no female   yes 10    no 6.03548
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## 1695   9  46     yes   1    no  yes     yes   male   yes 12    no 6.90575
## 1696  10  43     yes   1    no  yes     yes   male   yes 12    no 6.90575
## 1697  11  40     yes   1    no  yes     yes   male   yes 12    no 7.14520
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## 1722  43  46     yes   0   yes   no     yes   male   yes 10    no 6.62007
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## 1724  10  44     yes   0    no  yes      no female    no  7   yes 5.56068
## 1725  11  50     yes   0    no  yes      no female    no  7   yes 5.57973
## 1726  12  50     yes   0    no  yes      no female    no  7   yes 5.73657
## 1727  13  50     yes   0    no  yes      no female    no  7   yes 5.76832
## 1728  14  50     yes   0    no  yes      no female    no  7   yes 5.81413
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## 1731  11  50     yes   0    no  yes      no female    no 11    no 5.73657
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## 1763  30  48      no   0    no  yes     yes   male    no 17   yes 7.60090
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## 1779   3  48     yes   1    no   no      no female    no 12    no 6.05209
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## 1784   8  47     yes   1    no   no      no female   yes 12    no 6.56244
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## 1787   6  39      no   0   yes  yes     yes   male   yes 16    no 6.35437
## 1788   7  50      no   0   yes  yes     yes   male   yes 16    no 6.49979
## 1789   8  50      no   0   yes  yes     yes   male   yes 16    no 6.68461
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## 1791  10  49      no   0   yes  yes     yes   male   yes 16    no 7.00307
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## 1820  16  49      no   0    no  yes     yes   male    no 12    no 7.31322
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## 1822  17  50     yes   0   yes  yes     yes   male   yes 10    no 6.36130
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## 1831  15  49      no   0    no  yes     yes   male    no 16    no 6.91175
## 1832  16  49      no   0    no  yes     yes   male    no 16    no 7.31122
## 1833  17  50      no   0    no  yes     yes   male    no 16    no 7.18917
## 1834  18  49      no   0    no  yes     yes   male    no 16    no 7.37776
## 1835  10  37      no   1    no  yes      no female    no 12   yes 6.10925
## 1836  11  33      no   1    no  yes      no female    no 12   yes 6.20456
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## 1838  13  46      no   1    no  yes      no female    no 12   yes 6.39693
## 1839  14  48      no   1    no  yes      no female    no 12   yes 6.55108
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## 1842   3  48      no   0    no  yes      no female    no 16    no 6.30992
## 1843   4  35      no   0    no  yes      no female    no 16    no 6.29157
## 1844   5  40      no   0    no  yes      no female    no 16    no 6.30992
## 1845   6  36      no   0    no  yes      no female    no 16    no 6.65286
## 1846   7  28      no   0    no  yes      no female    no 16    no 6.62007
## 1847   8  51      no   0    no  yes      no female    no 16    no 6.57228
## 1848   9  50      no   0    no  yes      no female    no 16    no 7.04752
## 1849  15  49     yes   1   yes  yes     yes   male   yes 12    no 6.67834
## 1850  16  45     yes   1   yes  yes     yes   male   yes 12    no 6.75227
## 1851  17  48     yes   1   yes  yes     yes   male   yes 12    no 6.84162
## 1852  18  49     yes   1   yes  yes     yes   male   yes 12    no 6.95655
## 1853  19  47     yes   1   yes  yes     yes   male   yes 12    no 7.00307
## 1854  20  48     yes   1   yes  yes     yes   male   yes 12    no 7.15462
## 1855  21  47     yes   0   yes  yes     yes   male   yes 12    no 7.21524
## 1856  21  44      no   0    no  yes     yes   male   yes 17    no 6.90575
## 1857  22  41      no   0    no  yes     yes   male   yes 17    no 6.90575
## 1858  23  43      no   0    no  yes     yes   male   yes 17    no 7.02997
## 1859  24  41      no   0    no  yes     yes   male   yes 17    no 7.09008
## 1860  25  44      no   0    no  yes     yes   male   yes 17    no 7.20786
## 1861  26  43      no   0    no  yes     yes   male   yes 17    no 7.26193
## 1862  27  42      no   0    no  yes     yes   male   yes 17    no 7.27932
## 1863  14  49     yes   0   yes  yes     yes   male   yes 12    no 6.55962
## 1864  15  49     yes   0   yes  yes     yes   male   yes 12    no 6.60123
## 1865  16  49     yes   0   yes  yes     yes   male   yes 12    no 6.73221
## 1866  17  48     yes   0   yes  yes     yes   male   yes 12    no 6.79122
## 1867  18  48     yes   0   yes  yes     yes   male   yes 12    no 6.90776
## 1868  19  47     yes   0   yes  yes     yes   male   yes 12    no 7.00307
## 1869  20  46     yes   0   yes  yes     yes   male   yes 12    no 7.09008
## 1870   8  51     yes   0    no   no     yes   male    no 14    no 5.89715
## 1871   9  51     yes   0    no   no     yes   male    no 14    no 6.07993
## 1872  10  51     yes   0    no   no     yes   male    no 14    no 5.98141
## 1873  11  50     yes   0    no   no     yes   male    no 14    no 6.33328
## 1874  12  51      no   0    no   no     yes   male    no 14    no 6.27476
## 1875  13  52      no   0    no   no     yes   male    no 14    no 6.20456
## 1876  14  51      no   0    no   no     yes   male    no 14    no 6.58617
## 1877  21  50     yes   1    no  yes     yes   male   yes  9    no 6.44572
## 1878  22  50     yes   1    no  yes     yes   male   yes  9    no 6.74524
## 1879  23  52     yes   1    no  yes      no   male   yes  9    no 6.81892
## 1880  24  51     yes   1    no   no      no   male   yes  9    no 6.85646
## 1881  25  51     yes   1    no   no      no   male   yes  9    no 7.00307
## 1882  26  49     yes   1    no   no      no   male   yes  9    no 7.09008
## 1883  27  50     yes   1    no   no      no   male   yes  9    no 7.20786
## 1884  21  51      no   0   yes  yes     yes   male    no 16    no 6.90575
## 1885  22  49      no   0   yes  yes     yes   male    no 16    no 6.90575
## 1886  23  47      no   0   yes  yes     yes   male    no 16    no 7.91936
## 1887  24  47      no   0   yes  yes     yes   male    no 16    no 8.13153
## 1888  25  47      no   0   yes  yes     yes   male    no 16    no 8.02290
## 1889  26  47      no   0   yes  yes     yes   male    no 16    no 7.92516
## 1890  27  47      no   0   yes  yes     yes   male    no 16    no 7.84502
## 1891   7  50      no   0   yes  yes     yes   male    no 16    no 6.48920
## 1892   8  50      no   0   yes  yes     yes   male    no 16    no 6.55820
## 1893   9  50      no   0   yes  yes     yes   male    no 16    no 6.57786
## 1894  10  50      no   0   yes  yes     yes   male    no 16    no 6.68461
## 1895  11  50      no   0   yes  yes     yes   male    no 16    no 6.39693
## 1896  12  50      no   0   yes  yes     yes   male    no 16    no 7.09008
## 1897  13  50      no   0   yes  yes     yes   male    no 16    no 6.86693
## 1898   6  49      no   0    no   no     yes   male    no 16    no 6.35437
## 1899   7  49      no   0    no   no     yes   male    no 16    no 6.44572
## 1900   8  51      no   0    no   no     yes   male    no 16    no 6.80239
## 1901   9  49      no   0    no   no     yes   male    no 16    no 6.80239
## 1902  10  49      no   0    no   no     yes   male    no 16    no 6.90776
## 1903  11  50      no   0    no   no     yes   male    no 16    no 6.96602
## 1904  12  50      no   0    no   no     yes   male    no 16    no 7.09008
## 1905  24  50     yes   1    no  yes     yes   male   yes 12   yes 6.31173
## 1906  25  40     yes   1    no  yes     yes   male   yes 12   yes 6.54535
## 1907  26  50     yes   1    no  yes     yes   male   yes 12   yes 6.56386
## 1908  27  47     yes   1    no  yes     yes   male   yes 12   yes 6.63200
## 1909  28  48     yes   1    no  yes     yes   male   yes 12   yes 6.80239
## 1910  29  48      no   1    no  yes     yes   male   yes 12   yes 6.84162
## 1911  30  46     yes   1    no  yes     yes   male   yes 12   yes 6.89770
## 1912  14  49      no   0    no  yes     yes   male    no 17    no 6.64249
## 1913  15  48      no   0    no  yes     yes   male    no 17    no 6.75344
## 1914  16  49      no   0    no  yes     yes   male    no 17    no 6.81783
## 1915  17  48      no   0    no  yes     yes   male    no 17    no 6.91473
## 1916  18  49      no   0    no  yes     yes   male    no 17    no 6.95655
## 1917  19  48      no   0    no  yes     yes   male    no 17    no 7.01571
## 1918  20  48      no   0    no  yes     yes   male    no 17    no 7.09423
## 1919   1  30      no   0    no  yes     yes   male    no 17    no 6.21461
## 1920   2  50      no   0    no  yes     yes   male    no 17    no 6.17379
## 1921   3  50      no   0    no  yes     yes   male    no 17    no 6.35437
## 1922   4  50      no   0    no  yes     yes   male    no 17    no 6.55108
## 1923   5  50      no   0    no  yes     yes   male    no 17    no 6.45362
## 1924   6  50      no   0    no  yes     yes   male    no 17    no 6.21461
## 1925   7  49      no   0    no  yes     yes   male    no 17    no 7.82405
## 1926   4  51     yes   1    no  yes     yes   male   yes 12    no 6.55251
## 1927   5  52     yes   1    no  yes     yes   male   yes 12    no 6.62007
## 1928   6  51     yes   1    no  yes     yes   male   yes 12    no 6.68461
## 1929   7  43     yes   1    no  yes     yes   male   yes 12    no 6.72383
## 1930   8  50     yes   1    no  yes     yes   male   yes 12    no 6.82437
## 1931   9  48     yes   1    no  yes     yes   male   yes 12    no 6.95655
## 1932  10  49     yes   1    no  yes     yes   male   yes 12    no 7.00307
## 1933  33  47      no   0   yes   no     yes   male    no  8    no 6.42162
## 1934  34  48     yes   0   yes   no     yes   male    no  8    no 6.48920
## 1935  35  46     yes   0   yes   no     yes   male    no  8    no 6.72022
## 1936  36  47     yes   0   yes   no     yes   male    no  8    no 6.76964
## 1937  37  47     yes   0   yes   no     yes   male    no  8    no 6.80239
## 1938  38  47     yes   0   yes   no     yes   male    no  8    no 6.87730
## 1939  39  47     yes   0   yes   no     yes   male    no  8    no 6.99577
## 1940   7  51      no   0   yes  yes     yes   male    no 15    no 6.90575
## 1941   8  49      no   1   yes  yes     yes   male    no 15    no 6.90575
## 1942   9  49      no   0    no   no     yes   male    no 15    no 7.17012
## 1943  10  49      no   0    no   no     yes   male    no 15    no 7.28276
## 1944  11  48      no   0    no   no     yes   male    no 15    no 7.36201
## 1945  12  50      no   0    no   no     yes   male    no 15    no 7.33498
## 1946  13  48      no   1    no   no     yes   male    no 15    no 7.47534
## 1947  15  50     yes   0    no  yes     yes   male   yes 12    no 6.57368
## 1948  16  48     yes   0    no  yes     yes   male   yes 12    no 6.67960
## 1949  17  49     yes   0    no  yes     yes   male   yes 12    no 6.85857
## 1950  18  49     yes   0    no  yes     yes   male   yes 12    no 6.84268
## 1951  19  49     yes   0    no  yes     yes   male   yes 12    no 6.96791
## 1952  20  49     yes   0    no  yes     yes   male   yes 12    no 7.13090
## 1953  21  49     yes   0    no  yes     yes   male   yes 12    no 7.18992
## 1954  29  52      no   0    no  yes     yes   male   yes 13    no 6.05209
## 1955  30  46      no   0    no  yes     yes   male   yes 13    no 6.05209
## 1956  31  51     yes   0    no  yes     yes   male   yes 13    no 6.10925
## 1957  32  49     yes   0    no  yes     yes   male   yes 13    no 6.21461
## 1958  33  48     yes   0    no  yes     yes   male   yes 13    no 6.26340
## 1959  34  47      no   0    no  yes     yes   male   yes 13    no 6.26340
## 1960  35  50      no   0    no  yes     yes   male   yes 13    no 6.30992
## 1961   5  36     yes   1    no  yes     yes   male   yes 12    no 6.53088
## 1962   6  50     yes   1    no  yes     yes   male   yes 12    no 6.55962
## 1963   7  49     yes   1    no  yes     yes   male   yes 12    no 6.58064
## 1964   8  50     yes   1    no  yes     yes   male   yes 12    no 6.72383
## 1965   9  50     yes   1    no  yes     yes   male   yes 12    no 6.87626
## 1966  10  50     yes   1    no  yes     yes   male   yes 12    no 6.97541
## 1967  11  49     yes   1    no  yes     yes   male   yes 12    no 7.00307
## 1968  18  48      no   1    no  yes     yes   male    no 17    no 6.74524
## 1969  19  48      no   1    no  yes     yes   male    no 17    no 6.74524
## 1970  20  49      no   1    no  yes     yes   male    no 17    no 6.81344
## 1971  21  49      no   1    no  yes     yes   male    no 17    no 6.85118
## 1972  22  48      no   1    no  yes     yes   male    no 17    no 7.02554
## 1973  23  45      no   1    no  yes     yes   male    no 17    no 7.09008
## 1974  24  48      no   1    no  yes     yes   male    no 17    no 7.27932
## 1975  44  50     yes   0    no  yes     yes   male   yes  9    no 6.90575
## 1976  45  51      no   0    no  yes     yes   male   yes  9    no 6.21461
## 1977  46  50      no   0    no  yes     yes   male   yes  9    no 7.13090
## 1978  47  50      no   0    no  yes     yes   male   yes  9    no 6.90776
## 1979  48  50      no   0    no  yes     yes   male   yes  9    no 7.31322
## 1980  49  49      no   0    no  yes     yes   male   yes  9    no 7.46737
## 1981  50  49      no   0    no  yes     yes   male   yes  9    no 7.31322
## 1982  29  49      no   0    no  yes     yes   male   yes 12    no 6.44413
## 1983  30  46      no   0    no  yes     yes   male   yes 12    no 6.45362
## 1984  31  49      no   0    no  yes     yes   male   yes 12    no 6.52062
## 1985  32  48      no   0    no  yes     yes   male   yes 12    no 6.72743
## 1986  33  49      no   0    no  yes     yes   male   yes 12    no 6.59167
## 1987  34  49      no   0    no  yes     yes   male   yes 12    no 6.73815
## 1988  35  48      no   0    no  yes     yes   male   yes 12    no 6.77422
## 1989   5  49      no   0    no  yes     yes   male    no 12    no 6.48311
## 1990   6  47     yes   0    no  yes     yes   male    no 12    no 6.53233
## 1991   7  49      no   0    no  yes     yes   male    no 12    no 6.75227
## 1992   8  49      no   0    no  yes     yes   male    no 12    no 6.80017
## 1993   9  48      no   0    no  yes     yes   male    no 12    no 6.75926
## 1994  10  48     yes   0    no  yes     yes   male    no 12    no 6.96885
## 1995  11  48      no   0    no  yes     yes   male    no 12    no 6.90975
## 1996  11  47     yes   1    no   no     yes   male   yes 10    no 5.99146
## 1997  12  48     yes   1    no   no     yes   male   yes 10    no 6.38012
## 1998  13  48     yes   1    no   no     yes   male   yes 10    no 6.56526
## 1999  14  49     yes   1    no   no     yes   male   yes 10    no 6.73340
## 2000  15  48     yes   1    no   no     yes   male    no 10    no 6.74524
## 2001  16  48     yes   1    no   no     yes   male   yes 10    no 6.84588
## 2002  17  46     yes   1    no   no     yes   male   yes 10    no 6.74524
## 2003  15  41     yes   1   yes   no     yes   male   yes 10    no 6.50429
## 2004  16  42     yes   1   yes   no     yes   male   yes 10    no 6.47389
## 2005  17  47     yes   1   yes   no     yes   male   yes 10    no 6.56386
## 2006  18  47     yes   1   yes   no     yes   male   yes 10    no 6.75110
## 2007  19  48     yes   1   yes   no     yes   male   yes 10    no 6.88755
## 2008  20  38     yes   1   yes   no     yes   male   yes 10    no 6.99485
## 2009  21  40     yes   1   yes   no     yes   male   yes 10    no 7.08423
## 2010  13  49     yes   0   yes  yes     yes   male    no 12    no 6.86485
## 2011  14  49     yes   0   yes  yes     yes   male    no 12    no 6.90575
## 2012  15  49     yes   0   yes  yes     yes   male    no 12    no 7.02554
## 2013  16  49     yes   0   yes  yes     yes   male    no 12    no 7.15070
## 2014  17  49     yes   0   yes  yes     yes   male    no 12    no 7.24423
## 2015  18  47      no   0   yes   no     yes   male    no 12    no 6.95940
## 2016  19  46     yes   0   yes   no     yes   male    no 12    no 7.44132
## 2017  28  50      no   0    no  yes     yes   male    no 16    no 6.90575
## 2018  29  50      no   0    no  yes     yes   male    no 16    no 6.90575
## 2019  30  49      no   0    no  yes     yes   male    no 16    no 7.46737
## 2020  31  49      no   0    no  yes     yes   male    no 16    no 7.69621
## 2021  32  49      no   0    no  yes     yes   male    no 16    no 7.60090
## 2022  33  49      no   0    no  yes     yes   male    no 16    no 7.91936
## 2023  34  48      no   0    no  yes     yes   male    no 16    no 7.91936
## 2024   4  50      no   0   yes  yes     yes   male    no 13    no 6.28786
## 2025   5  49      no   0   yes  yes     yes   male    no 13    no 6.20456
## 2026   6  51      no   0   yes  yes     yes   male    no 13    no 6.24417
## 2027   7  50      no   0   yes  yes     yes   male    no 13    no 6.32794
## 2028   8  50      no   0   yes  yes     yes   male    no 13    no 6.53669
## 2029   9  49      no   0   yes  yes     yes   male    no 13    no 6.55108
## 2030  10  49      no   0   yes  yes     yes   male    no 13    no 6.62007
## 2031  36  49     yes   1    no   no     yes   male    no 12    no 6.80239
## 2032  37  46     yes   1    no   no     yes   male    no 12    no 6.82979
## 2033  38  50     yes   1    no   no     yes   male    no 12    no 6.98472
## 2034  39  49     yes   1    no   no     yes   male    no 12    no 7.00307
## 2035  40  48     yes   1    no   no     yes   male    no 12    no 6.70808
## 2036  41  47     yes   1    no   no     yes   male    no 12    no 6.96130
## 2037  42  47     yes   1    no   no     yes   male    no 12    no 6.96035
## 2038  27  48      no   1    no   no     yes   male    no 12    no 6.61607
## 2039  28  48      no   1    no   no     yes   male    no 12    no 6.57647
## 2040  29  47      no   1    no   no     yes   male    no 12    no 6.68461
## 2041  30  47      no   1    no   no     yes   male    no 12    no 6.74288
## 2042  31  48      no   1    no   no     yes   male    no 12    no 7.03615
## 2043  32  47      no   1    no   no     yes   male    no 12    no 7.02465
## 2044  33  48      no   1    no   no     yes   male    no 12    no 7.22621
## 2045  10  30     yes   1    no   no     yes   male   yes 12    no 6.06611
## 2046  11  50     yes   1    no   no     yes   male   yes 12    no 6.18826
## 2047  12  50     yes   1    no   no     yes   male   yes 12    no 6.31173
## 2048  13  50     yes   1    no   no     yes   male   yes 12    no 6.55678
## 2049  14  50     yes   1    no   no     yes   male   yes 12    no 6.55393
## 2050  15  50     yes   1    no   no     yes   male   yes 12    no 6.75227
## 2051  16  50     yes   1    no   no     yes   male   yes 12    no 6.92166
## 2052  16  49     yes   1    no   no     yes   male   yes 12    no 6.19644
## 2053  17  48     yes   1    no   no     yes   male   yes 12    no 6.26530
## 2054  18  41     yes   1    no   no     yes   male   yes 12    no 6.36475
## 2055  19  49     yes   1    no   no     yes   male   yes 12    no 6.43935
## 2056  20  47     yes   1    no   no     yes   male   yes 12    no 6.54391
## 2057  21  48     yes   1    no   no     yes   male   yes 12    no 6.61473
## 2058  22  47     yes   1    no   no     yes   male   yes 12    no 6.71659
## 2059  22  48      no   0    no  yes      no female   yes 12    no 6.33328
## 2060  23  48      no   0    no  yes      no female   yes 12    no 6.61473
## 2061  24  48      no   0    no  yes      no female   yes 12    no 6.73459
## 2062  25  46      no   0    no  yes      no female   yes 12    no 6.77422
## 2063  26  47      no   0    no  yes      no female   yes 12    no 6.86485
## 2064  27  47      no   0    no  yes      no female   yes 12    no 6.97073
## 2065  28  47      no   0    no  yes      no female   yes 12    no 7.04752
## 2066  30  50     yes   1    no   no     yes   male   yes  8    no 6.44572
## 2067  31  47     yes   1    no   no     yes   male    no  8    no 6.33328
## 2068  32  48     yes   1    no  yes     yes   male    no  8    no 6.39693
## 2069  33  48     yes   1    no  yes     yes   male   yes  8    no 6.48158
## 2070  34  39     yes   1    no  yes     yes   male   yes  8    no 6.59167
## 2071  35  50     yes   1    no  yes     yes   male   yes  8    no 6.59304
## 2072  36  50     yes   1    no  yes      no   male   yes  8    no 6.77878
## 2073  12  49     yes   0   yes   no     yes   male    no 12    no 6.42972
## 2074  13  48     yes   0   yes   no     yes   male    no 12    no 6.43133
## 2075  14  34     yes   0   yes   no     yes   male   yes 12    no 6.59441
## 2076  15  47     yes   0   yes   no     yes   male   yes 12    no 6.71174
## 2077  16  48     yes   0   yes   no     yes   male   yes 12    no 6.74524
## 2078  17  47     yes   0   yes   no     yes   male   yes 12    no 6.87730
## 2079  18  48     yes   0   yes   no     yes   male   yes 12    no 6.80239
## 2080  11  50     yes   1   yes  yes     yes   male    no 12   yes 6.49224
## 2081  12  50     yes   1   yes  yes     yes   male    no 12   yes 6.21461
## 2082  13  50     yes   1   yes  yes     yes   male    no 12   yes 6.72743
## 2083  14  49     yes   1   yes  yes     yes   male    no 12   yes 6.66568
## 2084  15  48      no   1   yes  yes      no   male    no 12   yes 6.30992
## 2085  16  50      no   1   yes  yes      no   male    no 12   yes 6.21461
## 2086  17  50      no   1   yes  yes      no   male    no 12   yes 6.21461
## 2087  35  49      no   0    no  yes      no female    no 16    no 6.30992
## 2088  36  50      no   0    no  yes      no female    no 16    no 6.30992
## 2089  37  49      no   0    no  yes      no female    no 16    no 6.30992
## 2090  38  50      no   0    no  yes      no female    no 16    no 6.30992
## 2091  39  50      no   0    no  yes      no female    no 16    no 6.55108
## 2092  40  50      no   0    no  yes      no female    no 16    no 6.62007
## 2093  41  50      no   0    no  yes      no female    no 16    no 6.74524
## 2094  33  51     yes   0    no   no     yes   male    no 12    no 6.14633
## 2095  34  51     yes   0    no   no     yes   male    no 12    no 6.25383
## 2096  35  51     yes   0    no   no     yes   male    no 12    no 6.30992
## 2097  36  47     yes   0    no   no     yes   male    no 12    no 6.35089
## 2098  37  49     yes   0    no   no     yes   male    no 12    no 6.46147
## 2099  38  47      no   0    no   no     yes   male    no 12    no 6.50279
## 2100  39  47     yes   0    no   no     yes   male    no 12    no 6.59715
## 2101   9  49      no   1    no  yes     yes   male    no 14    no 6.53669
## 2102  10  49      no   1    no  yes     yes   male    no 14    no 6.55108
## 2103  11  49      no   1    no  yes     yes   male    no 14    no 6.65929
## 2104  12  48      no   1    no  yes     yes   male    no 14    no 6.82979
## 2105  13  46      no   1    no  yes     yes   male    no 14    no 6.85646
## 2106  14  46      no   1    no  yes     yes   male    no 14    no 6.95655
## 2107  15  48      no   1    no  yes     yes   male    no 14    no 7.13090
## 2108  11  36      no   0    no  yes     yes   male   yes 17    no 6.22456
## 2109  12  36      no   0    no  yes     yes   male   yes 17    no 6.30992
## 2110  13  37      no   0    no  yes     yes   male   yes 17    no 6.47697
## 2111  14  38      no   0    no  yes     yes   male   yes 17    no 6.67834
## 2112  15  35      no   0    no  yes     yes   male   yes 17    no 6.77992
## 2113  16  35      no   0    no  yes     yes   male   yes 17    no 6.80461
## 2114  17  36      no   0    no  yes     yes   male   yes 17    no 6.85646
## 2115   2  50     yes   1   yes  yes     yes   male    no 13    no 5.75257
## 2116   3  50     yes   1   yes  yes     yes   male    no 13    no 5.85793
## 2117   4  49     yes   1   yes  yes     yes   male    no 13    no 6.07535
## 2118   5  49     yes   1   yes  yes     yes   male    no 13    no 8.51719
## 2119   6  51     yes   1   yes  yes     yes   male    no 13    no 6.51471
## 2120   7  49     yes   1   yes  yes     yes   male    no 13    no 6.58617
## 2121   8  48     yes   1   yes  yes     yes   male    no 13    no 6.70319
## 2122  11  50     yes   0   yes  yes     yes   male   yes  9    no 6.16331
## 2123  12  51     yes   0   yes  yes     yes   male   yes  9    no 6.26340
## 2124  13  51     yes   0   yes  yes     yes   male   yes  9    no 6.35437
## 2125  14  51     yes   0   yes  yes     yes   male   yes  9    no 6.43775
## 2126  15  51     yes   0   yes  yes     yes   male   yes  9    no 6.47697
## 2127  16  51     yes   0   yes  yes     yes   male   yes  9    no 6.55108
## 2128  17  51     yes   0   yes  yes     yes   male    no  9    no 6.40853
## 2129  18  50      no   0    no  yes     yes   male    no 16    no 6.90575
## 2130  19  49      no   0    no  yes     yes   male    no 16    no 6.90575
## 2131  20  49      no   0    no  yes     yes   male    no 16    no 7.25134
## 2132  21  49      no   0    no  yes     yes   male    no 16    no 7.25134
## 2133  22  50      no   0    no  yes     yes   male    no 16    no 6.90776
## 2134  23  47      no   0    no  yes     yes   male    no 16    no 7.23634
## 2135  24  48      no   0    no  yes     yes   male    no 16    no 7.27240
## 2136  18  50     yes   0    no   no     yes   male    no 12    no 6.49527
## 2137  19  50     yes   0    no   no     yes   male    no 12    no 6.60394
## 2138  20  50      no   0    no   no     yes   male    no 12    no 6.70073
## 2139  21  49     yes   0    no   no     yes   male    no 12    no 6.58617
## 2140  22  49     yes   0    no   no     yes   male    no 12    no 6.41836
## 2141  23  49     yes   0    no   no     yes   male    no 12    no 6.21461
## 2142  24  49     yes   0    no   no     yes   male    no 12    no 6.62007
## 2143   3  47     yes   1    no   no     yes   male   yes  8    no 6.45047
## 2144   4  52     yes   1    no   no     yes   male   yes  8    no 6.67203
## 2145   5  50     yes   1    no   no     yes   male   yes  8    no 6.56386
## 2146   6  47     yes   1    no   no     yes   male   yes  8    no 6.60665
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## 2148   8  47     yes   1    no   no     yes   male   yes  8    no 6.86171
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## 3224  32  49      no   1    no   no     yes   male    no 12    no 6.50728
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## 3226  34  49      no   1    no   no     yes   male    no 12    no 6.81344
## 3227  35  49      no   1    no   no     yes   male    no 12    no 6.85646
## 3228  36  39     yes   0    no  yes     yes   male    no  6    no 6.16331
## 3229  37  44     yes   0    no  yes     yes   male    no  6    no 6.39693
## 3230  38  25     yes   1    no  yes     yes   male    no  6    no 5.95584
## 3231  39  51     yes   1    no  yes     yes   male    no  6    no 6.07535
## 3232  40  50     yes   1    no  yes     yes   male    no  6    no 6.26340
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## 3247  45  49      no   1    no  yes      no female    no 12    no 6.43775
## 3248  46  49     yes   1    no  yes      no female    no 12    no 6.55536
## 3249   3  37      no   0    no  yes     yes   male   yes 16    no 6.21461
## 3250   4  39      no   0    no  yes     yes   male   yes 16    no 6.38012
## 3251   5  36      no   0    no  yes     yes   male   yes 16    no 6.35437
## 3252   6  39      no   0    no  yes     yes   male   yes 16    no 6.47697
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## 3261  33  48     yes   1    no  yes     yes   male   yes 12    no 6.68461
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## 3266  27  49     yes   1    no  yes     yes   male   yes 12    no 6.49375
## 3267  28  49     yes   1    no  yes     yes   male   yes 12    no 6.55108
## 3268  29  49     yes   1    no  yes     yes   male   yes 12    no 7.00307
## 3269  30  49     yes   1    no  yes     yes   male   yes 12    no 6.81014
## 3270  40  49      no   1    no  yes     yes   male    no 17    no 6.90575
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## 3273  43  49      no   0    no  yes     yes   male    no 17    no 7.31322
## 3274  44  49      no   1    no  yes     yes   male    no 17    no 7.31322
## 3275  45  49      no   1    no  yes     yes   male    no 17    no 7.37776
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## 3301   7  49      no   0   yes   no      no female    no 12    no 5.86647
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## 3306   6  48     yes   0    no   no     yes   male   yes 14    no 6.37502
## 3307   7  48     yes   0    no   no     yes   male   yes 14    no 6.58617
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## 3317  17  51      no   0   yes  yes     yes   male    no 17    no 7.43838
## 3318  18  52      no   0   yes  yes     yes   male    no 17    no 7.17702
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## 3327  27  49     yes   1    no  yes     yes   male   yes 10    no 5.85793
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## 3452  39  44     yes   1    no  yes      no female   yes 14   yes 5.94803
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## 3494   3  46      no   0    no   no     yes   male    no 17    no 6.62007
## 3495   4  48      no   0    no   no     yes   male    no 17    no 6.62007
## 3496   5  48      no   0    no   no     yes   male    no 17    no 6.68461
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## 3498   7  49      no   0    no   no     yes   male    no 17    no 6.85646
## 3499   8  49      no   0    no   no     yes   male    no 17    no 5.98896
## 3500   9  48      no   0   yes  yes     yes   male    no 17    no 6.12687
## 3501  28  46     yes   1   yes  yes     yes   male   yes 12    no 6.35957
## 3502  29  47     yes   1   yes  yes     yes   male   yes 12    no 6.45205
## 3503  30  47     yes   1   yes  yes     yes   male   yes 12    no 6.52942
## 3504  31  46     yes   1   yes  yes     yes   male   yes 12    no 6.63857
## 3505  32  46     yes   1   yes  yes     yes   male   yes 12    no 6.79122
## 3506  33  38     yes   1   yes  yes     yes   male   yes 12    no 6.95655
## 3507  34  45      no   1   yes  yes     yes   male   yes 12    no 7.03439
## 3508  14  44      no   0    no   no      no female    no 17    no 6.64639
## 3509  15  44      no   0    no   no      no female   yes 17    no 6.71538
## 3510  16  44      no   0    no   no      no female   yes 17    no 6.77422
## 3511  17  44      no   0    no   no      no female   yes 17    no 6.95655
## 3512  18  44      no   0    no   no      no female   yes 17    no 6.95655
## 3513  19  44      no   0    no   no      no female   yes 17    no 7.20786
## 3514  20  41      no   0    no   no      no female   yes 17    no 7.18917
## 3515   7  46     yes   0    no  yes     yes   male   yes 12    no 6.80239
## 3516   8  40     yes   0    no  yes     yes   male   yes 12    no 6.90575
## 3517   9  45     yes   0    no  yes     yes   male   yes 12    no 7.10250
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## 3520  12  46     yes   0    no  yes     yes   male   yes 12    no 7.35372
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## 3522   8  46      no   1    no  yes     yes   male   yes 12    no 6.49072
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## 3524  10  47     yes   1    no  yes      no   male    no 12    no 6.80239
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## 3526  12  40     yes   1    no  yes     yes   male    no 12    no 7.03703
## 3527  13  46     yes   1    no  yes     yes   male    no 12    no 6.49072
## 3528  14  48     yes   1    no  yes     yes   male   yes 12    no 7.31122
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## 3534  28  48      no   0    no   no     yes   male    no 16    no 7.62071
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## 3541  10  51     yes   0    no  yes     yes   male    no 12    no 6.68461
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## 3555  39  48      no   0    no   no     yes   male    no 12    no 6.45520
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## 3558  19  50     yes   1    no  yes     yes   male    no 12    no 6.49072
## 3559  20  49     yes   1    no  yes     yes   male    no 12    no 6.59578
## 3560  21  49      no   1    no  yes     yes   male    no 12    no 6.64118
## 3561  22  48      no   1    no  yes     yes   male    no 12    no 6.80239
## 3562  23  48      no   1    no  yes     yes   male    no 12    no 6.91870
## 3563  24  48      no   1    no  yes     yes   male    no 12    no 6.96035
## 3564   6  50      no   0    no  yes     yes   male    no 16    no 6.90575
## 3565   7  50      no   0    no  yes     yes   male    no 16    no 6.90575
## 3566   8  50      no   0    no  yes     yes   male    no 16    no 7.17012
## 3567   9  50      no   0    no  yes     yes   male    no 16    no 7.27932
## 3568  10  50      no   0    no  yes     yes   male    no 16    no 7.31322
## 3569  11  49      no   0    no  yes     yes   male    no 16    no 7.37776
## 3570  12  50      no   0    no  yes     yes   male    no 16    no 7.34923
## 3571  12  50     yes   0    no  yes     yes   male    no 13    no 6.19441
## 3572  13  48     yes   0    no  yes     yes   male    no 13    no 6.26340
## 3573  14  49     yes   0    no  yes     yes   male    no 13    no 6.29157
## 3574  15  47     yes   0    no  yes     yes   male    no 13    no 6.13123
## 3575  16  30     yes   0    no  yes     yes   male    no 13    no 6.74524
## 3576  17  49     yes   0    no   no      no   male    no 13    no 6.95655
## 3577  18  47     yes   0    no   no      no   male    no 13    no 6.84055
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## 3579   5  49     yes   1   yes   no     yes   male    no 10    no 6.39693
## 3580   6  47     yes   1   yes   no     yes   male    no 10    no 6.71538
## 3581   7  47     yes   1   yes   no     yes   male    no 10    no 6.58617
## 3582   8  47     yes   1   yes   no     yes   male   yes 10    no 6.81344
## 3583   9  46     yes   1   yes   no     yes   male   yes 10    no 6.90776
## 3584  10  48     yes   1   yes   no     yes   male   yes 10    no 7.00307
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## 3590  40  48     yes   0    no   no     yes   male    no  5    no 5.98896
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## 3593  19  37      no   0    no  yes     yes   male   yes 14    no 6.90575
## 3594  20  44      no   0    no  yes     yes   male   yes 14    no 6.95655
## 3595  21  42      no   0    no  yes     yes   male   yes 14    no 7.09008
## 3596  22  42      no   0    no  yes     yes   male   yes 14    no 7.04752
## 3597  23  41      no   0    no  yes     yes   male   yes 14    no 7.13090
## 3598  24  36      no   0    no  yes     yes   male   yes 14    no 7.34666
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## 3600   5  52     yes   0   yes  yes      no female    no 12   yes 5.50126
## 3601   6  51     yes   0   yes  yes      no female    no 12   yes 5.65249
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## 3603   8  50     yes   0   yes  yes      no female    no 12   yes 5.89990
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## 3605  10  49     yes   0   yes  yes      no female    no 12   yes 6.14204
## 3606  25  50     yes   1    no  yes     yes   male    no 14    no 6.77992
## 3607  26  47     yes   1    no  yes     yes   male    no 14    no 6.90575
## 3608  27  48     yes   1    no  yes     yes   male    no 14    no 6.98472
## 3609  28  47     yes   1    no  yes     yes   male    no 14    no 7.08841
## 3610  29  46     yes   1    no  yes     yes   male   yes 14    no 6.86171
## 3611  30  48     yes   1    no  yes     yes   male   yes 14    no 6.97635
## 3612  31  49     yes   1    no  yes     yes   male   yes 14    no 6.98101
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## 3619  13  48     yes   0   yes   no     yes   male    no 13    no 6.34564
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## 3622  16  50      no   1   yes   no     yes   male    no 11    no 6.11368
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## 3624  18  51     yes   0   yes   no     yes   male    no 11    no 6.36303
## 3625  19  51     yes   0   yes   no     yes   male    no 11    no 6.40523
## 3626  20  51     yes   0   yes   no     yes   male    no 11    no 6.47697
## 3627   3  49     yes   0    no  yes      no   male   yes 12   yes 5.78383
## 3628   4  50     yes   0    no  yes      no   male   yes 12   yes 5.99146
## 3629   5  52     yes   0    no  yes      no   male   yes 12   yes 5.89715
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## 3640  32  52     yes   1    no  yes     yes   male   yes 12    no 6.89366
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## 3646  22  50      no   0    no   no      no   male    no 16    no 6.86693
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## 3649   3  49     yes   1    no   no     yes   male    no  9    no 5.82895
## 3650   4  52     yes   1    no   no     yes   male   yes  9    no 5.76832
## 3651   5  49     yes   1    no   no     yes   male   yes  9    no 6.59851
## 3652   6  49     yes   1    no   no     yes   male   yes  9    no 6.67960
## 3653   7  35     yes   1    no   no     yes   male   yes  9    no 7.09008
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## 3655   3  39     yes   1   yes   no     yes   male   yes 10    no 6.18208
## 3656   4  48     yes   1   yes   no     yes   male   yes 10    no 6.26340
## 3657   5  50     yes   1   yes   no     yes   male   yes 10    no 6.39359
## 3658   6  49     yes   1   yes   no     yes   male   yes 10    no 6.44095
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## 3661   9  47     yes   1   yes   no     yes   male   yes 10    no 6.75344
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## 3663   6  45      no   0   yes   no     yes   male    no 16    no 6.39693
## 3664   7  49      no   0   yes   no     yes   male    no 16    no 6.39693
## 3665   8  49      no   0   yes   no     yes   male    no 16    no 6.56526
## 3666   9  49      no   0   yes   no     yes   male    no 16    no 6.70073
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## 3670  12  49      no   0   yes  yes     yes   male   yes 12   yes 6.33150
## 3671  13  49      no   0   yes  yes      no   male   yes 12   yes 6.40853
## 3672  14  49      no   0   yes  yes      no   male   yes 12   yes 6.48158
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## 3675  17  44      no   0   yes  yes      no   male   yes 12   yes 6.82437
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## 3678   3  47     yes   1    no  yes      no   male    no 14    no 6.10925
## 3679   4  48      no   1    no  yes      no   male    no 14    no 6.04025
## 3680   5  52      no   1    no  yes      no   male    no 14    no 6.35957
## 3681   6  49      no   1    no  yes      no   male    no 14    no 6.50429
## 3682   7  49      no   1    no  yes      no   male    no 14    no 6.57786
## 3683   5  50      no   0    no  yes     yes   male    no 16   yes 6.23441
## 3684   6  50      no   0    no  yes     yes   male    no 16   yes 6.39693
## 3685   7  50      no   0    no  yes     yes   male    no 16   yes 6.50728
## 3686   8  50      no   0    no  yes     yes   male    no 16   yes 6.65286
## 3687   9  49      no   0    no  yes     yes   male    no 16   yes 6.74524
## 3688  10  49      no   0    no  yes     yes   male    no 16   yes 7.13090
## 3689  11  50      no   0    no  yes     yes   male    no 16   yes 7.24423
## 3690   4  40      no   0   yes   no     yes   male    no 17    no 6.09807
## 3691   5  32      no   0   yes   no     yes   male    no 17    no 6.26910
## 3692   6  37      no   0   yes   no     yes   male    no 17    no 6.34036
## 3693   7  35      no   0   yes   no     yes   male    no 17    no 6.48768
## 3694   8  37      no   0   yes   no     yes   male    no 17    no 6.57786
## 3695   9  35      no   0   yes   no     yes   male    no 17    no 6.62007
## 3696  10  37      no   0   yes   no     yes   male    no 17    no 6.85646
## 3697  33  44      no   0    no  yes     yes   male    no 12    no 6.90575
## 3698  34  47      no   0    no  yes     yes   male    no 12    no 6.90575
## 3699  35  47      no   0    no  yes     yes   male    no 12    no 7.06048
## 3700  36  47      no   0    no  yes     yes   male   yes 12    no 7.09589
## 3701  37  45      no   0    no  yes     yes   male   yes 12    no 6.93342
## 3702  38  47      no   0    no  yes     yes   male    no 12    no 7.46737
## 3703  39  50      no   0    no  yes     yes   male    no 12    no 7.37776
## 3704   8  50      no   1    no  yes     yes   male    no 17    no 6.90575
## 3705   9  48      no   1    no  yes     yes   male    no 17    no 6.90575
## 3706  10  47      no   1    no  yes     yes   male    no 17    no 7.12930
## 3707  11  44      no   1    no  yes     yes   male    no 17    no 7.17012
## 3708  12  46      no   1    no  yes     yes   male    no 17    no 7.27031
## 3709  13  47      no   1    no  yes     yes   male    no 17    no 7.45991
## 3710  14  46      no   1    no  yes     yes   male    no 17    no 7.45703
## 3711   2  49      no   0    no  yes     yes   male    no 16    no 6.57647
## 3712   3  49      no   0    no  yes     yes   male    no 16    no 6.77422
## 3713   4  50      no   0    no  yes     yes   male    no 16    no 6.88244
## 3714   5  49      no   0    no  yes     yes   male    no 16    no 7.09008
## 3715   6  48      no   0    no  yes     yes   male    no 16    no 7.20786
## 3716   7  48      no   0    no  yes     yes   male    no 16    no 7.49554
## 3717   8  46      no   0    no  yes     yes   male    no 16    no 7.60090
## 3718   5  29     yes   0   yes   no     yes   male    no 12    no 5.73657
## 3719   6  49     yes   0   yes   no     yes   male    no 12    no 5.96615
## 3720   7  51     yes   0   yes   no     yes   male    no 12    no 6.07535
## 3721   8  49     yes   0   yes   no     yes   male    no 12    no 6.15698
## 3722   9  50     yes   0   yes   no     yes   male    no 12    no 6.26340
## 3723  10  46     yes   0   yes   no     yes   male    no 12    no 6.34739
## 3724  11  49     yes   0   yes   no     yes   male    no 12    no 6.44572
## 3725  32  50      no   0    no   no     yes   male    no 13    no 6.29157
## 3726  33  50      no   0    no   no     yes   male    no 13    no 6.39526
## 3727  34  48      no   0    no   no     yes   male    no 13    no 6.39693
## 3728  35  48      no   0    no   no     yes   male    no 13    no 6.39693
## 3729  36  49      no   0    no   no     yes   male    no 13    no 6.49072
## 3730  37  48      no   0    no   no     yes   male    no 13    no 6.59030
## 3731  38  49      no   0    no   no     yes   male    no 13    no 6.61740
## 3732   5  51      no   1   yes   no     yes   male    no 12    no 5.88610
## 3733   6  48      no   1   yes   no     yes   male    no 12    no 5.98394
## 3734   7  51     yes   1   yes   no     yes   male    no 12    no 5.98394
## 3735   8  51     yes   1   yes   no     yes   male    no 12    no 6.19848
## 3736   9  51     yes   1   yes   no     yes   male    no 12    no 5.78996
## 3737  10  50     yes   1   yes   no     yes   male    no 12    no 6.01127
## 3738  11  51     yes   1   yes   no     yes   male    no 12    no 6.11147
## 3739   9  51     yes   0   yes   no     yes   male    no 12    no 5.57973
## 3740  10  50     yes   0   yes   no     yes   male    no 12    no 5.66988
## 3741  11  51     yes   0   yes   no     yes   male    no 12    no 5.70378
## 3742  12  50     yes   0   yes   no     yes   male    no 12    no 5.82895
## 3743  13  49     yes   0   yes   no     yes   male    no 12    no 5.99146
## 3744  14  51     yes   0   yes   no     yes   male    no 12    no 6.07535
## 3745  15  50     yes   0   yes   no     yes   male    no 12    no 6.14204
## 3746   7  51      no   0    no  yes      no   male    no 17    no 6.69456
## 3747   8  51      no   0    no  yes      no   male    no 17    no 6.72743
## 3748   9  49      no   0    no  yes      no   male    no 17    no 6.85330
## 3749  10  50      no   0    no  yes      no   male    no 17    no 6.89669
## 3750  11  50      no   0    no  yes     yes   male    no 17    no 7.13090
## 3751  12  51      no   0    no  yes     yes   male    no 17    no 6.96508
## 3752  13  49      no   0    no  yes     yes   male    no 17    no 7.15462
## 3753   7  48      no   0    no  yes     yes   male    no 16    no 6.03787
## 3754   8  50      no   0    no  yes     yes   male    no 16    no 6.55108
## 3755   9  50      no   0    no  yes     yes   male    no 16    no 6.65673
## 3756  10  50      no   0    no  yes     yes   male    no 16    no 6.85646
## 3757  11  50      no   0    no  yes     yes   male    no 16    no 7.09008
## 3758  12  49      no   0   yes  yes     yes   male    no 16    no 6.74406
## 3759  13  49      no   0   yes  yes     yes   male    no 16    no 6.99485
## 3760  10  48      no   1    no  yes     yes   male    no 16    no 6.62007
## 3761  11  51      no   1    no  yes     yes   male    no 16    no 6.77422
## 3762  12  50      no   1    no  yes     yes   male    no 16    no 6.77422
## 3763  13  47      no   1    no  yes     yes   male    no 16    no 6.90776
## 3764  14  51      no   1    no  yes     yes   male    no 16    no 7.01481
## 3765  15  50      no   1    no  yes     yes   male    no 16    no 7.06219
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## 4035  12  52     yes   0    no   no     yes   male    no 12    no 6.10925
## 4036  13  50     yes   0    no   no     yes   male    no 12    no 6.21461
## 4037  14  51     yes   0    no   no     yes   male    no 12    no 6.26340
## 4038  15  51     yes   0    no   no     yes   male    no 12    no 6.39693
## 4039  16  50     yes   0    no   no     yes   male    no 12    no 6.55108
## 4040   6  40     yes   1    no   no     yes   male    no 13    no 6.39359
## 4041   7  49     yes   1    no   no     yes   male    no 13    no 6.46147
## 4042   8  49     yes   1    no   no     yes   male    no 13    no 6.44889
## 4043   9  49     yes   1    no   no     yes   male    no 13    no 6.63726
## 4044  10  50     yes   1    no   no     yes   male    no 13    no 6.75926
## 4045  11  46     yes   1    no   no     yes   male    no 13    no 6.83518
## 4046  12  45     yes   1    no   no     yes   male    no 13    no 6.91968
## 4047   3  51      no   0   yes  yes      no female    no 16    no 5.79606
## 4048   4  50      no   0   yes  yes      no female    no 16    no 5.92693
## 4049   5  50      no   0   yes  yes      no female    no 16    no 5.96615
## 4050   6  50      no   0   yes  yes      no female    no 16    no 6.17379
## 4051   7  47      no   0   yes  yes      no female    no 16    no 6.47697
## 4052   8  50      no   0   yes  yes      no female    no 16    no 6.70073
## 4053   9  51      no   0   yes  yes      no female    no 16    no 6.71296
## 4054   5  51     yes   1    no  yes     yes   male   yes 12    no 6.29157
## 4055   6  42     yes   1    no  yes     yes   male   yes 12    no 6.38856
## 4056   7  48     yes   1    no  yes     yes   male   yes 12    no 6.46147
## 4057   8  47     yes   1    no  yes     yes   male   yes 12    no 6.57925
## 4058   9  49     yes   1    no  yes     yes   male   yes 12    no 6.60665
## 4059  10  48     yes   0    no  yes     yes   male   yes 12    no 6.71538
## 4060  11  46     yes   1    no  yes     yes   male    no 12    no 6.99393
## 4061   8  39      no   0    no  yes     yes   male   yes 17    no 6.77422
## 4062   9  40      no   0    no  yes     yes   male   yes 17    no 6.77422
## 4063  10  41      no   0    no  yes     yes   male   yes 17    no 6.89264
## 4064  11  34      no   0    no   no     yes   male   yes 17    no 6.95655
## 4065  12  50      no   0    no  yes     yes   male   yes 17    no 6.95655
## 4066  13  40      no   0    no  yes     yes   male   yes 17    no 7.18917
## 4067  14  38      no   0    no  yes     yes   male   yes 17    no 7.28619
## 4068   2  47     yes   0    no  yes      no   male    no 12    no 5.70378
## 4069   3  31     yes   0    no  yes      no   male    no 12    no 6.11810
## 4070   4  45     yes   0    no  yes      no   male    no 12    no 6.39693
## 4071   5  51     yes   0    no  yes      no   male    no 12    no 6.72743
## 4072   6  49     yes   0    no  yes      no   male    no 12    no 6.78784
## 4073   7  50     yes   0    no  yes      no   male    no 12    no 6.91771
## 4074   8  51     yes   0    no  yes      no   male    no 12    no 6.96224
## 4075   7  50     yes   1    no   no     yes   male    no 12    no 6.29342
## 4076   8  50     yes   1    no   no     yes   male    no 12    no 6.51323
## 4077   9  46     yes   1    no   no     yes   male    no 12    no 6.64898
## 4078  10  47     yes   1    no   no     yes   male    no 12    no 6.88346
## 4079  11  43     yes   1    no   no     yes   male    no 12    no 7.04752
## 4080  12  44     yes   1    no   no     yes   male    no 12    no 7.12930
## 4081  13  47     yes   1    no   no     yes   male    no 12    no 7.16858
## 4082   5  52     yes   0    no  yes     yes   male    no 12    no 6.21461
## 4083   6  51     yes   0    no  yes     yes   male    no 12    no 6.30992
## 4084   7  49     yes   0    no  yes     yes   male    no 12    no 6.65286
## 4085   8  50     yes   0    no  yes     yes   male    no 12    no 6.53233
## 4086   9  49     yes   0    no  yes     yes   male    no 12    no 6.60259
## 4087  10  50     yes   0    no  yes     yes   male    no 12    no 6.70073
## 4088  11  50     yes   0    no  yes     yes   male    no 12    no 6.65286
## 4089   5  50      no   0    no  yes     yes   male    no 16    no 6.55108
## 4090   6  51      no   0    no  yes     yes   male    no 16    no 6.58617
## 4091   7  48      no   0    no  yes     yes   male    no 16    no 6.68461
## 4092   8  51      no   0    no  yes     yes   male    no 16    no 6.77992
## 4093   9  48      no   0    no  yes     yes   male    no 16    no 6.90776
## 4094  10  50      no   0    no  yes     yes   male    no 16    no 7.05704
## 4095  11  49      no   0    no  yes     yes   male    no 16    no 7.02731
## 4096  14  51     yes   1   yes   no     yes   male    no 10    no 5.68698
## 4097  15  51     yes   1   yes   no     yes   male    no 10    no 5.70378
## 4098  16  51     yes   1   yes   no     yes   male    no 10    no 5.84354
## 4099  17  51     yes   1   yes   no     yes   male    no 10    no 5.99146
## 4100  18  51     yes   1   yes   no     yes   male    no 10    no 6.06379
## 4101  19  50     yes   1   yes   no     yes   male    no 10    no 6.10925
## 4102  20  30     yes   1   yes   no     yes   male    no 10    no 5.99146
## 4103  12  50     yes   0    no  yes     yes   male   yes 12   yes 6.61874
## 4104  13  50     yes   0    no  yes     yes   male   yes 12   yes 6.70319
## 4105  14  49     yes   0    no  yes     yes   male   yes 12   yes 6.78897
## 4106  15  49     yes   0    no  yes     yes   male   yes 12   yes 6.88449
## 4107  16  48     yes   0    no  yes     yes   male   yes 12   yes 7.07834
## 4108  17  48     yes   0    no  yes     yes   male   yes 12   yes 7.11883
## 4109  18  48     yes   0    no  yes     yes   male   yes 12   yes 7.17931
## 4110   1  51      no   0   yes   no     yes   male    no 16    no 5.43808
## 4111   2  50      no   0   yes  yes     yes   male    no 16    no 5.92693
## 4112   3  49      no   0   yes  yes     yes   male    no 16    no 6.05209
## 4113   4  49      no   0   yes  yes     yes   male    no 16    no 6.10702
## 4114   5  49      no   0   yes  yes     yes   male    no 16    no 6.57786
## 4115   6  50      no   0   yes  yes     yes   male    no 16    no 6.35611
## 4116   7  50      no   0   yes  yes     yes   male    no 16    no 6.80239
## 4117  31  48     yes   0    no  yes     yes   male   yes 12    no 6.66696
## 4118  32  47     yes   0    no  yes     yes   male   yes 12    no 6.73697
## 4119  33  46     yes   0    no  yes     yes   male   yes 12    no 6.80461
## 4120  34  47     yes   0    no  yes     yes   male   yes 12    no 6.87523
## 4121  35  47     yes   0    no  yes     yes   male   yes 12    no 6.95081
## 4122  36  46     yes   0    no  yes     yes   male   yes 12    no 7.07834
## 4123  37  46     yes   0    no  yes     yes   male   yes 12    no 7.17012
## 4124   3  44     yes   1    no  yes     yes   male   yes 12    no 6.33683
## 4125   4  45     yes   1    no  yes     yes   male   yes 12    no 6.53379
## 4126   5  44     yes   1    no  yes     yes   male   yes 12    no 6.62007
## 4127   6  43     yes   1    no  yes     yes   male   yes 12    no 6.59304
## 4128   7  44     yes   1    no  yes     yes   male   yes 12    no 6.81124
## 4129   8  43     yes   1    no  yes     yes   male   yes 12    no 6.81344
## 4130   9  44     yes   1    no  yes     yes   male   yes 12    no 6.87005
## 4131  34  46     yes   1    no  yes     yes   male   yes  8    no 6.46459
## 4132  35  46     yes   1    no  yes     yes   male   yes  8    no 6.47697
## 4133  36  42     yes   1    no  yes     yes   male   yes  8    no 6.60935
## 4134  37  38     yes   1    no  yes     yes   male   yes  8    no 6.55108
## 4135  38  46     yes   1    no  yes     yes   male   yes  8    no 6.77079
## 4136  39  45     yes   1    no  yes     yes   male   yes  8    no 6.85646
## 4137  40  46     yes   1    no  yes     yes   male   yes  8    no 6.85646
## 4138   6  15     yes   1    no  yes     yes   male   yes 13    no 6.49979
## 4139   7  47     yes   1    no  yes     yes   male    no 13    no 6.51619
## 4140   8  49     yes   1    no  yes     yes   male   yes 13    no 6.65157
## 4141   9  47     yes   1    no  yes     yes   male   yes 13    no 6.76849
## 4142  10  50     yes   1    no  yes     yes   male   yes 13    no 6.83841
## 4143  11  49     yes   1    no  yes     yes   male   yes 13    no 6.86797
## 4144  12  47     yes   1    no  yes     yes   male   yes 13    no 7.06133
## 4145  10  39     yes   0   yes   no      no   male    no  8   yes 5.29832
## 4146  11  48     yes   0   yes   no      no   male    no  8   yes 5.41610
## 4147  12  40     yes   0   yes   no      no   male    no  8   yes 5.41610
## 4148  13  29     yes   0   yes   no      no   male    no  8   yes 5.41610
## 4149  14  40     yes   0   yes   no      no   male    no  8   yes 5.70378
## 4150  15  48     yes   0   yes   no      no   male    no  8   yes 5.70378
## 4151  16  40     yes   0   yes   no      no   male    no  8   yes 5.67675
## 4152   7  49     yes   1    no  yes     yes   male   yes 12    no 6.42487
## 4153   8  48     yes   1    no  yes     yes   male   yes 12    no 6.48004
## 4154   9  48     yes   1    no  yes     yes   male   yes 12    no 6.57368
## 4155  10  48     yes   1    no  yes     yes   male   yes 12    no 6.69084
## 4156  11  45     yes   1    no  yes     yes   male   yes 12    no 6.78672
## 4157  12  49     yes   1    no  yes     yes   male   yes 12    no 6.91968
## 4158  13  47     yes   1    no  yes     yes   male   yes 12    no 7.04752
## 4159   1  52      no   0    no  yes      no female    no 12    no 5.68698
## 4160   2  50      no   0    no  yes      no female    no 12    no 5.85793
## 4161   3  50      no   0    no  yes      no female    no 12    no 5.95324
## 4162   4  49      no   0    no  yes      no female    no 12    no 6.06379
## 4163   5  50      no   0    no  yes      no female    no 12    no 6.21461
## 4164   6  50      no   0    no  yes      no female    no 12    no 6.29157
## 4165   7  50      no   0    no  yes      no female    no 12    no 6.37161
##      WageLevel
## 1          Low
## 2          Low
## 3          Low
## 4          Low
## 5          Low
## 6          Low
## 7          Low
## 8          Low
## 9          Low
## 10         Low
## 11      Normal
## 12      Normal
## 13      Normal
## 14      Normal
## 15         Low
## 16      Normal
## 17      Normal
## 18      Normal
## 19      Normal
## 20      Normal
## 21      Normal
## 22         Low
## 23         Low
## 24         Low
## 25         Low
## 26      Normal
## 27      Normal
## 28      Normal
## 29      Normal
## 30      Normal
## 31      Normal
## 32      Normal
## 33   High Wage
## 34   High Wage
## 35   High Wage
## 36      Normal
## 37      Normal
## 38      Normal
## 39   High Wage
## 40   High Wage
## 41   High Wage
## 42   High Wage
## 43         Low
## 44         Low
## 45         Low
## 46         Low
## 47         Low
## 48      Normal
## 49      Normal
## 50         Low
## 51      Normal
## 52      Normal
## 53      Normal
## 54      Normal
## 55      Normal
## 56      Normal
## 57      Normal
## 58      Normal
## 59      Normal
## 60      Normal
## 61   High Wage
## 62   High Wage
## 63   High Wage
## 64         Low
## 65      Normal
## 66      Normal
## 67      Normal
## 68      Normal
## 69      Normal
## 70      Normal
## 71      Normal
## 72      Normal
## 73      Normal
## 74      Normal
## 75   High Wage
## 76   High Wage
## 77   High Wage
## 78      Normal
## 79      Normal
## 80      Normal
## 81      Normal
## 82      Normal
## 83      Normal
## 84   High Wage
## 85      Normal
## 86      Normal
## 87   High Wage
## 88   High Wage
## 89   High Wage
## 90   High Wage
## 91   High Wage
## 92      Normal
## 93      Normal
## 94      Normal
## 95   High Wage
## 96   High Wage
## 97   High Wage
## 98   High Wage
## 99         Low
## 100        Low
## 101        Low
## 102        Low
## 103        Low
## 104     Normal
## 105     Normal
## 106        Low
## 107        Low
## 108        Low
## 109        Low
## 110        Low
## 111        Low
## 112        Low
## 113     Normal
## 114     Normal
## 115     Normal
## 116     Normal
## 117  High Wage
## 118  High Wage
## 119  High Wage
## 120     Normal
## 121     Normal
## 122  High Wage
## 123  High Wage
## 124  High Wage
## 125  High Wage
## 126  High Wage
## 127        Low
## 128     Normal
## 129     Normal
## 130     Normal
## 131     Normal
## 132     Normal
## 133     Normal
## 134     Normal
## 135     Normal
## 136     Normal
## 137  High Wage
## 138  High Wage
## 139  High Wage
## 140  High Wage
## 141        Low
## 142        Low
## 143        Low
## 144        Low
## 145        Low
## 146     Normal
## 147     Normal
## 148     Normal
## 149     Normal
## 150     Normal
## 151     Normal
## 152     Normal
## 153     Normal
## 154  High Wage
## 155     Normal
## 156     Normal
## 157  High Wage
## 158  High Wage
## 159  High Wage
## 160  High Wage
## 161  High Wage
## 162        Low
## 163        Low
## 164        Low
## 165        Low
## 166        Low
## 167        Low
## 168        Low
## 169     Normal
## 170     Normal
## 171     Normal
## 172     Normal
## 173     Normal
## 174     Normal
## 175     Normal
## 176     Normal
## 177     Normal
## 178     Normal
## 179     Normal
## 180  High Wage
## 181  High Wage
## 182  High Wage
## 183        Low
## 184     Normal
## 185  High Wage
## 186  High Wage
## 187  High Wage
## 188     Normal
## 189  High Wage
## 190     Normal
## 191     Normal
## 192     Normal
## 193     Normal
## 194     Normal
## 195     Normal
## 196     Normal
## 197     Normal
## 198     Normal
## 199  High Wage
## 200  High Wage
## 201  High Wage
## 202  High Wage
## 203  High Wage
## 204        Low
## 205        Low
## 206        Low
## 207        Low
## 208     Normal
## 209     Normal
## 210     Normal
## 211     Normal
## 212     Normal
## 213  High Wage
## 214  High Wage
## 215  High Wage
## 216  High Wage
## 217  High Wage
## 218     Normal
## 219     Normal
## 220  High Wage
## 221  High Wage
## 222  High Wage
## 223  High Wage
## 224  High Wage
## 225     Normal
## 226     Normal
## 227  High Wage
## 228  High Wage
## 229  High Wage
## 230  High Wage
## 231  High Wage
## 232        Low
## 233        Low
## 234        Low
## 235        Low
## 236        Low
## 237        Low
## 238        Low
## 239     Normal
## 240     Normal
## 241        Low
## 242     Normal
## 243     Normal
## 244  High Wage
## 245  High Wage
## 246     Normal
## 247     Normal
## 248  High Wage
## 249  High Wage
## 250  High Wage
## 251     Normal
## 252  High Wage
## 253     Normal
## 254     Normal
## 255  High Wage
## 256  High Wage
## 257  High Wage
## 258  High Wage
## 259  High Wage
## 260        Low
## 261        Low
## 262        Low
## 263        Low
## 264     Normal
## 265     Normal
## 266     Normal
## 267     Normal
## 268     Normal
## 269     Normal
## 270     Normal
## 271     Normal
## 272     Normal
## 273     Normal
## 274        Low
## 275     Normal
## 276     Normal
## 277     Normal
## 278     Normal
## 279     Normal
## 280  High Wage
## 281     Normal
## 282     Normal
## 283  High Wage
## 284  High Wage
## 285  High Wage
## 286  High Wage
## 287  High Wage
## 288        Low
## 289     Normal
## 290     Normal
## 291     Normal
## 292     Normal
## 293     Normal
## 294  High Wage
## 295     Normal
## 296     Normal
## 297     Normal
## 298  High Wage
## 299  High Wage
## 300  High Wage
## 301  High Wage
## 302     Normal
## 303     Normal
## 304  High Wage
## 305  High Wage
## 306  High Wage
## 307  High Wage
## 308  High Wage
## 309        Low
## 310        Low
## 311        Low
## 312     Normal
## 313     Normal
## 314     Normal
## 315     Normal
## 316        Low
## 317        Low
## 318        Low
## 319        Low
## 320     Normal
## 321     Normal
## 322     Normal
## 323     Normal
## 324     Normal
## 325  High Wage
## 326  High Wage
## 327  High Wage
## 328  High Wage
## 329  High Wage
## 330     Normal
## 331     Normal
## 332  High Wage
## 333  High Wage
## 334  High Wage
## 335  High Wage
## 336  High Wage
## 337     Normal
## 338     Normal
## 339  High Wage
## 340  High Wage
## 341  High Wage
## 342  High Wage
## 343  High Wage
## 344        Low
## 345        Low
## 346     Normal
## 347     Normal
## 348     Normal
## 349     Normal
## 350     Normal
## 351     Normal
## 352     Normal
## 353  High Wage
## 354  High Wage
## 355  High Wage
## 356  High Wage
## 357  High Wage
## 358     Normal
## 359     Normal
## 360  High Wage
## 361  High Wage
## 362  High Wage
## 363  High Wage
## 364  High Wage
## 365     Normal
## 366     Normal
## 367     Normal
## 368     Normal
## 369  High Wage
## 370  High Wage
## 371  High Wage
## 372     Normal
## 373     Normal
## 374     Normal
## 375     Normal
## 376     Normal
## 377  High Wage
## 378  High Wage
## 379     Normal
## 380     Normal
## 381     Normal
## 382     Normal
## 383  High Wage
## 384  High Wage
## 385  High Wage
## 386        Low
## 387        Low
## 388        Low
## 389        Low
## 390     Normal
## 391     Normal
## 392     Normal
## 393        Low
## 394        Low
## 395        Low
## 396     Normal
## 397     Normal
## 398     Normal
## 399        Low
## 400     Normal
## 401     Normal
## 402     Normal
## 403     Normal
## 404  High Wage
## 405  High Wage
## 406  High Wage
## 407     Normal
## 408     Normal
## 409  High Wage
## 410  High Wage
## 411  High Wage
## 412  High Wage
## 413  High Wage
## 414        Low
## 415        Low
## 416        Low
## 417        Low
## 418        Low
## 419        Low
## 420        Low
## 421     Normal
## 422     Normal
## 423     Normal
## 424     Normal
## 425     Normal
## 426     Normal
## 427  High Wage
## 428     Normal
## 429     Normal
## 430     Normal
## 431     Normal
## 432     Normal
## 433  High Wage
## 434  High Wage
## 435     Normal
## 436     Normal
## 437  High Wage
## 438  High Wage
## 439  High Wage
## 440  High Wage
## 441  High Wage
## 442        Low
## 443     Normal
## 444     Normal
## 445     Normal
## 446     Normal
## 447     Normal
## 448     Normal
## 449     Normal
## 450     Normal
## 451     Normal
## 452     Normal
## 453     Normal
## 454  High Wage
## 455  High Wage
## 456        Low
## 457        Low
## 458     Normal
## 459     Normal
## 460     Normal
## 461     Normal
## 462     Normal
## 463        Low
## 464        Low
## 465        Low
## 466        Low
## 467        Low
## 468     Normal
## 469     Normal
## 470     Normal
## 471     Normal
## 472     Normal
## 473     Normal
## 474     Normal
## 475     Normal
## 476     Normal
## 477     Normal
## 478     Normal
## 479     Normal
## 480     Normal
## 481     Normal
## 482     Normal
## 483     Normal
## 484     Normal
## 485     Normal
## 486     Normal
## 487     Normal
## 488     Normal
## 489     Normal
## 490  High Wage
## 491     Normal
## 492     Normal
## 493     Normal
## 494     Normal
## 495  High Wage
## 496  High Wage
## 497  High Wage
## 498     Normal
## 499     Normal
## 500     Normal
## 501     Normal
## 502     Normal
## 503     Normal
## 504  High Wage
## 505     Normal
## 506     Normal
## 507     Normal
## 508     Normal
## 509     Normal
## 510     Normal
## 511  High Wage
## 512        Low
## 513        Low
## 514        Low
## 515        Low
## 516        Low
## 517        Low
## 518        Low
## 519        Low
## 520        Low
## 521        Low
## 522        Low
## 523        Low
## 524     Normal
## 525     Normal
## 526        Low
## 527        Low
## 528        Low
## 529        Low
## 530        Low
## 531        Low
## 532        Low
## 533        Low
## 534        Low
## 535        Low
## 536        Low
## 537        Low
## 538        Low
## 539        Low
## 540        Low
## 541        Low
## 542        Low
## 543        Low
## 544        Low
## 545        Low
## 546        Low
## 547        Low
## 548        Low
## 549        Low
## 550        Low
## 551        Low
## 552        Low
## 553        Low
## 554     Normal
## 555     Normal
## 556     Normal
## 557  High Wage
## 558  High Wage
## 559     Normal
## 560  High Wage
## 561        Low
## 562        Low
## 563     Normal
## 564        Low
## 565  High Wage
## 566  High Wage
## 567  High Wage
## 568     Normal
## 569     Normal
## 570     Normal
## 571     Normal
## 572     Normal
## 573     Normal
## 574  High Wage
## 575        Low
## 576        Low
## 577        Low
## 578        Low
## 579     Normal
## 580     Normal
## 581     Normal
## 582     Normal
## 583     Normal
## 584     Normal
## 585     Normal
## 586     Normal
## 587     Normal
## 588     Normal
## 589        Low
## 590        Low
## 591        Low
## 592     Normal
## 593     Normal
## 594     Normal
## 595     Normal
## 596        Low
## 597     Normal
## 598     Normal
## 599     Normal
## 600     Normal
## 601     Normal
## 602     Normal
## 603     Normal
## 604     Normal
## 605     Normal
## 606     Normal
## 607     Normal
## 608  High Wage
## 609  High Wage
## 610        Low
## 611        Low
## 612     Normal
## 613     Normal
## 614     Normal
## 615  High Wage
## 616  High Wage
## 617        Low
## 618        Low
## 619        Low
## 620        Low
## 621     Normal
## 622     Normal
## 623     Normal
## 624        Low
## 625        Low
## 626        Low
## 627        Low
## 628        Low
## 629        Low
## 630     Normal
## 631        Low
## 632     Normal
## 633     Normal
## 634     Normal
## 635     Normal
## 636  High Wage
## 637  High Wage
## 638     Normal
## 639     Normal
## 640     Normal
## 641     Normal
## 642     Normal
## 643     Normal
## 644     Normal
## 645        Low
## 646        Low
## 647        Low
## 648        Low
## 649     Normal
## 650     Normal
## 651     Normal
## 652     Normal
## 653     Normal
## 654     Normal
## 655     Normal
## 656  High Wage
## 657  High Wage
## 658  High Wage
## 659        Low
## 660        Low
## 661     Normal
## 662     Normal
## 663     Normal
## 664     Normal
## 665     Normal
## 666     Normal
## 667     Normal
## 668  High Wage
## 669  High Wage
## 670  High Wage
## 671  High Wage
## 672  High Wage
## 673        Low
## 674        Low
## 675        Low
## 676     Normal
## 677     Normal
## 678     Normal
## 679     Normal
## 680     Normal
## 681     Normal
## 682     Normal
## 683  High Wage
## 684  High Wage
## 685  High Wage
## 686  High Wage
## 687        Low
## 688        Low
## 689        Low
## 690        Low
## 691        Low
## 692        Low
## 693        Low
## 694        Low
## 695        Low
## 696        Low
## 697        Low
## 698     Normal
## 699     Normal
## 700     Normal
## 701     Normal
## 702     Normal
## 703     Normal
## 704     Normal
## 705     Normal
## 706  High Wage
## 707  High Wage
## 708     Normal
## 709     Normal
## 710     Normal
## 711  High Wage
## 712  High Wage
## 713  High Wage
## 714  High Wage
## 715        Low
## 716     Normal
## 717     Normal
## 718     Normal
## 719     Normal
## 720  High Wage
## 721     Normal
## 722        Low
## 723        Low
## 724        Low
## 725        Low
## 726        Low
## 727        Low
## 728        Low
## 729     Normal
## 730     Normal
## 731     Normal
## 732     Normal
## 733     Normal
## 734  High Wage
## 735  High Wage
## 736        Low
## 737     Normal
## 738     Normal
## 739     Normal
## 740     Normal
## 741     Normal
## 742     Normal
## 743     Normal
## 744     Normal
## 745  High Wage
## 746  High Wage
## 747  High Wage
## 748  High Wage
## 749  High Wage
## 750        Low
## 751        Low
## 752     Normal
## 753     Normal
## 754     Normal
## 755     Normal
## 756  High Wage
## 757     Normal
## 758     Normal
## 759     Normal
## 760  High Wage
## 761  High Wage
## 762  High Wage
## 763  High Wage
## 764     Normal
## 765     Normal
## 766     Normal
## 767     Normal
## 768  High Wage
## 769     Normal
## 770     Normal
## 771        Low
## 772        Low
## 773     Normal
## 774     Normal
## 775     Normal
## 776     Normal
## 777     Normal
## 778     Normal
## 779     Normal
## 780  High Wage
## 781  High Wage
## 782  High Wage
## 783  High Wage
## 784  High Wage
## 785     Normal
## 786     Normal
## 787  High Wage
## 788  High Wage
## 789  High Wage
## 790  High Wage
## 791  High Wage
## 792        Low
## 793        Low
## 794     Normal
## 795     Normal
## 796     Normal
## 797        Low
## 798     Normal
## 799     Normal
## 800     Normal
## 801     Normal
## 802  High Wage
## 803  High Wage
## 804  High Wage
## 805  High Wage
## 806     Normal
## 807     Normal
## 808     Normal
## 809     Normal
## 810  High Wage
## 811  High Wage
## 812  High Wage
## 813     Normal
## 814        Low
## 815     Normal
## 816     Normal
## 817     Normal
## 818     Normal
## 819  High Wage
## 820     Normal
## 821     Normal
## 822     Normal
## 823     Normal
## 824     Normal
## 825     Normal
## 826     Normal
## 827     Normal
## 828     Normal
## 829  High Wage
## 830  High Wage
## 831  High Wage
## 832  High Wage
## 833  High Wage
## 834        Low
## 835        Low
## 836     Normal
## 837     Normal
## 838     Normal
## 839     Normal
## 840     Normal
## 841     Normal
## 842     Normal
## 843  High Wage
## 844  High Wage
## 845  High Wage
## 846  High Wage
## 847  High Wage
## 848     Normal
## 849     Normal
## 850     Normal
## 851     Normal
## 852     Normal
## 853  High Wage
## 854  High Wage
## 855        Low
## 856     Normal
## 857     Normal
## 858     Normal
## 859     Normal
## 860     Normal
## 861  High Wage
## 862     Normal
## 863     Normal
## 864  High Wage
## 865  High Wage
## 866  High Wage
## 867  High Wage
## 868  High Wage
## 869        Low
## 870        Low
## 871        Low
## 872     Normal
## 873     Normal
## 874     Normal
## 875     Normal
## 876     Normal
## 877     Normal
## 878     Normal
## 879     Normal
## 880     Normal
## 881     Normal
## 882        Low
## 883     Normal
## 884     Normal
## 885  High Wage
## 886  High Wage
## 887  High Wage
## 888  High Wage
## 889  High Wage
## 890        Low
## 891        Low
## 892        Low
## 893     Normal
## 894     Normal
## 895     Normal
## 896     Normal
## 897        Low
## 898        Low
## 899        Low
## 900        Low
## 901        Low
## 902     Normal
## 903     Normal
## 904     Normal
## 905     Normal
## 906     Normal
## 907     Normal
## 908     Normal
## 909     Normal
## 910  High Wage
## 911     Normal
## 912     Normal
## 913     Normal
## 914     Normal
## 915     Normal
## 916     Normal
## 917  High Wage
## 918     Normal
## 919     Normal
## 920  High Wage
## 921  High Wage
## 922  High Wage
## 923  High Wage
## 924  High Wage
## 925        Low
## 926     Normal
## 927     Normal
## 928     Normal
## 929     Normal
## 930     Normal
## 931  High Wage
## 932        Low
## 933        Low
## 934        Low
## 935        Low
## 936        Low
## 937        Low
## 938     Normal
## 939     Normal
## 940     Normal
## 941  High Wage
## 942     Normal
## 943  High Wage
## 944  High Wage
## 945  High Wage
## 946     Normal
## 947     Normal
## 948  High Wage
## 949  High Wage
## 950  High Wage
## 951  High Wage
## 952  High Wage
## 953     Normal
## 954     Normal
## 955     Normal
## 956     Normal
## 957     Normal
## 958  High Wage
## 959  High Wage
## 960     Normal
## 961     Normal
## 962  High Wage
## 963  High Wage
## 964  High Wage
## 965  High Wage
## 966  High Wage
## 967     Normal
## 968     Normal
## 969     Normal
## 970     Normal
## 971  High Wage
## 972  High Wage
## 973  High Wage
## 974        Low
## 975        Low
## 976        Low
## 977     Normal
## 978     Normal
## 979     Normal
## 980  High Wage
## 981        Low
## 982        Low
## 983        Low
## 984        Low
## 985        Low
## 986     Normal
## 987     Normal
## 988     Normal
## 989     Normal
## 990     Normal
## 991     Normal
## 992     Normal
## 993     Normal
## 994  High Wage
## 995        Low
## 996     Normal
## 997     Normal
## 998     Normal
## 999     Normal
## 1000    Normal
## 1001    Normal
## 1002       Low
## 1003       Low
## 1004       Low
## 1005    Normal
## 1006    Normal
## 1007    Normal
## 1008 High Wage
## 1009    Normal
## 1010    Normal
## 1011 High Wage
## 1012 High Wage
## 1013    Normal
## 1014 High Wage
## 1015 High Wage
## 1016    Normal
## 1017    Normal
## 1018 High Wage
## 1019 High Wage
## 1020 High Wage
## 1021 High Wage
## 1022 High Wage
## 1023    Normal
## 1024    Normal
## 1025    Normal
## 1026 High Wage
## 1027 High Wage
## 1028 High Wage
## 1029 High Wage
## 1030       Low
## 1031       Low
## 1032       Low
## 1033    Normal
## 1034    Normal
## 1035    Normal
## 1036    Normal
## 1037    Normal
## 1038    Normal
## 1039    Normal
## 1040    Normal
## 1041    Normal
## 1042    Normal
## 1043    Normal
## 1044       Low
## 1045    Normal
## 1046    Normal
## 1047    Normal
## 1048    Normal
## 1049    Normal
## 1050    Normal
## 1051       Low
## 1052    Normal
## 1053    Normal
## 1054    Normal
## 1055    Normal
## 1056    Normal
## 1057    Normal
## 1058       Low
## 1059       Low
## 1060       Low
## 1061       Low
## 1062       Low
## 1063       Low
## 1064       Low
## 1065       Low
## 1066       Low
## 1067       Low
## 1068       Low
## 1069    Normal
## 1070    Normal
## 1071    Normal
## 1072    Normal
## 1073    Normal
## 1074    Normal
## 1075    Normal
## 1076    Normal
## 1077 High Wage
## 1078 High Wage
## 1079    Normal
## 1080    Normal
## 1081    Normal
## 1082 High Wage
## 1083 High Wage
## 1084 High Wage
## 1085 High Wage
## 1086    Normal
## 1087    Normal
## 1088    Normal
## 1089    Normal
## 1090 High Wage
## 1091 High Wage
## 1092 High Wage
## 1093    Normal
## 1094    Normal
## 1095    Normal
## 1096    Normal
## 1097    Normal
## 1098    Normal
## 1099    Normal
## 1100    Normal
## 1101    Normal
## 1102    Normal
## 1103    Normal
## 1104    Normal
## 1105 High Wage
## 1106 High Wage
## 1107    Normal
## 1108    Normal
## 1109    Normal
## 1110    Normal
## 1111    Normal
## 1112    Normal
## 1113    Normal
## 1114    Normal
## 1115    Normal
## 1116    Normal
## 1117    Normal
## 1118    Normal
## 1119 High Wage
## 1120 High Wage
## 1121       Low
## 1122       Low
## 1123       Low
## 1124    Normal
## 1125    Normal
## 1126    Normal
## 1127    Normal
## 1128       Low
## 1129       Low
## 1130       Low
## 1131       Low
## 1132       Low
## 1133    Normal
## 1134    Normal
## 1135       Low
## 1136       Low
## 1137       Low
## 1138       Low
## 1139    Normal
## 1140    Normal
## 1141    Normal
## 1142       Low
## 1143       Low
## 1144       Low
## 1145       Low
## 1146    Normal
## 1147    Normal
## 1148    Normal
## 1149       Low
## 1150       Low
## 1151    Normal
## 1152       Low
## 1153    Normal
## 1154    Normal
## 1155    Normal
## 1156    Normal
## 1157    Normal
## 1158    Normal
## 1159 High Wage
## 1160 High Wage
## 1161 High Wage
## 1162 High Wage
## 1163       Low
## 1164       Low
## 1165       Low
## 1166       Low
## 1167       Low
## 1168       Low
## 1169       Low
## 1170       Low
## 1171    Normal
## 1172    Normal
## 1173    Normal
## 1174 High Wage
## 1175 High Wage
## 1176 High Wage
## 1177    Normal
## 1178    Normal
## 1179 High Wage
## 1180 High Wage
## 1181 High Wage
## 1182 High Wage
## 1183 High Wage
## 1184       Low
## 1185       Low
## 1186       Low
## 1187       Low
## 1188       Low
## 1189       Low
## 1190       Low
## 1191       Low
## 1192       Low
## 1193       Low
## 1194       Low
## 1195       Low
## 1196    Normal
## 1197    Normal
## 1198    Normal
## 1199    Normal
## 1200 High Wage
## 1201 High Wage
## 1202 High Wage
## 1203 High Wage
## 1204 High Wage
## 1205    Normal
## 1206    Normal
## 1207 High Wage
## 1208 High Wage
## 1209 High Wage
## 1210 High Wage
## 1211 High Wage
## 1212       Low
## 1213    Normal
## 1214    Normal
## 1215    Normal
## 1216    Normal
## 1217    Normal
## 1218    Normal
## 1219       Low
## 1220       Low
## 1221       Low
## 1222       Low
## 1223       Low
## 1224       Low
## 1225    Normal
## 1226    Normal
## 1227    Normal
## 1228    Normal
## 1229    Normal
## 1230    Normal
## 1231 High Wage
## 1232 High Wage
## 1233    Normal
## 1234    Normal
## 1235       Low
## 1236    Normal
## 1237       Low
## 1238    Normal
## 1239    Normal
## 1240       Low
## 1241       Low
## 1242       Low
## 1243       Low
## 1244    Normal
## 1245    Normal
## 1246    Normal
## 1247       Low
## 1248       Low
## 1249       Low
## 1250       Low
## 1251       Low
## 1252       Low
## 1253       Low
## 1254       Low
## 1255       Low
## 1256    Normal
## 1257    Normal
## 1258 High Wage
## 1259    Normal
## 1260    Normal
## 1261    Normal
## 1262    Normal
## 1263    Normal
## 1264 High Wage
## 1265 High Wage
## 1266 High Wage
## 1267 High Wage
## 1268       Low
## 1269       Low
## 1270       Low
## 1271       Low
## 1272       Low
## 1273       Low
## 1274       Low
## 1275       Low
## 1276       Low
## 1277       Low
## 1278       Low
## 1279       Low
## 1280       Low
## 1281       Low
## 1282    Normal
## 1283    Normal
## 1284    Normal
## 1285    Normal
## 1286    Normal
## 1287    Normal
## 1288 High Wage
## 1289    Normal
## 1290    Normal
## 1291    Normal
## 1292    Normal
## 1293    Normal
## 1294 High Wage
## 1295 High Wage
## 1296    Normal
## 1297    Normal
## 1298    Normal
## 1299 High Wage
## 1300 High Wage
## 1301 High Wage
## 1302 High Wage
## 1303    Normal
## 1304    Normal
## 1305 High Wage
## 1306 High Wage
## 1307 High Wage
## 1308 High Wage
## 1309 High Wage
## 1310    Normal
## 1311    Normal
## 1312    Normal
## 1313    Normal
## 1314 High Wage
## 1315 High Wage
## 1316 High Wage
## 1317    Normal
## 1318    Normal
## 1319 High Wage
## 1320 High Wage
## 1321 High Wage
## 1322    Normal
## 1323 High Wage
## 1324       Low
## 1325       Low
## 1326    Normal
## 1327    Normal
## 1328    Normal
## 1329    Normal
## 1330    Normal
## 1331       Low
## 1332       Low
## 1333       Low
## 1334       Low
## 1335    Normal
## 1336    Normal
## 1337    Normal
## 1338       Low
## 1339    Normal
## 1340    Normal
## 1341    Normal
## 1342    Normal
## 1343    Normal
## 1344    Normal
## 1345    Normal
## 1346    Normal
## 1347 High Wage
## 1348 High Wage
## 1349 High Wage
## 1350 High Wage
## 1351 High Wage
## 1352    Normal
## 1353    Normal
## 1354    Normal
## 1355    Normal
## 1356    Normal
## 1357    Normal
## 1358    Normal
## 1359    Normal
## 1360    Normal
## 1361    Normal
## 1362    Normal
## 1363    Normal
## 1364    Normal
## 1365    Normal
## 1366       Low
## 1367       Low
## 1368    Normal
## 1369    Normal
## 1370    Normal
## 1371    Normal
## 1372    Normal
## 1373       Low
## 1374       Low
## 1375       Low
## 1376       Low
## 1377       Low
## 1378       Low
## 1379       Low
## 1380    Normal
## 1381    Normal
## 1382    Normal
## 1383    Normal
## 1384 High Wage
## 1385 High Wage
## 1386 High Wage
## 1387       Low
## 1388    Normal
## 1389    Normal
## 1390    Normal
## 1391    Normal
## 1392    Normal
## 1393 High Wage
## 1394       Low
## 1395       Low
## 1396       Low
## 1397       Low
## 1398    Normal
## 1399    Normal
## 1400    Normal
## 1401       Low
## 1402       Low
## 1403       Low
## 1404    Normal
## 1405    Normal
## 1406    Normal
## 1407    Normal
## 1408       Low
## 1409       Low
## 1410       Low
## 1411       Low
## 1412       Low
## 1413       Low
## 1414    Normal
## 1415       Low
## 1416       Low
## 1417       Low
## 1418       Low
## 1419       Low
## 1420       Low
## 1421       Low
## 1422    Normal
## 1423    Normal
## 1424    Normal
## 1425    Normal
## 1426    Normal
## 1427    Normal
## 1428 High Wage
## 1429    Normal
## 1430    Normal
## 1431    Normal
## 1432    Normal
## 1433    Normal
## 1434    Normal
## 1435 High Wage
## 1436    Normal
## 1437    Normal
## 1438 High Wage
## 1439 High Wage
## 1440 High Wage
## 1441 High Wage
## 1442 High Wage
## 1443    Normal
## 1444    Normal
## 1445 High Wage
## 1446 High Wage
## 1447    Normal
## 1448 High Wage
## 1449 High Wage
## 1450       Low
## 1451       Low
## 1452       Low
## 1453       Low
## 1454       Low
## 1455       Low
## 1456       Low
## 1457    Normal
## 1458    Normal
## 1459    Normal
## 1460    Normal
## 1461    Normal
## 1462    Normal
## 1463    Normal
## 1464    Normal
## 1465    Normal
## 1466    Normal
## 1467    Normal
## 1468    Normal
## 1469    Normal
## 1470    Normal
## 1471    Normal
## 1472    Normal
## 1473    Normal
## 1474 High Wage
## 1475 High Wage
## 1476 High Wage
## 1477 High Wage
## 1478    Normal
## 1479    Normal
## 1480 High Wage
## 1481 High Wage
## 1482 High Wage
## 1483 High Wage
## 1484 High Wage
## 1485    Normal
## 1486    Normal
## 1487 High Wage
## 1488 High Wage
## 1489 High Wage
## 1490 High Wage
## 1491 High Wage
## 1492       Low
## 1493       Low
## 1494    Normal
## 1495    Normal
## 1496    Normal
## 1497    Normal
## 1498    Normal
## 1499       Low
## 1500       Low
## 1501       Low
## 1502       Low
## 1503       Low
## 1504       Low
## 1505       Low
## 1506    Normal
## 1507    Normal
## 1508 High Wage
## 1509 High Wage
## 1510 High Wage
## 1511    Normal
## 1512 High Wage
## 1513       Low
## 1514       Low
## 1515       Low
## 1516       Low
## 1517    Normal
## 1518       Low
## 1519    Normal
## 1520       Low
## 1521       Low
## 1522    Normal
## 1523    Normal
## 1524    Normal
## 1525    Normal
## 1526    Normal
## 1527    Normal
## 1528    Normal
## 1529    Normal
## 1530 High Wage
## 1531 High Wage
## 1532 High Wage
## 1533 High Wage
## 1534    Normal
## 1535    Normal
## 1536    Normal
## 1537    Normal
## 1538    Normal
## 1539 High Wage
## 1540 High Wage
## 1541    Normal
## 1542    Normal
## 1543 High Wage
## 1544 High Wage
## 1545 High Wage
## 1546 High Wage
## 1547 High Wage
## 1548       Low
## 1549       Low
## 1550       Low
## 1551       Low
## 1552       Low
## 1553       Low
## 1554       Low
## 1555       Low
## 1556       Low
## 1557       Low
## 1558       Low
## 1559    Normal
## 1560    Normal
## 1561    Normal
## 1562    Normal
## 1563    Normal
## 1564 High Wage
## 1565 High Wage
## 1566 High Wage
## 1567 High Wage
## 1568 High Wage
## 1569       Low
## 1570       Low
## 1571       Low
## 1572    Normal
## 1573    Normal
## 1574    Normal
## 1575    Normal
## 1576       Low
## 1577       Low
## 1578       Low
## 1579       Low
## 1580       Low
## 1581       Low
## 1582       Low
## 1583    Normal
## 1584    Normal
## 1585 High Wage
## 1586 High Wage
## 1587    Normal
## 1588    Normal
## 1589    Normal
## 1590       Low
## 1591    Normal
## 1592    Normal
## 1593    Normal
## 1594 High Wage
## 1595 High Wage
## 1596 High Wage
## 1597    Normal
## 1598    Normal
## 1599    Normal
## 1600    Normal
## 1601    Normal
## 1602    Normal
## 1603    Normal
## 1604       Low
## 1605       Low
## 1606       Low
## 1607    Normal
## 1608    Normal
## 1609    Normal
## 1610    Normal
## 1611    Normal
## 1612    Normal
## 1613 High Wage
## 1614 High Wage
## 1615 High Wage
## 1616 High Wage
## 1617 High Wage
## 1618       Low
## 1619    Normal
## 1620    Normal
## 1621 High Wage
## 1622 High Wage
## 1623 High Wage
## 1624 High Wage
## 1625    Normal
## 1626    Normal
## 1627    Normal
## 1628    Normal
## 1629 High Wage
## 1630 High Wage
## 1631 High Wage
## 1632       Low
## 1633       Low
## 1634       Low
## 1635    Normal
## 1636    Normal
## 1637    Normal
## 1638    Normal
## 1639       Low
## 1640       Low
## 1641       Low
## 1642       Low
## 1643       Low
## 1644       Low
## 1645       Low
## 1646    Normal
## 1647    Normal
## 1648 High Wage
## 1649 High Wage
## 1650 High Wage
## 1651 High Wage
## 1652 High Wage
## 1653       Low
## 1654       Low
## 1655       Low
## 1656       Low
## 1657       Low
## 1658    Normal
## 1659    Normal
## 1660    Normal
## 1661    Normal
## 1662    Normal
## 1663    Normal
## 1664 High Wage
## 1665    Normal
## 1666 High Wage
## 1667    Normal
## 1668    Normal
## 1669 High Wage
## 1670 High Wage
## 1671 High Wage
## 1672 High Wage
## 1673 High Wage
## 1674    Normal
## 1675    Normal
## 1676 High Wage
## 1677 High Wage
## 1678 High Wage
## 1679 High Wage
## 1680 High Wage
## 1681    Normal
## 1682    Normal
## 1683    Normal
## 1684    Normal
## 1685    Normal
## 1686    Normal
## 1687    Normal
## 1688       Low
## 1689       Low
## 1690       Low
## 1691       Low
## 1692       Low
## 1693       Low
## 1694       Low
## 1695    Normal
## 1696    Normal
## 1697 High Wage
## 1698 High Wage
## 1699 High Wage
## 1700 High Wage
## 1701 High Wage
## 1702       Low
## 1703    Normal
## 1704    Normal
## 1705    Normal
## 1706    Normal
## 1707    Normal
## 1708    Normal
## 1709       Low
## 1710    Normal
## 1711    Normal
## 1712    Normal
## 1713    Normal
## 1714    Normal
## 1715    Normal
## 1716    Normal
## 1717       Low
## 1718       Low
## 1719    Normal
## 1720    Normal
## 1721    Normal
## 1722    Normal
## 1723       Low
## 1724       Low
## 1725       Low
## 1726       Low
## 1727       Low
## 1728       Low
## 1729       Low
## 1730       Low
## 1731       Low
## 1732       Low
## 1733       Low
## 1734       Low
## 1735       Low
## 1736       Low
## 1737    Normal
## 1738    Normal
## 1739    Normal
## 1740    Normal
## 1741    Normal
## 1742 High Wage
## 1743 High Wage
## 1744       Low
## 1745       Low
## 1746       Low
## 1747       Low
## 1748       Low
## 1749    Normal
## 1750    Normal
## 1751       Low
## 1752       Low
## 1753    Normal
## 1754       Low
## 1755    Normal
## 1756    Normal
## 1757    Normal
## 1758    Normal
## 1759    Normal
## 1760 High Wage
## 1761 High Wage
## 1762 High Wage
## 1763 High Wage
## 1764 High Wage
## 1765       Low
## 1766    Normal
## 1767    Normal
## 1768    Normal
## 1769    Normal
## 1770    Normal
## 1771    Normal
## 1772       Low
## 1773       Low
## 1774       Low
## 1775    Normal
## 1776    Normal
## 1777    Normal
## 1778    Normal
## 1779       Low
## 1780       Low
## 1781       Low
## 1782       Low
## 1783    Normal
## 1784    Normal
## 1785    Normal
## 1786       Low
## 1787       Low
## 1788    Normal
## 1789    Normal
## 1790    Normal
## 1791 High Wage
## 1792 High Wage
## 1793    Normal
## 1794    Normal
## 1795    Normal
## 1796    Normal
## 1797 High Wage
## 1798 High Wage
## 1799 High Wage
## 1800    Normal
## 1801    Normal
## 1802    Normal
## 1803    Normal
## 1804    Normal
## 1805    Normal
## 1806    Normal
## 1807       Low
## 1808       Low
## 1809       Low
## 1810       Low
## 1811       Low
## 1812       Low
## 1813       Low
## 1814    Normal
## 1815    Normal
## 1816    Normal
## 1817    Normal
## 1818 High Wage
## 1819 High Wage
## 1820 High Wage
## 1821       Low
## 1822       Low
## 1823    Normal
## 1824    Normal
## 1825    Normal
## 1826    Normal
## 1827    Normal
## 1828    Normal
## 1829    Normal
## 1830    Normal
## 1831    Normal
## 1832 High Wage
## 1833 High Wage
## 1834 High Wage
## 1835       Low
## 1836       Low
## 1837       Low
## 1838       Low
## 1839    Normal
## 1840    Normal
## 1841    Normal
## 1842       Low
## 1843       Low
## 1844       Low
## 1845    Normal
## 1846    Normal
## 1847    Normal
## 1848 High Wage
## 1849    Normal
## 1850    Normal
## 1851    Normal
## 1852    Normal
## 1853 High Wage
## 1854 High Wage
## 1855 High Wage
## 1856    Normal
## 1857    Normal
## 1858 High Wage
## 1859 High Wage
## 1860 High Wage
## 1861 High Wage
## 1862 High Wage
## 1863    Normal
## 1864    Normal
## 1865    Normal
## 1866    Normal
## 1867    Normal
## 1868 High Wage
## 1869 High Wage
## 1870       Low
## 1871       Low
## 1872       Low
## 1873       Low
## 1874       Low
## 1875       Low
## 1876    Normal
## 1877    Normal
## 1878    Normal
## 1879    Normal
## 1880    Normal
## 1881 High Wage
## 1882 High Wage
## 1883 High Wage
## 1884    Normal
## 1885    Normal
## 1886 High Wage
## 1887 High Wage
## 1888 High Wage
## 1889 High Wage
## 1890 High Wage
## 1891    Normal
## 1892    Normal
## 1893    Normal
## 1894    Normal
## 1895       Low
## 1896 High Wage
## 1897    Normal
## 1898       Low
## 1899    Normal
## 1900    Normal
## 1901    Normal
## 1902    Normal
## 1903    Normal
## 1904 High Wage
## 1905       Low
## 1906    Normal
## 1907    Normal
## 1908    Normal
## 1909    Normal
## 1910    Normal
## 1911    Normal
## 1912    Normal
## 1913    Normal
## 1914    Normal
## 1915    Normal
## 1916    Normal
## 1917 High Wage
## 1918 High Wage
## 1919       Low
## 1920       Low
## 1921       Low
## 1922    Normal
## 1923    Normal
## 1924       Low
## 1925 High Wage
## 1926    Normal
## 1927    Normal
## 1928    Normal
## 1929    Normal
## 1930    Normal
## 1931    Normal
## 1932 High Wage
## 1933    Normal
## 1934    Normal
## 1935    Normal
## 1936    Normal
## 1937    Normal
## 1938    Normal
## 1939    Normal
## 1940    Normal
## 1941    Normal
## 1942 High Wage
## 1943 High Wage
## 1944 High Wage
## 1945 High Wage
## 1946 High Wage
## 1947    Normal
## 1948    Normal
## 1949    Normal
## 1950    Normal
## 1951    Normal
## 1952 High Wage
## 1953 High Wage
## 1954       Low
## 1955       Low
## 1956       Low
## 1957       Low
## 1958       Low
## 1959       Low
## 1960       Low
## 1961    Normal
## 1962    Normal
## 1963    Normal
## 1964    Normal
## 1965    Normal
## 1966    Normal
## 1967 High Wage
## 1968    Normal
## 1969    Normal
## 1970    Normal
## 1971    Normal
## 1972 High Wage
## 1973 High Wage
## 1974 High Wage
## 1975    Normal
## 1976       Low
## 1977 High Wage
## 1978    Normal
## 1979 High Wage
## 1980 High Wage
## 1981 High Wage
## 1982    Normal
## 1983    Normal
## 1984    Normal
## 1985    Normal
## 1986    Normal
## 1987    Normal
## 1988    Normal
## 1989    Normal
## 1990    Normal
## 1991    Normal
## 1992    Normal
## 1993    Normal
## 1994    Normal
## 1995    Normal
## 1996       Low
## 1997       Low
## 1998    Normal
## 1999    Normal
## 2000    Normal
## 2001    Normal
## 2002    Normal
## 2003    Normal
## 2004    Normal
## 2005    Normal
## 2006    Normal
## 2007    Normal
## 2008    Normal
## 2009 High Wage
## 2010    Normal
## 2011    Normal
## 2012 High Wage
## 2013 High Wage
## 2014 High Wage
## 2015    Normal
## 2016 High Wage
## 2017    Normal
## 2018    Normal
## 2019 High Wage
## 2020 High Wage
## 2021 High Wage
## 2022 High Wage
## 2023 High Wage
## 2024       Low
## 2025       Low
## 2026       Low
## 2027       Low
## 2028    Normal
## 2029    Normal
## 2030    Normal
## 2031    Normal
## 2032    Normal
## 2033    Normal
## 2034 High Wage
## 2035    Normal
## 2036    Normal
## 2037    Normal
## 2038    Normal
## 2039    Normal
## 2040    Normal
## 2041    Normal
## 2042 High Wage
## 2043 High Wage
## 2044 High Wage
## 2045       Low
## 2046       Low
## 2047       Low
## 2048    Normal
## 2049    Normal
## 2050    Normal
## 2051    Normal
## 2052       Low
## 2053       Low
## 2054       Low
## 2055    Normal
## 2056    Normal
## 2057    Normal
## 2058    Normal
## 2059       Low
## 2060    Normal
## 2061    Normal
## 2062    Normal
## 2063    Normal
## 2064    Normal
## 2065 High Wage
## 2066    Normal
## 2067       Low
## 2068       Low
## 2069    Normal
## 2070    Normal
## 2071    Normal
## 2072    Normal
## 2073    Normal
## 2074    Normal
## 2075    Normal
## 2076    Normal
## 2077    Normal
## 2078    Normal
## 2079    Normal
## 2080    Normal
## 2081       Low
## 2082    Normal
## 2083    Normal
## 2084       Low
## 2085       Low
## 2086       Low
## 2087       Low
## 2088       Low
## 2089       Low
## 2090       Low
## 2091    Normal
## 2092    Normal
## 2093    Normal
## 2094       Low
## 2095       Low
## 2096       Low
## 2097       Low
## 2098    Normal
## 2099    Normal
## 2100    Normal
## 2101    Normal
## 2102    Normal
## 2103    Normal
## 2104    Normal
## 2105    Normal
## 2106    Normal
## 2107 High Wage
## 2108       Low
## 2109       Low
## 2110    Normal
## 2111    Normal
## 2112    Normal
## 2113    Normal
## 2114    Normal
## 2115       Low
## 2116       Low
## 2117       Low
## 2118 High Wage
## 2119    Normal
## 2120    Normal
## 2121    Normal
## 2122       Low
## 2123       Low
## 2124       Low
## 2125    Normal
## 2126    Normal
## 2127    Normal
## 2128    Normal
## 2129    Normal
## 2130    Normal
## 2131 High Wage
## 2132 High Wage
## 2133    Normal
## 2134 High Wage
## 2135 High Wage
## 2136    Normal
## 2137    Normal
## 2138    Normal
## 2139    Normal
## 2140    Normal
## 2141       Low
## 2142    Normal
## 2143    Normal
## 2144    Normal
## 2145    Normal
## 2146    Normal
## 2147    Normal
## 2148    Normal
## 2149 High Wage
## 2150    Normal
## 2151    Normal
## 2152    Normal
## 2153    Normal
## 2154    Normal
## 2155    Normal
## 2156 High Wage
## 2157       Low
## 2158       Low
## 2159       Low
## 2160       Low
## 2161       Low
## 2162       Low
## 2163       Low
## 2164       Low
## 2165       Low
## 2166    Normal
## 2167    Normal
## 2168    Normal
## 2169    Normal
## 2170    Normal
## 2171    Normal
## 2172    Normal
## 2173    Normal
## 2174    Normal
## 2175    Normal
## 2176    Normal
## 2177 High Wage
## 2178    Normal
## 2179    Normal
## 2180    Normal
## 2181    Normal
## 2182    Normal
## 2183    Normal
## 2184 High Wage
## 2185       Low
## 2186       Low
## 2187    Normal
## 2188    Normal
## 2189    Normal
## 2190    Normal
## 2191 High Wage
## 2192       Low
## 2193       Low
## 2194    Normal
## 2195    Normal
## 2196    Normal
## 2197    Normal
## 2198    Normal
## 2199       Low
## 2200       Low
## 2201       Low
## 2202    Normal
## 2203    Normal
## 2204    Normal
## 2205    Normal
## 2206    Normal
## 2207    Normal
## 2208 High Wage
## 2209 High Wage
## 2210 High Wage
## 2211 High Wage
## 2212 High Wage
## 2213       Low
## 2214       Low
## 2215    Normal
## 2216    Normal
## 2217       Low
## 2218    Normal
## 2219       Low
## 2220       Low
## 2221    Normal
## 2222    Normal
## 2223    Normal
## 2224    Normal
## 2225    Normal
## 2226    Normal
## 2227    Normal
## 2228    Normal
## 2229    Normal
## 2230    Normal
## 2231    Normal
## 2232    Normal
## 2233 High Wage
## 2234       Low
## 2235       Low
## 2236       Low
## 2237    Normal
## 2238    Normal
## 2239    Normal
## 2240    Normal
## 2241       Low
## 2242       Low
## 2243       Low
## 2244       Low
## 2245    Normal
## 2246    Normal
## 2247    Normal
## 2248    Normal
## 2249    Normal
## 2250    Normal
## 2251    Normal
## 2252 High Wage
## 2253 High Wage
## 2254 High Wage
## 2255    Normal
## 2256    Normal
## 2257    Normal
## 2258    Normal
## 2259    Normal
## 2260 High Wage
## 2261 High Wage
## 2262       Low
## 2263    Normal
## 2264    Normal
## 2265    Normal
## 2266    Normal
## 2267    Normal
## 2268 High Wage
## 2269       Low
## 2270       Low
## 2271       Low
## 2272       Low
## 2273    Normal
## 2274    Normal
## 2275    Normal
## 2276    Normal
## 2277    Normal
## 2278    Normal
## 2279    Normal
## 2280    Normal
## 2281 High Wage
## 2282 High Wage
## 2283       Low
## 2284       Low
## 2285       Low
## 2286       Low
## 2287    Normal
## 2288       Low
## 2289       Low
## 2290    Normal
## 2291    Normal
## 2292    Normal
## 2293    Normal
## 2294    Normal
## 2295    Normal
## 2296 High Wage
## 2297    Normal
## 2298    Normal
## 2299    Normal
## 2300    Normal
## 2301    Normal
## 2302    Normal
## 2303    Normal
## 2304    Normal
## 2305    Normal
## 2306    Normal
## 2307    Normal
## 2308    Normal
## 2309 High Wage
## 2310 High Wage
## 2311    Normal
## 2312    Normal
## 2313    Normal
## 2314 High Wage
## 2315 High Wage
## 2316 High Wage
## 2317 High Wage
## 2318       Low
## 2319       Low
## 2320       Low
## 2321       Low
## 2322       Low
## 2323       Low
## 2324       Low
## 2325    Normal
## 2326    Normal
## 2327    Normal
## 2328    Normal
## 2329    Normal
## 2330    Normal
## 2331    Normal
## 2332       Low
## 2333       Low
## 2334       Low
## 2335       Low
## 2336       Low
## 2337       Low
## 2338       Low
## 2339       Low
## 2340    Normal
## 2341    Normal
## 2342    Normal
## 2343    Normal
## 2344 High Wage
## 2345 High Wage
## 2346       Low
## 2347    Normal
## 2348    Normal
## 2349    Normal
## 2350    Normal
## 2351    Normal
## 2352    Normal
## 2353    Normal
## 2354    Normal
## 2355    Normal
## 2356    Normal
## 2357    Normal
## 2358 High Wage
## 2359 High Wage
## 2360       Low
## 2361       Low
## 2362       Low
## 2363       Low
## 2364    Normal
## 2365    Normal
## 2366    Normal
## 2367       Low
## 2368       Low
## 2369       Low
## 2370       Low
## 2371       Low
## 2372       Low
## 2373       Low
## 2374    Normal
## 2375    Normal
## 2376    Normal
## 2377    Normal
## 2378    Normal
## 2379    Normal
## 2380 High Wage
## 2381    Normal
## 2382    Normal
## 2383 High Wage
## 2384 High Wage
## 2385 High Wage
## 2386 High Wage
## 2387 High Wage
## 2388    Normal
## 2389    Normal
## 2390    Normal
## 2391    Normal
## 2392    Normal
## 2393 High Wage
## 2394 High Wage
## 2395    Normal
## 2396    Normal
## 2397 High Wage
## 2398 High Wage
## 2399 High Wage
## 2400 High Wage
## 2401 High Wage
## 2402    Normal
## 2403    Normal
## 2404 High Wage
## 2405 High Wage
## 2406 High Wage
## 2407 High Wage
## 2408 High Wage
## 2409       Low
## 2410       Low
## 2411       Low
## 2412    Normal
## 2413    Normal
## 2414    Normal
## 2415    Normal
## 2416    Normal
## 2417    Normal
## 2418    Normal
## 2419 High Wage
## 2420 High Wage
## 2421 High Wage
## 2422 High Wage
## 2423    Normal
## 2424    Normal
## 2425    Normal
## 2426    Normal
## 2427    Normal
## 2428 High Wage
## 2429 High Wage
## 2430    Normal
## 2431    Normal
## 2432 High Wage
## 2433 High Wage
## 2434 High Wage
## 2435 High Wage
## 2436 High Wage
## 2437       Low
## 2438    Normal
## 2439    Normal
## 2440    Normal
## 2441    Normal
## 2442 High Wage
## 2443 High Wage
## 2444    Normal
## 2445    Normal
## 2446    Normal
## 2447    Normal
## 2448    Normal
## 2449 High Wage
## 2450 High Wage
## 2451       Low
## 2452       Low
## 2453    Normal
## 2454    Normal
## 2455    Normal
## 2456    Normal
## 2457    Normal
## 2458    Normal
## 2459    Normal
## 2460    Normal
## 2461    Normal
## 2462    Normal
## 2463 High Wage
## 2464 High Wage
## 2465    Normal
## 2466    Normal
## 2467 High Wage
## 2468 High Wage
## 2469 High Wage
## 2470 High Wage
## 2471 High Wage
## 2472    Normal
## 2473    Normal
## 2474    Normal
## 2475    Normal
## 2476    Normal
## 2477 High Wage
## 2478 High Wage
## 2479       Low
## 2480       Low
## 2481    Normal
## 2482    Normal
## 2483       Low
## 2484       Low
## 2485       Low
## 2486       Low
## 2487    Normal
## 2488    Normal
## 2489    Normal
## 2490    Normal
## 2491    Normal
## 2492 High Wage
## 2493       Low
## 2494    Normal
## 2495    Normal
## 2496    Normal
## 2497    Normal
## 2498    Normal
## 2499 High Wage
## 2500    Normal
## 2501    Normal
## 2502    Normal
## 2503    Normal
## 2504    Normal
## 2505    Normal
## 2506    Normal
## 2507       Low
## 2508       Low
## 2509       Low
## 2510       Low
## 2511       Low
## 2512       Low
## 2513    Normal
## 2514    Normal
## 2515    Normal
## 2516 High Wage
## 2517    Normal
## 2518 High Wage
## 2519 High Wage
## 2520 High Wage
## 2521       Low
## 2522       Low
## 2523       Low
## 2524       Low
## 2525       Low
## 2526 High Wage
## 2527 High Wage
## 2528    Normal
## 2529    Normal
## 2530    Normal
## 2531    Normal
## 2532 High Wage
## 2533 High Wage
## 2534 High Wage
## 2535       Low
## 2536       Low
## 2537       Low
## 2538    Normal
## 2539    Normal
## 2540    Normal
## 2541    Normal
## 2542    Normal
## 2543       Low
## 2544    Normal
## 2545    Normal
## 2546    Normal
## 2547    Normal
## 2548    Normal
## 2549    Normal
## 2550    Normal
## 2551       Low
## 2552 High Wage
## 2553 High Wage
## 2554 High Wage
## 2555 High Wage
## 2556    Normal
## 2557    Normal
## 2558    Normal
## 2559       Low
## 2560    Normal
## 2561    Normal
## 2562    Normal
## 2563    Normal
## 2564    Normal
## 2565    Normal
## 2566    Normal
## 2567    Normal
## 2568    Normal
## 2569 High Wage
## 2570    Normal
## 2571    Normal
## 2572    Normal
## 2573    Normal
## 2574 High Wage
## 2575 High Wage
## 2576 High Wage
## 2577       Low
## 2578    Normal
## 2579    Normal
## 2580    Normal
## 2581    Normal
## 2582 High Wage
## 2583 High Wage
## 2584    Normal
## 2585    Normal
## 2586    Normal
## 2587    Normal
## 2588 High Wage
## 2589 High Wage
## 2590 High Wage
## 2591    Normal
## 2592    Normal
## 2593    Normal
## 2594    Normal
## 2595    Normal
## 2596 High Wage
## 2597 High Wage
## 2598    Normal
## 2599    Normal
## 2600    Normal
## 2601    Normal
## 2602    Normal
## 2603    Normal
## 2604    Normal
## 2605       Low
## 2606       Low
## 2607       Low
## 2608       Low
## 2609       Low
## 2610       Low
## 2611    Normal
## 2612       Low
## 2613       Low
## 2614       Low
## 2615       Low
## 2616       Low
## 2617       Low
## 2618       Low
## 2619       Low
## 2620       Low
## 2621       Low
## 2622       Low
## 2623       Low
## 2624       Low
## 2625       Low
## 2626    Normal
## 2627    Normal
## 2628    Normal
## 2629    Normal
## 2630    Normal
## 2631    Normal
## 2632    Normal
## 2633    Normal
## 2634    Normal
## 2635    Normal
## 2636 High Wage
## 2637 High Wage
## 2638    Normal
## 2639 High Wage
## 2640    Normal
## 2641    Normal
## 2642    Normal
## 2643    Normal
## 2644 High Wage
## 2645 High Wage
## 2646 High Wage
## 2647    Normal
## 2648    Normal
## 2649    Normal
## 2650    Normal
## 2651    Normal
## 2652    Normal
## 2653    Normal
## 2654       Low
## 2655    Normal
## 2656    Normal
## 2657    Normal
## 2658    Normal
## 2659    Normal
## 2660    Normal
## 2661       Low
## 2662    Normal
## 2663       Low
## 2664    Normal
## 2665    Normal
## 2666    Normal
## 2667    Normal
## 2668    Normal
## 2669    Normal
## 2670       Low
## 2671       Low
## 2672       Low
## 2673    Normal
## 2674    Normal
## 2675    Normal
## 2676    Normal
## 2677    Normal
## 2678    Normal
## 2679 High Wage
## 2680 High Wage
## 2681    Normal
## 2682       Low
## 2683       Low
## 2684       Low
## 2685       Low
## 2686       Low
## 2687       Low
## 2688    Normal
## 2689    Normal
## 2690    Normal
## 2691    Normal
## 2692    Normal
## 2693    Normal
## 2694 High Wage
## 2695 High Wage
## 2696    Normal
## 2697    Normal
## 2698 High Wage
## 2699 High Wage
## 2700 High Wage
## 2701 High Wage
## 2702 High Wage
## 2703    Normal
## 2704    Normal
## 2705    Normal
## 2706    Normal
## 2707    Normal
## 2708    Normal
## 2709 High Wage
## 2710    Normal
## 2711    Normal
## 2712 High Wage
## 2713 High Wage
## 2714 High Wage
## 2715 High Wage
## 2716 High Wage
## 2717    Normal
## 2718    Normal
## 2719 High Wage
## 2720 High Wage
## 2721 High Wage
## 2722 High Wage
## 2723 High Wage
## 2724    Normal
## 2725    Normal
## 2726    Normal
## 2727 High Wage
## 2728 High Wage
## 2729 High Wage
## 2730 High Wage
## 2731       Low
## 2732    Normal
## 2733       Low
## 2734    Normal
## 2735    Normal
## 2736    Normal
## 2737    Normal
## 2738       Low
## 2739       Low
## 2740    Normal
## 2741       Low
## 2742    Normal
## 2743    Normal
## 2744    Normal
## 2745    Normal
## 2746    Normal
## 2747    Normal
## 2748    Normal
## 2749    Normal
## 2750    Normal
## 2751 High Wage
## 2752       Low
## 2753       Low
## 2754    Normal
## 2755    Normal
## 2756    Normal
## 2757    Normal
## 2758    Normal
## 2759       Low
## 2760       Low
## 2761       Low
## 2762       Low
## 2763    Normal
## 2764    Normal
## 2765    Normal
## 2766       Low
## 2767       Low
## 2768       Low
## 2769       Low
## 2770    Normal
## 2771    Normal
## 2772    Normal
## 2773    Normal
## 2774    Normal
## 2775    Normal
## 2776    Normal
## 2777 High Wage
## 2778 High Wage
## 2779    Normal
## 2780    Normal
## 2781    Normal
## 2782    Normal
## 2783    Normal
## 2784    Normal
## 2785 High Wage
## 2786 High Wage
## 2787       Low
## 2788    Normal
## 2789    Normal
## 2790    Normal
## 2791    Normal
## 2792    Normal
## 2793    Normal
## 2794    Normal
## 2795    Normal
## 2796    Normal
## 2797    Normal
## 2798    Normal
## 2799    Normal
## 2800 High Wage
## 2801    Normal
## 2802    Normal
## 2803    Normal
## 2804    Normal
## 2805 High Wage
## 2806 High Wage
## 2807 High Wage
## 2808    Normal
## 2809    Normal
## 2810    Normal
## 2811 High Wage
## 2812 High Wage
## 2813 High Wage
## 2814 High Wage
## 2815    Normal
## 2816    Normal
## 2817 High Wage
## 2818 High Wage
## 2819 High Wage
## 2820 High Wage
## 2821 High Wage
## 2822    Normal
## 2823    Normal
## 2824    Normal
## 2825    Normal
## 2826    Normal
## 2827 High Wage
## 2828 High Wage
## 2829    Normal
## 2830    Normal
## 2831 High Wage
## 2832 High Wage
## 2833 High Wage
## 2834 High Wage
## 2835 High Wage
## 2836       Low
## 2837    Normal
## 2838    Normal
## 2839    Normal
## 2840    Normal
## 2841    Normal
## 2842    Normal
## 2843    Normal
## 2844    Normal
## 2845 High Wage
## 2846 High Wage
## 2847 High Wage
## 2848 High Wage
## 2849 High Wage
## 2850       Low
## 2851       Low
## 2852       Low
## 2853       Low
## 2854    Normal
## 2855    Normal
## 2856    Normal
## 2857       Low
## 2858    Normal
## 2859    Normal
## 2860    Normal
## 2861    Normal
## 2862    Normal
## 2863    Normal
## 2864       Low
## 2865       Low
## 2866       Low
## 2867       Low
## 2868       Low
## 2869       Low
## 2870       Low
## 2871       Low
## 2872       Low
## 2873       Low
## 2874    Normal
## 2875    Normal
## 2876    Normal
## 2877    Normal
## 2878       Low
## 2879    Normal
## 2880    Normal
## 2881 High Wage
## 2882 High Wage
## 2883 High Wage
## 2884 High Wage
## 2885    Normal
## 2886    Normal
## 2887    Normal
## 2888    Normal
## 2889 High Wage
## 2890 High Wage
## 2891 High Wage
## 2892    Normal
## 2893    Normal
## 2894    Normal
## 2895    Normal
## 2896    Normal
## 2897    Normal
## 2898 High Wage
## 2899       Low
## 2900       Low
## 2901       Low
## 2902       Low
## 2903       Low
## 2904       Low
## 2905    Normal
## 2906    Normal
## 2907    Normal
## 2908    Normal
## 2909    Normal
## 2910    Normal
## 2911    Normal
## 2912 High Wage
## 2913       Low
## 2914       Low
## 2915       Low
## 2916       Low
## 2917       Low
## 2918       Low
## 2919       Low
## 2920    Normal
## 2921    Normal
## 2922    Normal
## 2923    Normal
## 2924    Normal
## 2925    Normal
## 2926    Normal
## 2927    Normal
## 2928    Normal
## 2929    Normal
## 2930    Normal
## 2931    Normal
## 2932 High Wage
## 2933 High Wage
## 2934       Low
## 2935       Low
## 2936    Normal
## 2937    Normal
## 2938    Normal
## 2939    Normal
## 2940    Normal
## 2941       Low
## 2942       Low
## 2943       Low
## 2944       Low
## 2945    Normal
## 2946    Normal
## 2947    Normal
## 2948       Low
## 2949       Low
## 2950    Normal
## 2951    Normal
## 2952    Normal
## 2953    Normal
## 2954    Normal
## 2955    Normal
## 2956    Normal
## 2957    Normal
## 2958    Normal
## 2959       Low
## 2960    Normal
## 2961 High Wage
## 2962    Normal
## 2963    Normal
## 2964    Normal
## 2965    Normal
## 2966 High Wage
## 2967 High Wage
## 2968 High Wage
## 2969       Low
## 2970    Normal
## 2971    Normal
## 2972    Normal
## 2973    Normal
## 2974    Normal
## 2975 High Wage
## 2976    Normal
## 2977    Normal
## 2978    Normal
## 2979    Normal
## 2980    Normal
## 2981    Normal
## 2982    Normal
## 2983    Normal
## 2984    Normal
## 2985 High Wage
## 2986 High Wage
## 2987 High Wage
## 2988 High Wage
## 2989 High Wage
## 2990       Low
## 2991       Low
## 2992       Low
## 2993       Low
## 2994    Normal
## 2995    Normal
## 2996    Normal
## 2997       Low
## 2998    Normal
## 2999    Normal
## 3000    Normal
## 3001    Normal
## 3002    Normal
## 3003    Normal
## 3004       Low
## 3005       Low
## 3006       Low
## 3007       Low
## 3008       Low
## 3009       Low
## 3010       Low
## 3011       Low
## 3012       Low
## 3013       Low
## 3014       Low
## 3015       Low
## 3016    Normal
## 3017    Normal
## 3018    Normal
## 3019    Normal
## 3020 High Wage
## 3021 High Wage
## 3022 High Wage
## 3023 High Wage
## 3024 High Wage
## 3025    Normal
## 3026    Normal
## 3027    Normal
## 3028    Normal
## 3029    Normal
## 3030    Normal
## 3031    Normal
## 3032    Normal
## 3033    Normal
## 3034    Normal
## 3035    Normal
## 3036    Normal
## 3037    Normal
## 3038 High Wage
## 3039    Normal
## 3040    Normal
## 3041    Normal
## 3042    Normal
## 3043    Normal
## 3044 High Wage
## 3045 High Wage
## 3046    Normal
## 3047    Normal
## 3048    Normal
## 3049    Normal
## 3050    Normal
## 3051    Normal
## 3052       Low
## 3053       Low
## 3054       Low
## 3055       Low
## 3056       Low
## 3057       Low
## 3058       Low
## 3059    Normal
## 3060       Low
## 3061       Low
## 3062    Normal
## 3063    Normal
## 3064    Normal
## 3065    Normal
## 3066    Normal
## 3067       Low
## 3068    Normal
## 3069    Normal
## 3070    Normal
## 3071 High Wage
## 3072 High Wage
## 3073 High Wage
## 3074       Low
## 3075       Low
## 3076       Low
## 3077       Low
## 3078       Low
## 3079       Low
## 3080    Normal
## 3081       Low
## 3082       Low
## 3083       Low
## 3084       Low
## 3085    Normal
## 3086    Normal
## 3087    Normal
## 3088       Low
## 3089       Low
## 3090       Low
## 3091       Low
## 3092    Normal
## 3093    Normal
## 3094    Normal
## 3095       Low
## 3096       Low
## 3097       Low
## 3098       Low
## 3099       Low
## 3100       Low
## 3101       Low
## 3102    Normal
## 3103    Normal
## 3104    Normal
## 3105    Normal
## 3106    Normal
## 3107    Normal
## 3108 High Wage
## 3109    Normal
## 3110    Normal
## 3111 High Wage
## 3112 High Wage
## 3113 High Wage
## 3114 High Wage
## 3115 High Wage
## 3116       Low
## 3117       Low
## 3118       Low
## 3119       Low
## 3120    Normal
## 3121       Low
## 3122    Normal
## 3123       Low
## 3124       Low
## 3125       Low
## 3126       Low
## 3127       Low
## 3128       Low
## 3129       Low
## 3130    Normal
## 3131    Normal
## 3132    Normal
## 3133    Normal
## 3134    Normal
## 3135    Normal
## 3136 High Wage
## 3137       Low
## 3138       Low
## 3139       Low
## 3140    Normal
## 3141    Normal
## 3142 High Wage
## 3143 High Wage
## 3144    Normal
## 3145    Normal
## 3146    Normal
## 3147    Normal
## 3148    Normal
## 3149    Normal
## 3150 High Wage
## 3151       Low
## 3152    Normal
## 3153    Normal
## 3154    Normal
## 3155    Normal
## 3156    Normal
## 3157 High Wage
## 3158       Low
## 3159       Low
## 3160       Low
## 3161       Low
## 3162       Low
## 3163    Normal
## 3164    Normal
## 3165    Normal
## 3166    Normal
## 3167    Normal
## 3168    Normal
## 3169 High Wage
## 3170 High Wage
## 3171 High Wage
## 3172    Normal
## 3173    Normal
## 3174    Normal
## 3175    Normal
## 3176 High Wage
## 3177 High Wage
## 3178 High Wage
## 3179       Low
## 3180       Low
## 3181       Low
## 3182       Low
## 3183       Low
## 3184    Normal
## 3185    Normal
## 3186    Normal
## 3187    Normal
## 3188    Normal
## 3189    Normal
## 3190    Normal
## 3191    Normal
## 3192    Normal
## 3193       Low
## 3194       Low
## 3195       Low
## 3196       Low
## 3197       Low
## 3198       Low
## 3199       Low
## 3200    Normal
## 3201    Normal
## 3202    Normal
## 3203    Normal
## 3204    Normal
## 3205 High Wage
## 3206    Normal
## 3207       Low
## 3208    Normal
## 3209    Normal
## 3210    Normal
## 3211 High Wage
## 3212 High Wage
## 3213 High Wage
## 3214    Normal
## 3215    Normal
## 3216    Normal
## 3217    Normal
## 3218    Normal
## 3219    Normal
## 3220 High Wage
## 3221       Low
## 3222    Normal
## 3223    Normal
## 3224    Normal
## 3225    Normal
## 3226    Normal
## 3227    Normal
## 3228       Low
## 3229       Low
## 3230       Low
## 3231       Low
## 3232       Low
## 3233       Low
## 3234    Normal
## 3235    Normal
## 3236    Normal
## 3237    Normal
## 3238    Normal
## 3239    Normal
## 3240 High Wage
## 3241 High Wage
## 3242       Low
## 3243       Low
## 3244       Low
## 3245       Low
## 3246       Low
## 3247    Normal
## 3248    Normal
## 3249       Low
## 3250       Low
## 3251       Low
## 3252    Normal
## 3253    Normal
## 3254    Normal
## 3255    Normal
## 3256       Low
## 3257       Low
## 3258    Normal
## 3259    Normal
## 3260    Normal
## 3261    Normal
## 3262    Normal
## 3263       Low
## 3264       Low
## 3265    Normal
## 3266    Normal
## 3267    Normal
## 3268 High Wage
## 3269    Normal
## 3270    Normal
## 3271    Normal
## 3272 High Wage
## 3273 High Wage
## 3274 High Wage
## 3275 High Wage
## 3276 High Wage
## 3277       Low
## 3278       Low
## 3279       Low
## 3280       Low
## 3281       Low
## 3282       Low
## 3283       Low
## 3284    Normal
## 3285    Normal
## 3286    Normal
## 3287 High Wage
## 3288 High Wage
## 3289 High Wage
## 3290 High Wage
## 3291    Normal
## 3292    Normal
## 3293    Normal
## 3294    Normal
## 3295 High Wage
## 3296 High Wage
## 3297 High Wage
## 3298       Low
## 3299       Low
## 3300       Low
## 3301       Low
## 3302       Low
## 3303       Low
## 3304       Low
## 3305    Normal
## 3306       Low
## 3307    Normal
## 3308    Normal
## 3309    Normal
## 3310    Normal
## 3311    Normal
## 3312    Normal
## 3313    Normal
## 3314    Normal
## 3315    Normal
## 3316 High Wage
## 3317 High Wage
## 3318 High Wage
## 3319    Normal
## 3320    Normal
## 3321 High Wage
## 3322 High Wage
## 3323 High Wage
## 3324 High Wage
## 3325 High Wage
## 3326       Low
## 3327       Low
## 3328       Low
## 3329       Low
## 3330    Normal
## 3331       Low
## 3332    Normal
## 3333       Low
## 3334    Normal
## 3335    Normal
## 3336    Normal
## 3337    Normal
## 3338    Normal
## 3339 High Wage
## 3340       Low
## 3341    Normal
## 3342    Normal
## 3343    Normal
## 3344    Normal
## 3345    Normal
## 3346    Normal
## 3347    Normal
## 3348    Normal
## 3349 High Wage
## 3350 High Wage
## 3351 High Wage
## 3352 High Wage
## 3353 High Wage
## 3354       Low
## 3355       Low
## 3356       Low
## 3357       Low
## 3358    Normal
## 3359    Normal
## 3360    Normal
## 3361       Low
## 3362       Low
## 3363       Low
## 3364       Low
## 3365       Low
## 3366       Low
## 3367       Low
## 3368       Low
## 3369       Low
## 3370    Normal
## 3371    Normal
## 3372    Normal
## 3373    Normal
## 3374    Normal
## 3375       Low
## 3376       Low
## 3377    Normal
## 3378    Normal
## 3379    Normal
## 3380    Normal
## 3381    Normal
## 3382    Normal
## 3383    Normal
## 3384    Normal
## 3385    Normal
## 3386 High Wage
## 3387 High Wage
## 3388 High Wage
## 3389       Low
## 3390    Normal
## 3391    Normal
## 3392    Normal
## 3393    Normal
## 3394    Normal
## 3395    Normal
## 3396    Normal
## 3397    Normal
## 3398    Normal
## 3399 High Wage
## 3400 High Wage
## 3401 High Wage
## 3402 High Wage
## 3403    Normal
## 3404    Normal
## 3405    Normal
## 3406    Normal
## 3407 High Wage
## 3408 High Wage
## 3409 High Wage
## 3410    Normal
## 3411    Normal
## 3412    Normal
## 3413    Normal
## 3414 High Wage
## 3415 High Wage
## 3416 High Wage
## 3417    Normal
## 3418    Normal
## 3419    Normal
## 3420    Normal
## 3421    Normal
## 3422    Normal
## 3423    Normal
## 3424    Normal
## 3425    Normal
## 3426    Normal
## 3427 High Wage
## 3428 High Wage
## 3429    Normal
## 3430 High Wage
## 3431       Low
## 3432    Normal
## 3433    Normal
## 3434    Normal
## 3435    Normal
## 3436 High Wage
## 3437 High Wage
## 3438       Low
## 3439       Low
## 3440       Low
## 3441       Low
## 3442    Normal
## 3443    Normal
## 3444       Low
## 3445    Normal
## 3446    Normal
## 3447    Normal
## 3448    Normal
## 3449    Normal
## 3450 High Wage
## 3451    Normal
## 3452       Low
## 3453       Low
## 3454       Low
## 3455       Low
## 3456       Low
## 3457       Low
## 3458       Low
## 3459       Low
## 3460       Low
## 3461    Normal
## 3462    Normal
## 3463    Normal
## 3464    Normal
## 3465    Normal
## 3466    Normal
## 3467    Normal
## 3468 High Wage
## 3469 High Wage
## 3470 High Wage
## 3471 High Wage
## 3472 High Wage
## 3473    Normal
## 3474    Normal
## 3475 High Wage
## 3476 High Wage
## 3477 High Wage
## 3478 High Wage
## 3479 High Wage
## 3480       Low
## 3481       Low
## 3482       Low
## 3483       Low
## 3484    Normal
## 3485    Normal
## 3486    Normal
## 3487       Low
## 3488    Normal
## 3489    Normal
## 3490    Normal
## 3491    Normal
## 3492    Normal
## 3493    Normal
## 3494    Normal
## 3495    Normal
## 3496    Normal
## 3497    Normal
## 3498    Normal
## 3499       Low
## 3500       Low
## 3501       Low
## 3502    Normal
## 3503    Normal
## 3504    Normal
## 3505    Normal
## 3506    Normal
## 3507 High Wage
## 3508    Normal
## 3509    Normal
## 3510    Normal
## 3511    Normal
## 3512    Normal
## 3513 High Wage
## 3514 High Wage
## 3515    Normal
## 3516    Normal
## 3517 High Wage
## 3518 High Wage
## 3519 High Wage
## 3520 High Wage
## 3521 High Wage
## 3522    Normal
## 3523    Normal
## 3524    Normal
## 3525    Normal
## 3526 High Wage
## 3527    Normal
## 3528 High Wage
## 3529    Normal
## 3530    Normal
## 3531 High Wage
## 3532 High Wage
## 3533    Normal
## 3534 High Wage
## 3535 High Wage
## 3536       Low
## 3537    Normal
## 3538    Normal
## 3539    Normal
## 3540    Normal
## 3541    Normal
## 3542    Normal
## 3543       Low
## 3544       Low
## 3545       Low
## 3546       Low
## 3547    Normal
## 3548    Normal
## 3549    Normal
## 3550       Low
## 3551    Normal
## 3552    Normal
## 3553    Normal
## 3554    Normal
## 3555    Normal
## 3556    Normal
## 3557       Low
## 3558    Normal
## 3559    Normal
## 3560    Normal
## 3561    Normal
## 3562    Normal
## 3563    Normal
## 3564    Normal
## 3565    Normal
## 3566 High Wage
## 3567 High Wage
## 3568 High Wage
## 3569 High Wage
## 3570 High Wage
## 3571       Low
## 3572       Low
## 3573       Low
## 3574       Low
## 3575    Normal
## 3576    Normal
## 3577    Normal
## 3578       Low
## 3579       Low
## 3580    Normal
## 3581    Normal
## 3582    Normal
## 3583    Normal
## 3584 High Wage
## 3585       Low
## 3586       Low
## 3587       Low
## 3588       Low
## 3589       Low
## 3590       Low
## 3591       Low
## 3592    Normal
## 3593    Normal
## 3594    Normal
## 3595 High Wage
## 3596 High Wage
## 3597 High Wage
## 3598 High Wage
## 3599       Low
## 3600       Low
## 3601       Low
## 3602       Low
## 3603       Low
## 3604       Low
## 3605       Low
## 3606    Normal
## 3607    Normal
## 3608    Normal
## 3609 High Wage
## 3610    Normal
## 3611    Normal
## 3612    Normal
## 3613       Low
## 3614       Low
## 3615       Low
## 3616       Low
## 3617       Low
## 3618       Low
## 3619       Low
## 3620       Low
## 3621       Low
## 3622       Low
## 3623       Low
## 3624       Low
## 3625    Normal
## 3626    Normal
## 3627       Low
## 3628       Low
## 3629       Low
## 3630       Low
## 3631       Low
## 3632       Low
## 3633    Normal
## 3634       Low
## 3635    Normal
## 3636    Normal
## 3637    Normal
## 3638       Low
## 3639       Low
## 3640    Normal
## 3641    Normal
## 3642    Normal
## 3643    Normal
## 3644    Normal
## 3645 High Wage
## 3646    Normal
## 3647 High Wage
## 3648       Low
## 3649       Low
## 3650       Low
## 3651    Normal
## 3652    Normal
## 3653 High Wage
## 3654    Normal
## 3655       Low
## 3656       Low
## 3657       Low
## 3658    Normal
## 3659    Normal
## 3660    Normal
## 3661    Normal
## 3662       Low
## 3663       Low
## 3664       Low
## 3665    Normal
## 3666    Normal
## 3667    Normal
## 3668    Normal
## 3669       Low
## 3670       Low
## 3671    Normal
## 3672    Normal
## 3673    Normal
## 3674    Normal
## 3675    Normal
## 3676       Low
## 3677       Low
## 3678       Low
## 3679       Low
## 3680       Low
## 3681    Normal
## 3682    Normal
## 3683       Low
## 3684       Low
## 3685    Normal
## 3686    Normal
## 3687    Normal
## 3688 High Wage
## 3689 High Wage
## 3690       Low
## 3691       Low
## 3692       Low
## 3693    Normal
## 3694    Normal
## 3695    Normal
## 3696    Normal
## 3697    Normal
## 3698    Normal
## 3699 High Wage
## 3700 High Wage
## 3701    Normal
## 3702 High Wage
## 3703 High Wage
## 3704    Normal
## 3705    Normal
## 3706 High Wage
## 3707 High Wage
## 3708 High Wage
## 3709 High Wage
## 3710 High Wage
## 3711    Normal
## 3712    Normal
## 3713    Normal
## 3714 High Wage
## 3715 High Wage
## 3716 High Wage
## 3717 High Wage
## 3718       Low
## 3719       Low
## 3720       Low
## 3721       Low
## 3722       Low
## 3723       Low
## 3724    Normal
## 3725       Low
## 3726       Low
## 3727       Low
## 3728       Low
## 3729    Normal
## 3730    Normal
## 3731    Normal
## 3732       Low
## 3733       Low
## 3734       Low
## 3735       Low
## 3736       Low
## 3737       Low
## 3738       Low
## 3739       Low
## 3740       Low
## 3741       Low
## 3742       Low
## 3743       Low
## 3744       Low
## 3745       Low
## 3746    Normal
## 3747    Normal
## 3748    Normal
## 3749    Normal
## 3750 High Wage
## 3751    Normal
## 3752 High Wage
## 3753       Low
## 3754    Normal
## 3755    Normal
## 3756    Normal
## 3757 High Wage
## 3758    Normal
## 3759    Normal
## 3760    Normal
## 3761    Normal
## 3762    Normal
## 3763    Normal
## 3764 High Wage
## 3765 High Wage
## 3766 High Wage
## 3767       Low
## 3768    Normal
## 3769    Normal
## 3770    Normal
## 3771 High Wage
## 3772 High Wage
## 3773 High Wage
## 3774    Normal
## 3775    Normal
## 3776 High Wage
## 3777 High Wage
## 3778 High Wage
## 3779 High Wage
## 3780 High Wage
## 3781    Normal
## 3782    Normal
## 3783    Normal
## 3784    Normal
## 3785    Normal
## 3786    Normal
## 3787 High Wage
## 3788    Normal
## 3789    Normal
## 3790    Normal
## 3791    Normal
## 3792    Normal
## 3793 High Wage
## 3794 High Wage
## 3795    Normal
## 3796    Normal
## 3797    Normal
## 3798    Normal
## 3799    Normal
## 3800    Normal
## 3801 High Wage
## 3802    Normal
## 3803    Normal
## 3804 High Wage
## 3805 High Wage
## 3806 High Wage
## 3807    Normal
## 3808 High Wage
## 3809    Normal
## 3810    Normal
## 3811 High Wage
## 3812 High Wage
## 3813 High Wage
## 3814 High Wage
## 3815 High Wage
## 3816    Normal
## 3817    Normal
## 3818    Normal
## 3819    Normal
## 3820    Normal
## 3821 High Wage
## 3822 High Wage
## 3823    Normal
## 3824    Normal
## 3825    Normal
## 3826    Normal
## 3827    Normal
## 3828    Normal
## 3829 High Wage
## 3830    Normal
## 3831    Normal
## 3832    Normal
## 3833    Normal
## 3834 High Wage
## 3835    Normal
## 3836    Normal
## 3837       Low
## 3838       Low
## 3839       Low
## 3840       Low
## 3841       Low
## 3842       Low
## 3843       Low
## 3844    Normal
## 3845    Normal
## 3846    Normal
## 3847    Normal
## 3848    Normal
## 3849 High Wage
## 3850 High Wage
## 3851       Low
## 3852       Low
## 3853       Low
## 3854    Normal
## 3855       Low
## 3856    Normal
## 3857    Normal
## 3858       Low
## 3859    Normal
## 3860    Normal
## 3861    Normal
## 3862    Normal
## 3863    Normal
## 3864    Normal
## 3865       Low
## 3866       Low
## 3867       Low
## 3868       Low
## 3869       Low
## 3870    Normal
## 3871    Normal
## 3872       Low
## 3873       Low
## 3874       Low
## 3875       Low
## 3876       Low
## 3877       Low
## 3878       Low
## 3879    Normal
## 3880    Normal
## 3881 High Wage
## 3882 High Wage
## 3883 High Wage
## 3884 High Wage
## 3885 High Wage
## 3886    Normal
## 3887    Normal
## 3888    Normal
## 3889    Normal
## 3890 High Wage
## 3891 High Wage
## 3892 High Wage
## 3893       Low
## 3894    Normal
## 3895    Normal
## 3896    Normal
## 3897    Normal
## 3898    Normal
## 3899    Normal
## 3900       Low
## 3901       Low
## 3902       Low
## 3903       Low
## 3904    Normal
## 3905       Low
## 3906    Normal
## 3907       Low
## 3908       Low
## 3909    Normal
## 3910    Normal
## 3911    Normal
## 3912    Normal
## 3913    Normal
## 3914       Low
## 3915       Low
## 3916       Low
## 3917       Low
## 3918       Low
## 3919    Normal
## 3920    Normal
## 3921       Low
## 3922       Low
## 3923 High Wage
## 3924    Normal
## 3925    Normal
## 3926    Normal
## 3927    Normal
## 3928    Normal
## 3929    Normal
## 3930    Normal
## 3931    Normal
## 3932 High Wage
## 3933 High Wage
## 3934 High Wage
## 3935    Normal
## 3936    Normal
## 3937    Normal
## 3938    Normal
## 3939    Normal
## 3940    Normal
## 3941    Normal
## 3942    Normal
## 3943    Normal
## 3944    Normal
## 3945    Normal
## 3946 High Wage
## 3947 High Wage
## 3948 High Wage
## 3949    Normal
## 3950    Normal
## 3951 High Wage
## 3952 High Wage
## 3953 High Wage
## 3954    Normal
## 3955 High Wage
## 3956       Low
## 3957    Normal
## 3958       Low
## 3959    Normal
## 3960 High Wage
## 3961 High Wage
## 3962 High Wage
## 3963       Low
## 3964       Low
## 3965       Low
## 3966       Low
## 3967       Low
## 3968       Low
## 3969       Low
## 3970    Normal
## 3971    Normal
## 3972    Normal
## 3973    Normal
## 3974    Normal
## 3975    Normal
## 3976    Normal
## 3977    Normal
## 3978    Normal
## 3979    Normal
## 3980    Normal
## 3981 High Wage
## 3982 High Wage
## 3983 High Wage
## 3984       Low
## 3985       Low
## 3986       Low
## 3987       Low
## 3988       Low
## 3989       Low
## 3990       Low
## 3991       Low
## 3992    Normal
## 3993    Normal
## 3994    Normal
## 3995    Normal
## 3996 High Wage
## 3997    Normal
## 3998       Low
## 3999       Low
## 4000       Low
## 4001    Normal
## 4002       Low
## 4003    Normal
## 4004       Low
## 4005       Low
## 4006       Low
## 4007       Low
## 4008       Low
## 4009    Normal
## 4010    Normal
## 4011    Normal
## 4012       Low
## 4013       Low
## 4014    Normal
## 4015    Normal
## 4016    Normal
## 4017    Normal
## 4018    Normal
## 4019       Low
## 4020       Low
## 4021       Low
## 4022       Low
## 4023       Low
## 4024       Low
## 4025    Normal
## 4026       Low
## 4027       Low
## 4028       Low
## 4029    Normal
## 4030       Low
## 4031    Normal
## 4032    Normal
## 4033       Low
## 4034       Low
## 4035       Low
## 4036       Low
## 4037       Low
## 4038       Low
## 4039    Normal
## 4040       Low
## 4041    Normal
## 4042    Normal
## 4043    Normal
## 4044    Normal
## 4045    Normal
## 4046    Normal
## 4047       Low
## 4048       Low
## 4049       Low
## 4050       Low
## 4051    Normal
## 4052    Normal
## 4053    Normal
## 4054       Low
## 4055       Low
## 4056    Normal
## 4057    Normal
## 4058    Normal
## 4059    Normal
## 4060    Normal
## 4061    Normal
## 4062    Normal
## 4063    Normal
## 4064    Normal
## 4065    Normal
## 4066 High Wage
## 4067 High Wage
## 4068       Low
## 4069       Low
## 4070       Low
## 4071    Normal
## 4072    Normal
## 4073    Normal
## 4074    Normal
## 4075       Low
## 4076    Normal
## 4077    Normal
## 4078    Normal
## 4079 High Wage
## 4080 High Wage
## 4081 High Wage
## 4082       Low
## 4083       Low
## 4084    Normal
## 4085    Normal
## 4086    Normal
## 4087    Normal
## 4088    Normal
## 4089    Normal
## 4090    Normal
## 4091    Normal
## 4092    Normal
## 4093    Normal
## 4094 High Wage
## 4095 High Wage
## 4096       Low
## 4097       Low
## 4098       Low
## 4099       Low
## 4100       Low
## 4101       Low
## 4102       Low
## 4103    Normal
## 4104    Normal
## 4105    Normal
## 4106    Normal
## 4107 High Wage
## 4108 High Wage
## 4109 High Wage
## 4110       Low
## 4111       Low
## 4112       Low
## 4113       Low
## 4114    Normal
## 4115       Low
## 4116    Normal
## 4117    Normal
## 4118    Normal
## 4119    Normal
## 4120    Normal
## 4121    Normal
## 4122 High Wage
## 4123 High Wage
## 4124       Low
## 4125    Normal
## 4126    Normal
## 4127    Normal
## 4128    Normal
## 4129    Normal
## 4130    Normal
## 4131    Normal
## 4132    Normal
## 4133    Normal
## 4134    Normal
## 4135    Normal
## 4136    Normal
## 4137    Normal
## 4138    Normal
## 4139    Normal
## 4140    Normal
## 4141    Normal
## 4142    Normal
## 4143    Normal
## 4144 High Wage
## 4145       Low
## 4146       Low
## 4147       Low
## 4148       Low
## 4149       Low
## 4150       Low
## 4151       Low
## 4152    Normal
## 4153    Normal
## 4154    Normal
## 4155    Normal
## 4156    Normal
## 4157    Normal
## 4158 High Wage
## 4159       Low
## 4160       Low
## 4161       Low
## 4162       Low
## 4163       Low
## 4164       Low
## 4165       Low

Part 2: Loops

Chunk 1: Checking Geometric Series Proof with for loop

Geometric Series: \(a, ar, ar^2, ar^3,...\)

Formula of Sum: \(\sum_{k=0}^\infty ar^k=\frac{a}{1-r}\), for \(|r|<1\).

a=1 #Any Number
r=1/2 #Any Number Between -1 and 1: abs(r)<1

theoretical.limit=a/(1-r)

START=a

FINISH.1 = START + a*r^1

FINISH.2 = FINISH.1 + a*r^2

FINISH.3 = FINISH.2 + a*r^3

# Notice the repeated pattern above: FINISH.k = FINISH.(k-1) + a*r^k
###---------------------------------------------###
FINISH.10 = a 
for(k in 1:10){
  FINISH.10=FINISH.10+a*r^k
}

FINISH.100 = a 
for(k in 1:100){
  FINISH.100=FINISH.100+a*r^k
}

DATA = tibble(k=c(1,2,3,10,100,"Infinity"),
            SUMMATION=c(FINISH.1,FINISH.2,FINISH.3,
                        FINISH.10,FINISH.100,
                        theoretical.limit))
print(DATA)

ABSOLUTE.ERROR = abs(FINISH.100-theoretical.limit)
print(ABSOLUTE.ERROR)

Excercise 4

set.seed(4)
u = rnorm(100)

Use for loop to calculate sum of the squares of the first 10 elements of vector u. Hint: ^ (Exponents), 3^2=9

sum10 = 0
for(i in 1:10){
  sum10 = sum10 + u[i]^2
}
print(sum10)
## [1] 13.08209

Use for loop and if statement to calculate the sum of squares of the elements with even indices of vector u. Hint: %% gives the remainder of division.

sum_even = 0
for(i in 1:100){
  if(i%%2==0){
    sum_even = sum_even + u[i]^2
  }
}
print(sum_even)
## [1] 37.33534

Chunk 2: Checking Geometric Series Proof with while loop

a=1
r=2

FINISH=a
k=0
while(abs(FINISH-a/(1-r)) > 1e-10) {
  k=k+1
  FINISH = FINISH + a*r^k
  if(k>100) break
}
print(c(k,FINISH))

Chunk 3: Saving Steps in Geometric Series for Figure

a=1
r=-0.5
theoretical.limit=a/(1-r)

K=100 #How Many Steps Do You Want to Save?

summation=rep(NA,(K+1))
summation[1]=a
for (k in 1:K) {
  summation[k+1]=summation[k] + a*r^k
}

ggplot() +
  geom_line(aes(x=1:(K+1),y=summation)) +
  geom_hline(yintercept=theoretical.limit,
             linetype="dashed")

Excercise 5

Write for loops to generate 100 random samples from normal distributions with means of 0 to 99 and save the random samples to a vector a.

  • The kth component of a is generated from \(N(k-1,1)\).
  • Hint: Function for generating random samples from normal distribution rnorm.
set.seed(100)
a = rep(NA,100)
for (k in 1:100){
  a[k] = rnorm(1,k-1,1)
}
a
##   [1] -0.5021924  1.1315312  1.9210829  3.8867848  4.1169713  5.3186301
##   [7]  5.4182093  7.7145327  7.1747406  8.6401379 10.0898861 11.0962745
##  [13] 11.7983660 13.7398405 14.1233795 14.9706833 15.6111458 17.5108563
##  [19] 17.0861858 21.3102968 19.5619100 21.7640606 22.2619613 23.7734046
##  [25] 23.1856209 24.5615494 25.2797784 27.2309445 26.8422705 29.2470760
##  [31] 29.9088864 32.7573756 31.8620704 32.8888065 33.3099857 34.7782058
##  [37] 36.1829077 37.4173233 39.0654023 39.9702020 39.8983708 42.4032035
##  [43] 40.2232244 43.6228674 43.4777166 46.3222310 45.6365597 48.3190657
##  [49] 48.0437791 47.1213441 49.5529378 49.2614021 52.1788648 54.8974657
##  [55] 51.7280745 55.9804641 54.6011744 58.8248724 59.3812987 58.1611481
##  [61] 59.7380042 60.9311560 61.6211164 65.5819589 64.1298341 64.2869750
##  [67] 66.6379942 67.2016916 67.9300831 68.9075101 70.4489033 69.9356443
##  [73] 70.8375807 74.6485217 71.9379040 75.0127497 74.9124717 77.2705395
##  [79] 79.0084519 76.9255952 80.8968223 80.9500042 80.6546507 81.0687885
##  [85] 84.7095816 84.8420950 86.2163679 87.8173621 89.7271758 88.8962297
##  [91] 89.4428777 92.4283014 91.1070426 91.8424288 93.4697035 97.4456828
##  [97] 95.1675042 97.4135198 96.8213169 97.8259652