Notebook Instructions


Task 1

Installing packages in R/RStudio.

We are going to use tidyverse a collection of R packages designed for data science. All packages share an underlying design philosophy, grammar, and data structures. *Info:* https://www.tidyverse.org/

## Loading required package: tidyverse
## ── Attaching packages ─────────────────────────────────────────────────────── tidyverse 1.2.1 ──
## ✔ ggplot2 2.2.1     ✔ purrr   0.2.4
## ✔ tibble  1.4.2     ✔ dplyr   0.7.4
## ✔ tidyr   0.7.2     ✔ stringr 1.2.0
## ✔ readr   1.1.1     ✔ forcats 0.2.0
## ── Conflicts ────────────────────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag()    masks stats::lag()

1A) Read the csv file into R Studio and display the dataset.

  • Name your dataset ‘mydata’ so it easy to work with.
  • Commands: read_csv() head()
mydata = read_csv("data/data - Scoring.csv")
## Parsed with column specification:
## cols(
##   Status = col_character(),
##   Seniority = col_integer(),
##   Home = col_character(),
##   Time = col_integer(),
##   Age = col_integer(),
##   Marital = col_character(),
##   Records = col_character(),
##   Job = col_character(),
##   Expenses = col_integer(),
##   Income = col_integer(),
##   Assets = col_integer(),
##   Debt = col_integer(),
##   Amount = col_character(),
##   Price = col_character(),
##   Finrat = col_double(),
##   Savings = col_double()
## )
head(mydata)
## # A tibble: 6 x 16
##   Status Seniority Home   Time   Age Marital Records Job   Expenses Income
##   <chr>      <int> <chr> <int> <int> <chr>   <chr>   <chr>    <int>  <int>
## 1 good           9 rent     60    30 married no_rec  free…       73    129
## 2 good          17 rent     60    58 widow   no_rec  fixed       48    131
## 3 bad           10 owner    36    46 married yes_rec free…       90    200
## 4 good           0 rent     60    24 single  no_rec  fixed       63    182
## 5 good           0 rent     36    26 single  no_rec  fixed       46    107
## 6 good           1 owner    60    36 married no_rec  fixed       75    214
## # ... with 6 more variables: Assets <int>, Debt <int>, Amount <chr>,
## #   Price <chr>, Finrat <dbl>, Savings <dbl>

Extract the assigned features (columns) to perform some analytics

To extract the features (columns) from the dataset, use the name of the dataset follow by ‘$’ sign and the name the specific column.

Extract the first feature (column)

#Extracting the expenses Column
expenses = mydata$Expenses 

#Calling the income Column
expenses 
##    [1]  73  48  90  63  46  75  75  35  90  90  60  60  75  75  35  75  35
##   [18]  65  45  35  46  45 105  74  45  60  75  75  75  45  45  75  75  35
##   [35]  45  45  75  70  45  44  75  35  45  75  35  35  75  48  60  60  75
##   [52] 105  75  60  85  35  45  60  90  70  90  35  75  75  75  75  60  45
##   [69]  93  60  60  45  75  75  86  90  45  70  45  60  60  60  35  75  35
##   [86]  47  60  40  60  35  35 101  95 140  75  45  35 120  89  45  73  75
##  [103]  78  35  75  76  90  45  35  79  45  90  35  60  75  35  75  45  35
##  [120]  75  57  75  66 114  45  35  75  35  90  75  45  75  60  65  75  60
##  [137]  45  60  45  47  60  90  75 119  35 105  60  35  45  60  35  45  60
##  [154]  35  75  78  35  45  75  90  75  35  60  57  60  45  75  42  75  45
##  [171]  77  75  74  75  35  35  60  75  45  45 113  75  75  75  75  75  60
##  [188]  78  46  45 120  75  90  45  60  75  87 126  45  35  90  45  75  75
##  [205]  60  45  35  75 105  75  75  35  35  45  45  60  60  45  90 105  60
##  [222]  60  60  35  35  75  60  45  35  35 100  56  45  57  45  62  45  45
##  [239]  90  90  90  60  35  45  35  35  45  45  45  45  73  94 105  60  60
##  [256]  77  60  88  45  93  60 105  60  75  35  45  75  60  60  60  60  44
##  [273]  60  35  35  75  56  35  45  75  35  60  60  60  75  60  45  75  60
##  [290]  75  60  90  73  60  90  45  45  45  45  35  35  75  90  59  87  35
##  [307]  60  90  85  75  60  60  96  45  45  45  45  45  87  60  35  90  35
##  [324]  71  75  45  75  60  75  60  75  90  35  45  75  90  60  45  60 173
##  [341]  60  60  60  60  90  60 110  45  70  60  75  60  35  45  35  75  75
##  [358]  45  45  75  35  75  35  90  60 113  60  75  76  45  90  45  75  35
##  [375]  35  90  72  60  49  58  66  35  75  75  60  60  35  35  75  68  90
##  [392]  60  75  60  35  45  75  70  60  60  75  35  49  45  75  45  45  60
##  [409]  66  45  45  63  45  67  84  90  35  35  75  75  60  82  86  35  35
##  [426]  60  71  60  80  45  54  51  60  75  86  60  75  45  95  45  60  35
##  [443]  45  55  45  85  63  35  75  45  45  50  60  45  60  60  45  45  75
##  [460]  35  35  45  75  75  49  60  60  60  75  60  90  45  75  60  58  35
##  [477]  45 107  45  54  35  90  75  60  60  54  45  43  45  60  60  60  75
##  [494]  35  62  35  35  35  45  75  35  66  35  35  90  75  68  90  60  45
##  [511]  45  75  52  45  68  77  45  45  46  45  35  45  45  75  60  60  45
##  [528]  75  60  35  59  75  69  45  45  75  35  60 101  45  60  60  75  75
##  [545]  75  75  35  75  60  44  75  75  75  60  64  66  45  91  35  45  90
##  [562]  35  35 135  60  75  90  45  45  45  45  88  45  45  75  75  60 120
##  [579]  93  35  90  60  45  75  75  35  35 105  90  45  75  75  90  60  75
##  [596]  76  45  35  90  35  84  60 105  75  60  75 103  90  35  56  75 105
##  [613]  45  35  90  90  45  60  69  77  75  90  45  55  60  60  74  56  60
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##  [817] 105  45  60  90  35  45 105  75  35  64  90  45  75  60  75  35  90
##  [834]  70  45  60  60  75  85  53  90  45 105  60  90  35  35  90  35  35
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##  [868]  90  45 100  45  75  75  97  90  60  45  90  35  75  72  70  60  35
##  [885] 105  60  75  35  55  35  75  45  58  74  60  45  60  35  51  45  35
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## [3044]  35  35  45  45  35  35  45  35  60  35  35  35  60  75  35  90  35
## [3061]  43  35  45  60  35  35  35  47  35  60  45  60  35  48  45  35  35
## [3078]  47  35  45  35  35  58  35  35  60  45  48  60  60  35  53  60  45
## [3095]  43  45  35  35  60  35  35  45  60  90  70  45  60  45  83  45  35
## [3112]  35  45  75  35  60  59  45  54  60  47  45  35  60  35  35  45  35
## [3129]  35  35  60  35  45  45  35  45  45  35  35  35  60  45  45 105  35
## [3146]  60  60  56  90  45  60  35  75  68  35  60  49  60  35  35  60  64
## [3163]  45  35  66  45  35  60  45  45  60 168  35  35  35  35  75  60  35
## [3180]  45  46  45  52  74  35  35  45  60  45  45  60  35  75  60  54  60
## [3197]  35  35  60  42  45  45  89  35  60  87  45  35  35  45  60  41  75
## [3214]  45  45  45  75  45  51  60  66  35  82  35  60  35  60  35  35  35
## [3231]  90  49  60  72  35  60  35  75  60  75  35  35  80  44  35 108  60
## [3248]  60  35  35  45  46  35  75  35  60  45  41  60  60  60  45  75  45
## [3265]  54  60  35  35  45  60 100  60  35  61  35  60  60  45  60  35  35
## [3282]  35  42  48  35  58  35  35  45  35  35  47  35  90  45  35  60  35
## [3299]  35  35  35  35  35  35  35  45  35  35  60  60  58  75  45  45  60
## [3316]  45  35  35  77  35  45  35  60  60  35  35  60  60  35  60  47  35
## [3333]  45  35  35  45  60  35  45  35  45  55  35  35  35  46  45  75  50
## [3350]  56  60  51  35  55  46  60  45  35  60  35  57  35  54  72  60  60
## [3367]  35  35  35  55  35  35  35  45  45  90  35  60  75  45  78  35  35
## [3384]  35  35  35  35  35  44  51  35  45  35  75  79  73  45  60  60  35
## [3401]  35  45  35  35  75  45  60  60  60  35  60  90  59  90  35  42  45
## [3418]  60  35  60  60  35  45  45  45  60  35  51  60  35  45  60  35  35
## [3435]  42  45  60  35  35  44  35  45  35  35  75  35  60  45  70  35  46
## [3452]  45  60  45  45  35  35  75  60  45  45  65  45  35  45  45  45  54
## [3469]  60  90  56  53  35  35  45  45  45  35  75  35  75  55  45  45  35
## [3486]  35  35  35  35  35  35  45  45  60  35  84  75  45  60  45  35  58
## [3503]  60  45  60  35  35  35  35  35  45  35  60  35  60  45  60  75  45
## [3520]  45  35  45  35  45  35  35  35  35  45  75  45  35  45  68  59  60
## [3537]  35  45  35  55  54  45  45  35  77  35  45  35  44  88  80  60  35
## [3554]  35  37  60  47  45  35  35  60  35  60  60  75  35  45  65  35  75
## [3571]  35  75  60  75  45  35  45  35  35  79  60  35  45  35  90  60  75
## [3588]  81  76  35  59 103  45  60  35  35  62  45  60  75  35  90  35  43
## [3605]  35  35  35  35  35  35  45  45  75  45  60  35  64  35  35  45  35
## [3622]  60  45  35  75  45  45  60  54  45  45  82  60  35  60  35  35  35
## [3639]  45  35  35  35  35  35  60  45  46  35  35  35  35  63  75  35  57
## [3656]  35  35  35  35  35  60  45  45  62  60  60  60  35  60  35  45  60
## [3673]  35  54  35  45  60  60  45  60  35  35  75  35  69  35  35  57  96
## [3690]  45  54  72  35  46  45  45  64  45  45  55  75  60  35  45  60  35
## [3707]  60  45  35  45  60  35  35  60  60  35  59  45  35  75  60  35  35
## [3724]  35  35  90  65  35  45  35  35  45  35  60  53  35  35  56  53  35
## [3741]  60  53  60  45  60  92  60 104  45  35  75  35  52  35  45  35  42
## [3758]  42  73  45  35  35  60  45  35  45  51  35  35  45  35  35  60  35
## [3775]  60  60  45  35  60  47  35  45  60  35  58 105  60  35  43  45  35
## [3792]  60  45  60  35  35  35  60  60  35  35  60  42  35  35  63  35  72
## [3809]  35  75  35  35  60  60  45  60  35  75  60  35  35  45  35  35  35
## [3826]  90  60  35  55  75  35  35  60  60  71  35  60  60  35  35  60  35
## [3843]  35  47  60  75  35  45  35  45  35  45  56  45  60  75  35  35  35
## [3860]  51  35  45  57  35  60  45  60  45  45  56  50  60  61  45  38  42
## [3877]  60  57  45  45  45  45  35  75  35  35  55  35  60  45  35  40  60
## [3894]  35  60  41  45  55  60  60  35  35  45  47  38  35  60  60  35  45
## [3911]  42  35  60  60  35  35  44  60  60  45  35  75  75  60  60  35  76
## [3928]  60  45  55  75  43  45  35  65  35  45  60  35  60  35  35  45  35
## [3945]  60  35  35  35  45  35  45  45  44  60  35  45  86  75  60  45  45
## [3962]  35  35  48  35  60  89  60  60  72  35  49  80  35  74  35  60  35
## [3979]  35  35  35  35  55  60  45  45  70  45  35  35  54  35  60  45  60
## [3996]  35  35  75  35  77  45  84  35  35  39  35  35  46  35  35  97  60
## [4013]  35  45  75  35  35  35  45  44  35  35  45  60  75  53  70  45  41
## [4030]  35  52  69  56  57  35  35  73  35  60 106  35  90  35  35  35  35
## [4047]  45  45  35  75  90  60  47  60  45  45  35  35  69  35  45  45  75
## [4064]  35  45  60  35  35  35  90  35  77  35  75  35  60  35  60  45  60
## [4081]  45  60  84  60  35  45  35  35  75  46  45  75  35  35  35  45  35
## [4098]  35  35  54  75  35  60  35  65  64  35  45  45  60  35  75  68  60
## [4115]  35  45  75  45  60  35  35  35  35  35  75  35  35  35  35  35  35
## [4132]  45  45  35  75  50  62  49  45  60  35  60  35  35  60  45  35  35
## [4149]  60  60  35  75  35  60  35  45  75  60  35  35  35  35  46  45  35
## [4166]  35  60  35  35  45  35  51  45  45  35  94  35  43  60  45  46  45
## [4183]  45  35  35  90  45  45  75  35 105  52  60  35  35  45  35  35  46
## [4200]  49  84  35  45  45  70  35  42  35  35  45  45  35  35  35  45  60
## [4217]  60  45  60  45  45  35  35  35  60  97  60  71  35  35  47  60  60
## [4234]  43  60  48  35  45  45  77  60  45  45  60  60  35  35  90  60  45
## [4251]  45  35  57  60  45  35  35  85 105  35  75  35  35  75  72  35  45
## [4268]  45  45  60  35  60  45  75  35  35  56  66  45  40  35  45  35  60
## [4285]  48  35  35  45  35  47  45  35  35  70  45  45  35  41  35  35  35
## [4302]  47  60  35  60  35  35  70  35  60  71  35  60  69  35  48  47  35
## [4319]  90  45  35  60  35  45  35  35  35  35  35  35  35  35  35  35  60
## [4336]  58  60  35  60  48  60  75  60  70  35  35  60  45  45  35  35  60
## [4353]  45  35  35  35  61  45  51  60  45  60  75  45  60  44  45  60  60
## [4370]  35  75  45  35  45  45  35  60  45  35  35  45  48  74  60  35  45
## [4387]  35  60  35  45  45  35  35  74  35  54  35  42  57  46  45  60  45
## [4404]  35  45  45  53  45  45  45  45  35  45  35  66  35  45  35  60  75
## [4421]  45  75  45  75  35  35  45  45  35  45  75  60  35  45  35  35  35
## [4438]  90  45  35  75  69  60  60  49  60

Now, use the same procedure to extract the other feature

#Extracting the feature (column)
savings = mydata$Savings
#Calling the  feature (column)
savings
##    [1]  4.20000000  4.98000000  1.98000000  7.93333333  7.08387097
##    [6] 12.83076923  1.87500000  2.70000000  0.85000000 -0.40000000
##   [11]  2.71304348  3.37846154  3.96000000  5.54400000  0.67500000
##   [16]  1.49333333  4.72000000  4.60000000  3.70909091  4.89600000
##   [21]  2.44000000 15.21818182  0.20000000  4.16842105  4.35555556
##   [26]  3.60000000  6.30000000  3.52000000  0.40000000  3.14181818
##   [31]  6.93000000  6.56000000  2.70000000  4.41818182  2.53714286
##   [36]  7.82400000  2.40000000  1.64842105  4.00000000  1.69846154
##   [41]  4.13333333 12.31578947  3.21600000 -0.16000000  4.43478261
##   [46]  4.37142857  5.13600000  6.40000000  4.32000000  2.81250000
##   [51]  1.00000000  9.80000000  4.52000000  2.16000000  0.72000000
##   [56]  3.90000000  3.30000000  3.80000000 18.75000000  5.73770492
##   [61]  2.61818182  2.45000000  2.76000000  2.77200000  2.26666667
##   [66]  3.18000000  6.25000000  8.82352941  2.49000000  7.12000000
##   [71]  2.82000000 12.40000000 13.32000000  0.61714286  1.32000000
##   [76]  9.84000000  0.00000000  3.70285714  2.93333333  0.36000000
##   [81]  5.89090909  0.42352941 13.68000000  7.50000000  0.62400000
##   [86]  7.30000000  2.73492286  0.57692308  5.16000000  2.21052632
##   [91]  2.81879195 14.97600000  8.59500000  7.20000000  4.50000000
##   [96] 13.39200000  2.84210526  2.11200000  3.60000000  0.41600000
##  [101]  3.10909091  3.80000000  5.64923077  2.58461539 14.40000000
##  [106]  3.52000000 11.75000000  2.85000000  7.61142857  6.69473684
##  [111]  2.27200000  8.28358209  1.51200000 13.82686567  0.66000000
##  [116]  7.42500000  3.83478261  2.47578947 13.71428571  5.00000000
##  [121]  3.86666667  1.83333333  6.83076923 15.05454545  9.17647059
##  [126]  2.57142857  4.83870968  1.84615385  2.23200000  4.10526316
##  [131]  0.64285714  4.84615385  7.50000000 11.57142857  7.70769231
##  [136]  4.66666667  2.86956522  2.45454545  2.90400000  5.47500000
##  [141]  1.26000000  1.64210526  5.00400000 20.23533333  3.04615385
##  [146] -0.12705882 16.28571429  2.20000000  4.60000000 14.40000000
##  [151]  2.30400000  8.45454545  0.00000000  7.28571429  0.78400000
##  [156]  4.04000000  1.36000000 12.85714286  1.77600000  2.32258064
##  [161]  3.40363636  8.61600000 16.02000000  3.78000000 17.54838710
##  [166]  1.60000000  3.00000000  2.56000000  0.50769231  6.72000000
##  [171]  3.91111111  1.48235294  2.74285714  9.00000000  2.13785790
##  [176]  7.90000000  5.20000000 20.62500000  2.60000000  1.60000000
##  [181]  4.43368421  0.42857143  5.35200000  2.50000000  3.17142857
##  [186]  5.45629091  2.25000000  2.10000000  2.29714286  5.28000000
##  [191]  6.48000000  5.10000000  1.68000000  0.99000000  2.10000000
##  [196]  0.63157895  1.68224299  9.64137931  1.75000000  1.82857143
##  [201]  2.78400000  8.92941176  8.09142857  6.00000000 -1.12800000
##  [206]  5.96000000  1.80000000  3.78000000  1.53000000  3.70800000
##  [211]  3.30000000  1.00800000  2.54400000  4.75000000  5.60000000
##  [216]  1.25454545  3.02400000  3.72000000  4.47272727  6.00000000
##  [221]  8.14736842  3.37226277  3.50400000  7.01219512  6.22800000
##  [226]  7.00000000  2.91000000  4.76666667  3.06000000  2.20000000
##  [231]  0.00000000  4.74000000  2.86956522  3.60000000  2.57142857
##  [236]  3.18000000  2.96470588 12.10000000  6.61714286  2.62222222
##  [241]  3.84000000  3.60000000 11.46000000  6.95294118  1.26315789
##  [246]  9.90000000 14.25000000  1.33333333  4.83116883  4.75000000
##  [251]  4.45714286  4.55000000  3.13090909  4.50000000  3.60000000
##  [256]  4.29230769 15.14040000  2.01600000  5.70857143  6.30000000
##  [261] 11.24000000  2.68915663  4.92000000  9.28800000  7.01298701
##  [266]  6.42857143  1.68000000  8.49600000  5.82000000  1.76842105
##  [271]  3.48000000  2.82000000  4.20000000  2.54400000  4.53333333
##  [276] -0.30000000  4.61538461 11.34000000  1.92000000  3.46909091
##  [281]  6.16000000  3.78000000  0.52941176 13.96363636  6.80000000
##  [286]  3.50000000  5.01818182  6.54000000  6.57000000  5.91428571
##  [291]  2.16000000  0.12000000  3.14563107  1.50000000  4.52571429
##  [296]  0.86400000  8.22000000  0.67200000  0.31578947  5.48571429
##  [301]  1.85142857 -0.99130435 -0.20000000  2.16000000  1.52307692
##  [306]  7.44000000  2.00571429 -0.14400000  0.70000000  0.94153846
##  [311] 10.84615385  1.44000000  3.90857143  2.35714286  3.12000000
##  [316]  0.80000000 14.56000000  2.45000000  1.22181818  6.17142857
##  [321]  3.00000000  7.77000000  7.10924370  2.03478261  2.68965517
##  [326] 14.36842105 -0.90000000 12.78000000  4.07272727  0.38888889
##  [331]  4.95789474 -1.60135922  7.12500000 13.28571429  3.34588235
##  [336]  2.77161290  3.00000000  4.08000000  2.92000000  3.10909091
##  [341]  5.64000000 -0.62500000  5.62909091  5.54571429 -1.81621622
##  [346] -1.41176471 -7.20000000  7.68000000  1.44000000  2.60400000
##  [351]  5.73033708 -1.80000000  8.88000000  2.02500000  1.44000000
##  [356]  3.05806452  4.09090909 14.96000000  3.60000000  6.42857143
##  [361]  4.33333333  0.12000000  5.60000000  2.34000000  2.65116279
##  [366]  7.54200000  4.80000000 -0.48000000  5.92500000 15.00000000
##  [371]  7.98000000  3.09230769  3.73846154  2.64000000  1.55454545
##  [376] -4.08060000  2.76000000  5.52000000  4.12800000  2.68000000
##  [381]  5.11200000  1.92000000 10.20000000 13.50000000  1.66153846
##  [386]  4.30588235  5.28000000  4.80000000  8.47200000  6.60000000
##  [391]  5.47058824 -0.67200000  2.74285714 -1.18681319  4.56000000
##  [396]  6.72000000  3.50000000  7.63636364  1.80000000  3.75000000
##  [401]  3.77777778  4.85000000  2.84869565  4.92857143  3.12857143
##  [406]  3.49714286  2.08000000  2.25600000  4.42105263  7.94625000
##  [411]  4.54285714  4.03200000  3.05142857  0.22784810  0.09000000
##  [416] -5.88000000  1.30434783  5.30000000  5.52000000  3.99272727
##  [421]  4.26666667 -0.56727273  2.05714286  1.27058823  2.18571429
##  [426]  4.48000000  2.00881057  2.35955056  6.70909091  2.76000000
##  [431]  7.45411765  7.80000000  8.10000000  7.89230769  1.36421053
##  [436]  7.07200000  1.34400000  4.00000000  9.98400000 -0.17142857
##  [441] 12.85714286  1.98697674  2.32941177  4.74545455  1.78378378
##  [446]  0.35820895  5.23636364  0.42666667  1.03448276  8.34545455
##  [451]  2.82857143  3.60000000  7.30000000  6.24000000  6.08571429
##  [456]  1.63636364  3.22758621  7.40000000  5.55555556  5.48000000
##  [461]  1.26816380  3.00000000  3.04285714  0.44444444  3.48000000
##  [466]  1.63636364  4.58181818  2.40000000  0.25714286  2.85882353
##  [471]  1.00000000  1.15000000  6.50000000  8.97600000 12.52500000
##  [476]  5.25000000 -0.58666667 12.17142857  3.16000000  1.98000000
##  [481]  3.78000000 -0.72000000  0.72857143  1.84615385  2.91600000
##  [486]  2.34000000  5.54666667  2.28000000  2.35555556  4.07142857
##  [491]  5.82000000  4.21621622  1.66956522  2.58947368  3.60000000
##  [496]  8.40000000  2.33333333  1.50000000  1.40000000  0.36000000
##  [501]  4.16000000  4.48000000  1.87200000  4.08000000  5.92941177
##  [506]  5.58750000  0.72000000  5.70000000  1.63636364  5.74020619
##  [511]  1.90909091  3.60000000 12.13714286  2.20000000  7.24615385
##  [516]  2.42727273  6.97500000  1.82000000  2.30400000  5.60000000
##  [521] 30.42000000  4.00000000 20.86153846 10.75000000  5.33333333
##  [526]  1.68000000  2.67428571  6.27692308  3.24000000  7.15636364
##  [531]  2.98800000  0.20769231  3.45600000  2.88000000  1.65245902
##  [536]  3.60000000  6.17647059  7.84000000  5.72400000  3.05000000
##  [541] 10.66666667  7.04000000  3.48000000 -0.56250000  0.46989474
##  [546]  0.41379310  3.22314050  7.40000000  7.32000000  2.64000000
##  [551]  2.96000000  0.34698795 -1.02857143  6.83636364 -0.90625000
##  [556] -0.18000000  6.67058824  2.47058824  3.49411765  6.51428571
##  [561]  1.12000000  2.06400000  1.32000000  9.90000000  0.25714286
##  [566]  5.08000000  2.85818182  2.66197183  6.64705882  1.88000000
##  [571]  2.54050909  1.18400000  2.65000000  8.61176471  2.92000000
##  [576]  7.90000000  3.36000000  0.15517241  3.48000000  2.85000000
##  [581]  1.96363636  1.74545455  3.35172414 10.50000000  2.88000000
##  [586]  7.74000000  8.70000000  1.47692308  6.64285714  2.94545455
##  [591]  1.57500000  0.54545455  1.72800000  1.98000000  1.36363636
##  [596]  3.36000000  4.16326531  3.14285714  6.73200000  4.01454546
##  [601]  0.12000000  2.33333333 20.28000000  2.37913043  8.22857143
##  [606] 13.32000000  3.00000000  0.00000000  0.80000000  5.10000000
##  [611] 13.50000000  3.00000000  3.69552000  0.67764706  4.51764706
##  [616]  2.40000000  1.89473684  6.51678832  0.67764706  3.14181818
##  [621]  3.60000000 -0.15000000  7.20000000  2.40000000  2.26666667
##  [626]  6.64615385  3.96000000  2.78181818  2.16000000 10.73684211
##  [631] 17.24444444  2.32615385  9.00000000  0.38181818  8.20000000
##  [636]  1.50000000  2.40000000  3.10909091  3.64285714  0.96923077
##  [641]  0.11250000 -1.33333333  3.78461538  2.61428571 -0.25714286
##  [646]  2.92800000  3.02608696  3.36461539  1.53846154 10.80000000
##  [651]  1.22400000  2.75000000  0.11250000  9.06000000  8.70000000
##  [656]  9.83132530  6.34736842  5.58620690  1.38000000  2.92173913
##  [661]  7.20000000  9.21428571  0.30000000  4.50000000  7.90000000
##  [666] 12.40000000  4.10714286  7.50000000  3.24000000 -0.48610909
##  [671]  0.90000000  3.67500000  5.42769231  7.04516129 -0.21739130
##  [676]  3.71076923  3.44571429 16.40000000  2.90909091  0.90000000
##  [681]  7.71428571 14.88000000  6.15652174  4.86486487  1.08000000
##  [686]  1.34400000  2.18181818 18.90000000  3.56250000  0.28173913
##  [691]  3.78947368  3.16800000  8.46000000  7.02000000  7.77777778
##  [696]  3.45000000  3.25333333  7.06666667  0.63380282  0.44000000
##  [701]  6.00000000  6.55058824 -0.42580645  0.72000000  3.30000000
##  [706]  3.57333333  5.18400000  2.10000000  3.53684210  5.07692308
##  [711]  4.88000000  1.26720000 -1.47867299  2.31428571 -0.14769231
##  [716]  1.28571429  0.68571429  2.34000000  6.90000000  5.81250000
##  [721]  2.36800000  3.35172414  3.78947368  5.38666667  4.25454545
##  [726] -0.37500000  0.73636364  6.13333333  3.30000000  1.80000000
##  [731]  3.73714286  2.52857143 11.05714286  6.62400000  2.34000000
##  [736]  1.13207547  4.25000000  1.95692308  3.39120000  2.90080000
##  [741]  7.77600000  4.04444444  2.40000000  4.89473684  0.90000000
##  [746] -0.57600000  3.73333333  2.09142857  5.25000000  6.72000000
##  [751]  0.12000000  1.23966942 23.10000000  3.36923077 -1.60000000
##  [756]  5.13303628  6.13333333  2.80000000  6.50000000  2.82352941
##  [761]  3.06000000  3.27272727  2.25000000  3.20000000  0.54500000
##  [766]  3.45600000  2.25000000  0.34285714  0.80000000  2.80000000
##  [771]  9.17647059 20.48571429  4.82400000  6.17142857  3.27272727
##  [776]  9.51428571  0.62222222 11.70000000 -0.66000000  1.17000000
##  [781] -0.33750000  3.80000000  1.00285714  2.44285714  1.67400000
##  [786] 12.73584906  4.50000000  2.72307692  3.42857143  1.68000000
##  [791] 11.50000000  2.29500000  0.24000000  2.76000000  1.92000000
##  [796]  2.33333333  6.78000000  4.14000000  5.41714286  4.53333333
##  [801]  1.10400000  4.20705882  5.37391304  3.71368421 18.72000000
##  [806]  2.95578947 -0.42000000  5.69142857  4.71540000  8.32000000
##  [811] 13.66666667  3.68098159 10.08849558  1.65000000  5.85000000
##  [816]  6.00000000  2.94000000  9.00000000  4.70769231  3.42857143
##  [821]  3.65454546  2.76000000 -2.70000000  4.32000000  3.06000000
##  [826] -1.46086957  1.40400000  5.33333333  3.53454545 -0.08000000
##  [831]  1.89913044  4.11428571  2.97600000  9.00000000  1.99200000
##  [836]  3.42000000 30.20000000  6.91764706  0.90000000  4.05000000
##  [841] 10.50000000  3.45600000  5.95636364  6.16000000  1.92000000
##  [846]  3.89647059  0.28800000 -0.90000000  1.53000000  3.90000000
##  [851]  7.08196721  4.62000000  2.06000000  7.57894737  0.99130435
##  [856]  4.15384615  4.45263158  2.16666667  5.31428571  0.54545455
##  [861]  2.83333333  2.18536585 -1.29600000 -1.08000000  3.00000000
##  [866]  6.00000000  2.17674419  2.10000000  3.69818182  4.70400000
##  [871]  9.46153846  2.93333333  5.28000000 -1.92000000  4.34057143
##  [876]  6.65142857  5.19587629  2.58750000  3.53454545  0.78000000
##  [881]  1.28000000  2.00000000  3.00000000  3.12000000 -1.05882353
##  [886]  6.45000000 -0.34500000  3.60000000  3.52000000  3.36000000
##  [891]  5.04000000  3.78000000  5.06666667  2.56000000  1.88976378
##  [896]  5.30769231  3.71666667  2.27027027  0.30857143  1.02000000
##  [901]  7.69090909  3.00000000  7.50857143  2.37500000  4.20000000
##  [906]  2.84210526  3.12000000  2.55483871  4.08000000  4.32000000
##  [911]  1.58400000  3.16800000  4.59428571  1.65818182  3.78000000
##  [916]  7.61538461 26.00000000 16.25769231  2.70000000  2.40000000
##  [921]  1.87826087  3.85714286  1.08000000  8.00000000  1.50000000
##  [926]  3.71200000  2.27027027  7.48800000  2.25600000  5.37428571
##  [931]  2.27586207 -0.39000000  8.06163328  2.93647059  1.92857143
##  [936]  0.00000000 -2.80000000  8.00000000  5.41090909  7.20000000
##  [941]  0.24705882 -0.51428571  0.11076923  2.56994819  5.14285714
##  [946]  8.25688073  0.93750000 -1.67441861 -0.54000000 11.60000000
##  [951]  2.16000000  3.00000000  0.91200000  6.54545455  4.70400000
##  [956]  2.52000000  5.40000000  2.85957447 -8.16000000  8.53714286
##  [961]  4.62000000  1.85000000  3.10588235  1.74315789  6.83478261
##  [966]  0.57142857  3.36000000  6.35294118  2.60000000  3.78000000
##  [971]  3.00000000  0.96000000  4.08000000  8.46000000  2.06250000
##  [976] 11.20000000 13.02857143 10.66666667  1.92000000 -1.25000000
##  [981]  4.22012903  1.26000000  2.21052632  5.53333333  1.41000000
##  [986]  1.37647059  4.08000000  1.45000000  7.80000000  2.40000000
##  [991]  1.80000000  6.00000000  4.84137931  2.40000000  9.61200000
##  [996]  2.82000000  5.12640000  3.24705882  2.01000000  1.50000000
## [1001]  5.40000000  8.64000000  8.00000000  6.02880000  3.82736842
## [1006]  9.64800000  1.54285714  9.78947368  2.89411765  2.21250000
## [1011]  4.64132231  1.84000000  5.28000000  5.92340426  2.82352941
## [1016] -0.14754098  3.96000000  3.18857143 -2.58461539 -2.58461539
## [1021]  2.96000000  5.32800000  3.07200000  6.36631579  5.38064516
## [1026]  1.95000000 -1.20000000  3.78666667  6.60000000  3.29142857
## [1031]  3.51562500  4.92000000 15.86666667  7.50000000  3.82153846
## [1036]  1.12258064  0.81818182  2.19272727  3.34054054  2.40000000
## [1041]  2.46315790  9.37500000  2.18571429  3.40363636  2.62222222
## [1046]  4.20923077  4.87500000  6.85714286  1.14352941  3.80470588
## [1051]  8.75000000  4.10400000  2.55000000  3.94285714  0.96000000
## [1056]  3.40800000  3.96000000  6.08000000  4.38000000 20.40000000
## [1061]  2.41200000  3.60000000  1.11111111  2.30400000  0.21428571
## [1066]  2.03636364  1.29000000  6.38181818 11.62105263  0.72000000
## [1071]  2.22631579  1.40400000  5.42400000  4.11428571 -0.08727273
## [1076] 13.20000000 17.14285714  0.36000000  7.20000000  5.27331190
## [1081]  5.16000000  6.09022556  1.20000000  1.74315789  3.66666667
## [1086]  0.09000000  1.08000000  3.15243243  5.76000000  2.01600000
## [1091] -1.20000000  6.84000000  0.15000000  1.87636364  4.75384615
## [1096] 13.12941176 -0.60631579  5.62105263  7.80000000  9.44000000
## [1101]  3.69230769 -0.09000000  3.63750000  5.64000000  3.78000000
## [1106]  6.62400000  2.78571429  3.96000000  8.49600000  7.60000000
## [1111]  3.30612245  6.60000000  0.82877698  6.52800000  5.08000000
## [1116]  1.75000000  2.45454545  1.98000000 -0.76000000 -1.02857143
## [1121]  5.22000000  1.34400000 10.04651163 17.70000000  4.50000000
## [1126]  8.96000000  3.56000000  2.77714286  4.60000000 -1.98000000
## [1131]  4.63636364  9.85714286  7.83360000  1.52727273  1.89913044
## [1136] -0.64000000 -1.20000000  5.47500000 -0.52000000  9.00000000
## [1141]  3.61111111 13.11428571  1.21263158  2.10000000  5.04000000
## [1146] 16.14857143  2.88000000  7.05882353 -0.88000000  0.42000000
## [1151]  3.42000000  2.64000000 -0.72000000  2.55000000 10.46400000
## [1156]  0.99310345  2.52000000  7.38947368 20.25000000  3.50769231
## [1161] 12.60000000  6.30000000  5.00000000  1.74000000  1.09090909
## [1166]  1.98000000  4.86857143  0.09756098 -0.18000000  2.40857143
## [1171]  1.58297872  2.72000000 -1.36320000  3.60000000  3.64000000
## [1176]  4.70000000  1.57714286 22.20000000  2.08000000  6.42000000
## [1181]  3.30000000 11.28000000 23.85000000  3.83076923  1.05882353
## [1186]  1.03500000  1.00173913  2.40000000  3.52500000  2.05714286
## [1191]  3.67200000  4.12673684  5.93513514  3.04615385 30.60000000
## [1196]  6.81600000  2.49230769  2.61000000  1.90285714  1.80000000
## [1201]  5.88957055  6.30000000  1.12500000  4.68000000  4.56000000
## [1206]  4.12844037  0.00000000  0.81818182  3.00000000 20.31428571
## [1211]  4.96000000  2.00000000  1.44000000  0.16000000 16.86857143
## [1216]  3.06000000  1.43119266  3.99000000  2.98800000  6.60000000
## [1221]  3.61875000 11.12307692  5.76000000  7.56000000  4.42285714
## [1226]  9.89714286  1.44000000  5.23200000  3.11320755  2.16000000
## [1231]  3.39692308  3.53684210  1.87826087  2.88000000  3.04363636
## [1236]  7.50000000 -2.74698795  1.68000000 20.70000000  5.35384615
## [1241]  3.42000000  6.17142857  3.66666667  2.78400000  7.04191617
## [1246]  2.28000000  3.91384615  4.90909091  2.00000000  3.96000000
## [1251]  3.55200000  0.38571429  6.43795620  1.16129032  2.60571429
## [1256]  4.34823529  0.10344828  5.52000000  9.12000000  0.58666667
## [1261]  0.78260870  2.44285714  1.00000000  5.49300000  2.98181818
## [1266]  4.52000000  4.44000000  4.72421053  4.06451613  3.25000000
## [1271] 10.66666667 -3.30352941  1.26720000  1.68152866 17.48571429
## [1276]  5.92000000  1.05600000 -0.55384615  5.52000000  5.92000000
## [1281]  5.94000000  9.15000000  4.38000000  4.80000000  1.74000000
## [1286]  4.46666667  2.20000000  3.36000000  2.49145090  2.58461539
## [1291]  0.67200000  6.92307692  0.88258064  2.52000000 -1.08000000
## [1296]  3.88000000 -0.36000000  1.98000000  8.45419355  2.79652174
## [1301]  3.04615385 -0.10610526  3.24000000 11.52000000 -0.30000000
## [1306]  5.37600000  0.60000000  1.48736842 11.07428571  0.54000000
## [1311]  0.78000000  3.00000000  4.76742857 -1.15714286  9.82500000
## [1316]  2.48571429  3.32307692  5.43000000 10.40000000  2.97931035
## [1321]  1.23076923  2.52631579  1.81714286  2.37600000  6.54000000
## [1326]  4.38857143  3.38400000  5.10000000  2.64000000  3.32038835
## [1331] -5.08800000  3.60000000  3.36000000  1.35000000  5.23255814
## [1336]  0.29333333  2.85000000  1.25820000  3.03529412 -0.12000000
## [1341]  1.78000000 13.33846154 -0.80000000  1.92000000  2.08421053
## [1346]  3.45600000  7.59652174  1.88571429  7.20000000  1.18588235
## [1351]  0.70153846  1.60000000 -0.72000000  1.77600000  0.49655172
## [1356]  2.33969849  2.48727273  5.40000000  1.57894737  0.27428571
## [1361]  0.12000000 -0.86896552  1.04727273 17.47572816  0.72000000
## [1366] 13.28000000  1.44000000  6.09230769  3.48235294  3.82153846
## [1371]  1.92000000  1.61454546  1.74000000  1.44000000  0.90000000
## [1376]  3.12000000  3.54782609  0.98181818  1.02857143  1.66666667
## [1381]  0.36000000  3.43384615  3.92307692  0.87500000  2.76000000
## [1386]  4.26315789  1.32923077 -7.24800000  0.36750000  3.24000000
## [1391]  4.20000000  1.96800000  3.40363636  2.40000000  0.45000000
## [1396]  3.98181818  6.68307692  7.48800000  0.86400000  1.16000000
## [1401]  4.66909091  0.86896552  3.42000000  6.16000000 -0.17454545
## [1406]  1.98113208  4.96363636  6.42857143  1.35000000  3.88800000
## [1411]  0.32400000  3.60000000  4.95652174  2.16000000 12.31200000
## [1416]  5.44927536  5.96363636  5.82000000  4.80000000 -1.68000000
## [1421]  2.04000000  1.88571429  1.76250000 33.25000000  0.61200000
## [1426]  2.95384615 10.12000000  2.43692308  3.24000000  2.10191083
## [1431]  4.26000000 12.30240000  4.59000000  2.37600000  6.90000000
## [1436] 13.44827586  2.08800000  4.99200000  3.07692308  5.52857143
## [1441]  6.30000000  1.31657143  9.12000000  6.63428571 10.50000000
## [1446]  3.69737143  3.00000000  4.63636364 -1.02000000  4.56000000
## [1451]  3.87096774 10.72800000  4.25250000  0.90731707  5.25000000
## [1456]  3.72000000  0.00000000  0.07384615 10.97142857  1.20000000
## [1461] 17.33333333  0.86400000  0.57600000 -1.56000000  0.25714286
## [1466]  2.14468085 11.25000000  1.62461539 -3.86086956 17.16923077
## [1471]  1.38461539  4.36708861  3.42857143 -2.37714286  0.00000000
## [1476]  2.97087379  1.60000000 -1.44771429 -0.83076923  5.58000000
## [1481]  2.95200000  1.41000000  3.31500000  1.86666667  1.05600000
## [1486]  0.13846154  3.31200000  0.96551724  4.42597403  2.51076923
## [1491] -0.90000000  2.74411765  3.56000000  0.57296842  5.31428571
## [1496]  3.70909091 18.59016393  4.66666667  4.95000000  3.41333333
## [1501]  0.85714286  4.72500000  5.12000000 -2.33142857  1.60000000
## [1506]  6.59478261  7.82400000  2.59200000  0.54000000  9.48000000
## [1511]  2.06400000  1.62857143  1.32631579  1.25000000  3.58400000
## [1516]  3.03157895  2.46260870  1.44000000  3.70758621  3.48444444
## [1521]  4.12800000  1.53191489  3.91578947  2.08695652  3.03750000
## [1526]  0.76000000  1.80000000  2.37600000  0.40000000  5.25000000
## [1531]  0.21176471  0.49333333  4.83750000  3.90000000  2.60000000
## [1536]  1.30434783  0.72000000  5.70000000  4.08000000  4.86000000
## [1541]  4.32000000  3.92307692  6.54545455  1.47692308  5.43529412
## [1546]  0.08000000  5.40000000  6.37714286  3.42000000  3.98400000
## [1551]  0.13636364  0.40000000  1.53103448  0.81818182  2.70000000
## [1556]  3.49200000  1.24800000  1.20000000  2.34418605  7.37500000
## [1561]  4.12800000  8.20320000  2.10000000 10.50000000  3.91500000
## [1566] -0.40000000  3.72000000  3.32307692  4.95000000  5.20000000
## [1571]  3.20000000  4.12800000  1.61194030  4.65454546  4.68000000
## [1576]  5.62909091  1.63636364  0.98914286  1.70666667  3.21428571
## [1581]  3.47586207 -0.16000000  5.53846154  8.00000000  3.33333333
## [1586]  4.92000000  1.20000000  0.62000000  1.36363636  3.93600000
## [1591]  5.40000000  1.93500000  4.36363636  1.40400000  2.55652174
## [1596]  0.40000000  4.17600000  5.61600000 -0.07200000  1.98000000
## [1601]  0.72000000  6.93750000  2.81538462  3.12000000  0.91200000
## [1606]  0.24000000  4.23000000  6.00000000  2.30400000  0.90666667
## [1611]  4.50000000  4.92857143  1.80000000  4.62857143  2.03610108
## [1616] 16.41600000  2.31428571  0.79200000 -0.18000000  3.02400000
## [1621]  5.29200000  1.08000000  9.04615385  4.20000000  1.44000000
## [1626]  4.68000000  4.67142857  4.68000000  3.24923077  3.19148936
## [1631]  1.87826087  4.85454546  1.08000000  1.96875000 -0.30000000
## [1636] -0.24000000  4.12500000  0.00000000  1.68000000  3.54545455
## [1641]  2.52000000  4.29139073  4.48000000  0.61714286  5.03269448
## [1646]  1.91076923  3.32307692  0.26181818  2.46400000  5.28000000
## [1651]  2.52000000  3.02222222  1.25333333  4.89942857 11.50909091
## [1656] 23.80800000  7.80000000  0.58000000 -0.81176471 -0.36000000
## [1661]  9.54000000 -0.96000000  2.41283423  2.16000000  1.13684210
## [1666] 18.35675676  6.96000000  1.15714286  7.01538462  1.80000000
## [1671]  1.25000000  0.27692308  2.67272727  3.81818182  1.80000000
## [1676]  2.28000000  1.64210526  3.74358974  2.70000000  1.85454546
## [1681]  4.50000000 -0.21176471  6.41284404  3.37358491 11.14285714
## [1686]  8.75000000 -0.96000000  7.23529412  3.46153846  4.73142857
## [1691] -2.62588235  2.56000000  5.55000000  1.20000000  3.16800000
## [1696]  0.96000000  0.07200000  5.69142857  2.01428571  8.40000000
## [1701]  5.28813559  1.66265060  3.79200000  3.47142857  2.31272727
## [1706]  1.20000000  0.24000000  1.91142857  4.04000000  3.30000000
## [1711]  3.34285714 -1.68000000  2.52800000  1.32000000 10.64000000
## [1716]  2.65500000  2.66400000  5.28000000  3.48000000  5.80000000
## [1721]  2.82593857 -0.16941176  2.56309091  9.98181818  3.58066667
## [1726]  5.15555556  6.41454545 -0.30857143 -0.95121951  5.78666667
## [1731] -2.05714286  0.36923077  3.85714286  0.12000000  4.75714286
## [1736]  0.10000000  2.35200000  0.33491803  5.04000000  2.18769231
## [1741]  0.36000000  4.56000000  0.68571429  7.68000000 -0.60000000
## [1746]  3.93442623 12.23076923  0.80181818  1.40000000  3.87000000
## [1751]  2.88000000  5.76000000  7.05600000  2.57142857  4.86315789
## [1756]  4.25000000  7.29432314  7.60000000  4.03200000 -0.70588235
## [1761]  5.40000000  8.40000000  4.05000000  5.65714286  2.30400000
## [1766]  3.16000000 10.90909091  6.20000000  5.86153846  2.51162791
## [1771] 10.49840933  2.68000000  4.96000000  3.36000000  4.16326531
## [1776]  1.27058823  0.88888889  4.44000000  2.19310345 -0.84000000
## [1781]  4.41428571  2.72307692  1.02666667  2.49000000  0.15000000
## [1786]  1.02000000  0.25000000  4.09655172  2.40000000  4.80916030
## [1791]  2.77333333 -0.34909091  0.89411765  5.82352941  0.34064516
## [1796]  4.03636364  5.44461305 -0.64000000  4.33043478  5.16000000
## [1801]  5.25000000  3.46666667  5.66400000  4.80000000  3.43636364
## [1806]  1.92000000  0.46530909  5.11304348  0.96774194  4.44000000
## [1811]  5.18777293  2.04750000  1.58400000  2.05714286  2.55000000
## [1816]  1.72800000  3.89090909  1.18000000  3.94285714  4.22222222
## [1821]  3.09230769  1.20000000  3.38181818  6.64285714  0.91764706
## [1826]  3.16800000  4.87500000  6.81600000  5.85000000  2.12903226
## [1831]  2.46486487  2.70000000  1.92000000  6.77647059  1.84000000
## [1836]  0.46956522 -1.44000000  2.40000000  4.11428571  2.03880000
## [1841]  2.62745098  3.49090909  4.92000000  4.83018868  6.72000000
## [1846] -0.64800000 -0.40000000  4.59000000  0.65454546 11.47500000
## [1851]  1.95555556  1.75500000  0.76800000  2.28000000  6.32727273
## [1856]  1.04972376  3.54000000  1.50000000  2.37176471  4.63636364
## [1861]  0.08888889  0.12480000  3.18461538  5.76923077  1.10250000
## [1866]  1.83600000  0.32914286  3.84000000  4.95000000  4.05405405
## [1871]  0.57600000  0.53647059  1.95394286  1.68000000  6.30000000
## [1876]  1.56521739  0.58909091  6.12000000  2.64000000  5.04000000
## [1881]  2.89411765  2.58750000  6.44869565 -0.31927273  2.84000000
## [1886] -1.57500000  5.11578947  0.07196400  2.40000000  9.30000000
## [1891]  2.76480000  3.60000000  1.35428571 -0.28800000  0.04615385
## [1896] -0.48000000  4.00000000  1.75500000  5.76000000  1.24137931
## [1901]  2.56363636  0.93600000  0.55384615  2.97777778  4.80722892
## [1906]  0.33600000  0.90000000  5.14285714 11.82857143  4.29000000
## [1911]  6.60000000  1.62000000  8.40857143  4.08000000  5.72000000
## [1916] -0.98086956  3.33333333  3.90000000  1.00000000  0.80000000
## [1921]  1.14000000  4.23529412  1.68000000  0.70200000  0.77142857
## [1926]  0.66359447  0.21600000  2.10000000  1.84285714  4.32000000
## [1931]  2.30400000  1.71428571 31.42800000  2.58620690  6.50602410
## [1936] -1.44000000  1.44000000  0.86400000  1.66500000  8.14285714
## [1941]  4.42666667 -0.25263158  1.20000000  0.91800000  1.51200000
## [1946]  2.67000000  1.35000000  0.95250000  8.05714286  1.89000000
## [1951] -1.56705882  3.96000000  3.60000000  2.88000000  2.40000000
## [1956]  0.42666667  2.64000000  3.74400000  7.80000000  4.45000000
## [1961]  1.83529412  7.80000000  5.30181818  3.84000000  0.30720000
## [1966]  3.76363636 14.86285714 10.12500000  4.20000000  1.02857143
## [1971]  8.50000000  7.40000000  7.96363636  4.72800000  2.36571429
## [1976]  5.33333333  6.08000000  0.49253731  6.33600000  3.42222222
## [1981]  2.11200000  2.40000000  2.92061539  4.00000000  2.96250000
## [1986]  3.12000000  5.85600000 -1.56600000  9.63692308  0.00000000
## [1991]  5.14285714  3.19846154  3.13600000 13.02857143  6.17142857
## [1996]  7.53600000  4.63636364  3.16800000  6.78400000  0.30000000
## [2001]  1.26000000  2.07000000  9.74400000  2.70000000  1.44000000
## [2006]  3.70909091  1.42857143  2.16000000 -0.86800000  0.32307692
## [2011]  4.06285714  2.84689655  1.91111111  2.04000000  3.23076923
## [2016]  3.15300000  0.84000000  1.12500000  1.18956522  8.22000000
## [2021]  1.12500000  1.34117647  1.08000000  1.44000000  6.00000000
## [2026]  2.94193548  1.65000000  0.14400000  2.48000000  0.36000000
## [2031]  0.18000000 -0.60000000  0.00000000  2.05714286  5.20000000
## [2036]  0.28800000 -0.03529412  0.32400000  5.40000000  3.37500000
## [2041]  9.85714286  3.27272727  4.06451613  6.12000000  3.03600000
## [2046]  7.27272727  2.88000000 10.58400000  3.16050000  1.25454545
## [2051] 15.60000000  4.44444444  1.13684210  2.10000000  2.04000000
## [2056]  2.78625000  2.48275862  1.47600000  0.78260870  0.07500000
## [2061]  3.91680000  2.88000000  4.50000000  5.42222222 -1.62000000
## [2066]  1.70322581  4.68000000  4.35000000  2.18741538  2.58461539
## [2071] -1.17333333 25.32000000  3.86400000  6.89454546  1.37739130
## [2076]  0.67289720  3.36000000  2.07500000  1.20000000  1.98461538
## [2081]  1.58400000  4.02000000  0.21600000  4.92000000  0.38461538
## [2086]  0.76500000  1.83333333 -0.64000000  1.40869565  8.20800000
## [2091] 10.77333333  3.72857143  5.38666667  4.56000000  4.66285714
## [2096]  1.22400000  5.10000000  1.59428571  2.28000000  4.20000000
## [2101]  2.40000000  3.78000000  3.62571429  0.74880000  3.80874873
## [2106]  7.20000000  0.90000000  0.65454546  3.90000000  5.40000000
## [2111]  0.66666667  3.54206897  2.92000000  0.24000000  1.60000000
## [2116]  5.70000000  3.86250000  1.44000000 12.90000000 -0.26086957
## [2121]  3.55263158  1.98000000 -2.76705882  7.29600000  2.16000000
## [2126]  3.82909091  3.48000000 -1.20000000 -0.73846154  0.20509091
## [2131]  2.14545455  4.25000000  7.60000000  1.02857143  1.86000000
## [2136]  3.60000000 -0.04800000  1.80000000  3.04000000  0.44444444
## [2141] 13.74545455  3.48000000 14.46545455  2.89655172  2.70000000
## [2146]  1.52380952  5.96363636  6.26086957  7.28275862  3.02400000
## [2151]  1.97777778  8.55000000  5.30526316  6.72000000  4.50000000
## [2156]  3.54929578 -0.55680000  4.09090909  3.60000000  3.00000000
## [2161]  2.24000000 -2.10000000  8.10000000  3.25000000  0.96428571
## [2166]  0.54000000  3.60000000  9.90000000  2.08571429  3.52000000
## [2171] 12.00000000 -1.33333333  5.88000000  4.14000000  3.56043956
## [2176]  1.11600000  2.22000000  2.34666667  1.67278196  1.11272727
## [2181]  2.20000000 -0.96000000  4.49454545  1.98370909 -2.23200000
## [2186]  2.50000000  1.40585774  3.91304348  4.39384615  5.75000000
## [2191]  5.90769231  1.75182482  5.03225806  3.68000000  1.06666667
## [2196]  0.67500000  4.69714286  8.67692308  3.28000000  7.38000000
## [2201]  4.32000000  6.00000000  6.81818182  1.65517241 -0.72000000
## [2206] -0.86400000  2.00000000 -5.84000000  4.49142857  3.60000000
## [2211] -0.42000000  1.64571429  1.02857143  5.40000000  1.20000000
## [2216]  1.50857143  0.06000000  2.81250000 -2.00000000  5.94285714
## [2221]  4.32000000 -0.56842105  3.66666667  4.55672727  2.64000000
## [2226]  1.61538461  7.63636364  1.77600000  1.67272727  3.18315789
## [2231]  3.17241379  2.39940000  1.56000000  2.40000000  2.62285714
## [2236]  0.93103448  5.33333333  4.17000000  4.26000000  7.11428571
## [2241]  0.33333333  2.00000000  1.32000000  1.04000000  0.40000000
## [2246]  2.35200000  3.30000000 -0.14400000  2.76666667  8.52923077
## [2251]  1.70181818  3.20400000  1.20000000  1.37142857  1.92000000
## [2256]  0.60000000  3.60000000  3.00000000  1.80000000  2.28571429
## [2261]  8.28000000 -3.18750000  0.36923077  0.00000000 -0.36705882
## [2266]  6.56250000  1.30909091  5.34857143  2.93647059  1.06666667
## [2271]  3.00000000  1.01284404  4.11428571  9.92000000  6.18461538
## [2276]  0.00000000  9.60000000  6.78857143  5.04000000  2.97600000
## [2281]  1.42372881  3.02400000  2.40000000  3.52000000  3.30000000
## [2286]  1.18800000  0.11707317  3.52941176 -0.60000000  2.97600000
## [2291] -0.66000000  3.70285714  2.70000000  5.84347826  6.00000000
## [2296]  3.48000000  0.50400000  2.50000000 20.16000000  3.14181818
## [2301] -1.41176471  1.20000000  2.68800000  1.20000000 -0.26181818
## [2306] 11.73600000  6.96000000  4.05000000  3.43636364  5.37882353
## [2311]  2.10841121  1.80000000  5.77777778  5.81142857  8.34000000
## [2316]  2.25000000  0.28400000  4.45500000  5.61600000  3.26400000
## [2321]  2.56000000 -1.44000000 -0.88200000  3.48000000  1.08000000
## [2326]  0.25600000  1.44000000  6.84000000  0.00000000  0.15157895
## [2331]  3.70800000  0.68000000  2.54769231  4.00000000  2.25000000
## [2336]  3.17647059  1.09090909  2.11372064 -1.44000000  3.60000000
## [2341]  1.76470588  3.81818182  5.30769231 -0.61090909  2.07000000
## [2346]  2.70000000 11.10000000  3.36551724  3.30000000 10.93333333
## [2351]  7.36666667  3.47734457  3.25000000  2.94117647  1.90909091
## [2356]  3.11040000  9.60000000  8.00000000  2.48000000  4.06588235
## [2361] -2.16000000  4.20000000  3.73333333 -0.37333333  2.26909091
## [2366]  0.00000000  2.70000000  2.16000000  3.48923077  3.88000000
## [2371]  4.12500000  5.55428571  2.41200000  4.35789474  8.57647059
## [2376]  9.00000000  1.44000000  7.87500000  2.30400000  0.48600000
## [2381]  3.16000000  3.14666667  5.48571429  6.24000000 12.60000000
## [2386]  3.76000000  4.22400000  1.32000000  1.78983051  3.60000000
## [2391]  4.30588235  0.50000000  4.72800000  1.80000000  2.40000000
## [2396]  2.61600000 -0.73333333  3.79862069  5.95636364  5.42400000
## [2401]  6.62400000  4.47428571  9.90000000 12.96000000  4.99200000
## [2406]  1.40400000  1.68000000  2.29090909  0.75857143  1.35000000
## [2411]  0.47142857  8.71200000  0.00000000  4.00800000  1.75000000
## [2416]  0.13846154  0.48888889  7.35483871  4.32000000  1.95789474
## [2421]  0.95172414  0.63419689  0.00000000  5.31428571  3.53684210
## [2426]  2.00727273  2.80000000  0.88888889  2.89344000  3.78000000
## [2431]  2.85600000  8.52000000  2.70000000  2.46857143  1.23750000
## [2436]  1.78000000  6.05217391  4.84800000  2.91692308 -0.07200000
## [2441] -1.61379310  3.66000000 -0.48032000  5.19512195 21.00000000
## [2446]  1.89230769  3.18352941  3.36000000  0.93750000  4.84363636
## [2451]  1.80000000  7.42153846  1.69200000  1.16307692  0.75000000
## [2456]  1.40000000  2.95384615 -2.01600000  2.40000000  2.88000000
## [2461]  1.62857143  1.30285714 -0.33000000  1.20000000  0.92903226
## [2466]  0.90000000  2.05714286  5.46909091 -2.48470588  3.16800000
## [2471]  0.60000000 10.36800000  5.46000000  4.60000000  1.08000000
## [2476]  4.51377778  3.32571429 -0.41142857  1.15714286  7.06666667
## [2481]  4.08000000  0.72000000  5.52000000  0.30000000  6.72000000
## [2486] 12.38400000  2.30400000  6.53538461  4.46896552  2.67272727
## [2491]  0.73600000  2.18181818  6.06666667  1.68000000  2.37600000
## [2496]  2.43750000  6.60000000  7.00000000 -0.12705882  0.82758621
## [2501]  1.15384615 -1.44000000 15.50822846  1.66153846  1.35000000
## [2506]  1.16571429  1.12000000 -2.26560000  3.10000000  0.76220690
## [2511]  3.64285714  3.55764706 16.60000000  4.00000000  2.47500000
## [2516]  3.88571429  2.95714286 13.00000000  0.00000000  1.61538461
## [2521]  1.36363636  2.58715596  1.29600000  0.84000000 -0.80000000
## [2526]  1.14000000 -1.54666667  8.61081081  2.36470588 10.65600000
## [2531]  2.40000000  4.35000000  1.73333333 10.69090909  0.56666667
## [2536]  1.60000000  4.62315790  5.89090909  6.40000000  2.87671233
## [2541]  2.27727992  2.70000000  2.10000000  5.55428571  3.48000000
## [2546]  0.25000000 11.04000000  2.88000000  6.46363636  4.92000000
## [2551]  7.92000000  2.74285714  2.64000000  4.74545455 -1.24800000
## [2556]  4.17391304  3.45000000  1.46086957 -1.52000000  1.68000000
## [2561]  7.68000000  1.67142857  3.96923077  2.05090909  2.52000000
## [2566]  3.36000000  0.21600000  3.43384615  1.63636364  2.28545454
## [2571] -1.17647059  5.52000000  3.73333333  1.35272727  1.84000000
## [2576]  1.02857143  0.04225352  3.88571429  0.17142857  9.40438871
## [2581]  2.40000000  6.33600000  5.89090909 14.00000000  1.96800000
## [2586]  2.98666667  0.80000000  0.54400000 -0.36571429 -3.31200000
## [2591]  4.49142857  5.92500000  2.53846154  1.26228571  1.00000000
## [2596]  6.21818182 11.71200000  7.47692308  9.89538461  1.85000000
## [2601] -0.60000000  5.72222222  3.99000000  3.93750000  1.25454545
## [2606]  2.46857143 -3.69000000 -0.46153846 -0.92307692  1.64571429
## [2611]  4.00000000  2.04000000 11.88000000  5.54482759  0.66000000
## [2616]  9.90000000  0.65000000  1.80000000  0.82000000  1.66500000
## [2621]  3.64500000  2.43692308  2.52000000  5.23200000  3.96000000
## [2626] -0.96000000  4.06956522  2.88000000 -1.32000000  6.85714286
## [2631]  6.07594937  2.37913043  2.22000000  5.18400000  4.17600000
## [2636]  3.15000000  3.84000000  1.02000000  1.35000000  1.29600000
## [2641]  2.83636364  4.60000000 11.60000000  2.55000000  1.44000000
## [2646]  6.36923077  0.75673846  0.85714286 18.25714286  6.60000000
## [2651]  2.97290323  3.12000000  5.10104530  4.44000000  2.75294118
## [2656]  6.90000000  2.97777778  2.25000000  5.67692308  0.48000000
## [2661]  6.15529412  2.22000000  5.28428571  7.14000000  2.16000000
## [2666]  4.80000000  6.83520000  1.00000000  9.13586087  8.46315790
## [2671]  3.30000000  1.17000000  1.44000000  2.70000000  0.95000000
## [2676]  2.81250000  1.61052632  3.87176471  3.64285714 12.64615385
## [2681]  3.12000000  2.31111111  0.12600000  0.17066667  3.33333333
## [2686] -0.90000000  8.85517241  1.68000000  5.97777778  3.96800000
## [2691]  0.62439024  0.62500000  1.51011236  8.45000000  5.60000000
## [2696]  1.56000000  3.67200000  0.24000000  2.70000000  2.66181818
## [2701]  5.15555556  3.80000000  5.18709677  4.88000000 28.32000000
## [2706] -1.37142857  0.85714286  0.75000000  2.37642857  1.02000000
## [2711]  5.06181818  4.92631579  2.47500000  9.86666667  0.75789474
## [2716]  3.00000000  0.90000000  3.00000000  5.23333333 -0.75000000
## [2721]  5.04000000  5.25000000  0.50400000  1.39200000  5.37600000
## [2726] -1.59556787  0.60000000  2.64406780  4.20000000  3.36000000
## [2731] 11.70000000  4.32000000  1.08000000  1.73076923  5.85142857
## [2736]  6.30000000  2.25882353  4.28000000  4.10000000 14.56000000
## [2741]  0.55200000 10.80000000  1.73333333  4.16000000  1.86666667
## [2746]  8.28000000  6.28285714  4.86000000 -3.10000000  4.84444444
## [2751]  5.52000000  3.33333333  1.08069164  1.53750000  0.18000000
## [2756]  2.16000000 12.24000000  5.20000000  3.87692308  2.85000000
## [2761] 13.55294118  4.51764706  4.96000000  5.40000000  3.60000000
## [2766]  3.60000000  4.58181818  1.72000000  0.95172414  1.92000000
## [2771]  7.20000000  2.22000000  4.14000000  2.22000000  0.44727273
## [2776]  2.12571429 14.76000000  6.92307692  1.38947368  4.13538462
## [2781]  3.50857143  9.67058824  2.12000000  1.64000000 17.92771084
## [2786]  2.28000000 11.25000000  1.50000000  7.56000000  3.15000000
## [2791]  7.80000000  4.16666667  6.00000000  1.62782609  2.96250000
## [2796]  7.14000000  0.66666667 18.51428571 -1.83750000  2.48571429
## [2801]  0.03600000  0.72000000  3.79534884 -0.16363636  4.65000000
## [2806]  6.84000000  2.01600000  3.00000000  0.32400000  0.23040000
## [2811]  6.14400000  4.08000000  0.97142857  6.16000000 -0.22153846
## [2816]  2.31000000  3.84000000  4.62000000  3.27000000  3.91764706
## [2821]  6.51666667  3.42000000  3.84000000 26.50909091  4.94117647
## [2826]  4.80000000 -1.08480000  1.09714286  0.64000000  3.00000000
## [2831]  5.11111111  2.77241379  3.70000000  0.60000000  4.62857143
## [2836]  1.91172414  3.37500000  5.38666667 -0.72000000  1.95000000
## [2841]  3.09333333  2.04923077  2.82000000  3.37500000  2.16000000
## [2846]  2.16240000  3.66315789  0.74880000  3.18750000  1.36533333
## [2851]  0.58000000  5.89565217  7.46250000  9.69230769  2.96727273
## [2856]  2.01600000  4.54153846  7.34908136  5.47794994  2.40000000
## [2861]  0.68000000  2.05714286  9.18000000  4.73286713  3.00000000
## [2866]  1.92000000 27.21600000  5.28000000  4.08000000  3.38400000
## [2871]  4.43076923  5.52000000  2.17777778  1.80000000  0.49200000
## [2876]  0.24000000  6.10909091  3.96000000  2.08800000  1.90800000
## [2881]  2.34000000 -1.39764706  6.21000000 -0.73846154 10.38857143
## [2886]  3.87692308 -0.83400000  5.10000000  5.55000000 12.17520000
## [2891]  1.95555556  6.42461539  2.27200000  5.34857143  5.10000000
## [2896]  1.61538461  5.55428571 21.49714286  7.92000000  2.50434783
## [2901]  0.73972603  3.31200000  0.36000000  9.54782609  2.65411765
## [2906]  3.49367089  5.04000000  4.32000000  4.64516129  3.90000000
## [2911]  4.10400000  3.60000000  5.22000000  4.37142857  2.00000000
## [2916]  1.53333333  0.12000000  4.72500000  2.55600000  5.18400000
## [2921]  6.84000000  1.60000000  6.97500000  6.97500000  3.65714286
## [2926]  8.82857143  8.16000000  2.28000000 -0.18000000  4.80000000
## [2931]  3.40000000  3.90000000  1.60363636  2.91428571  5.08800000
## [2936]  5.23200000  7.11428571  0.66857143  1.20670391 17.64705882
## [2941] -0.09600000  1.92000000  1.48000000  1.36421053  0.41988000
## [2946] 24.00000000 10.02000000  0.05760000 -1.80000000  2.70000000
## [2951]  3.16363636  9.36000000  2.00000000  3.86086956  9.24000000
## [2956]  8.78400000  2.50000000  0.99428571  3.60000000  3.55714286
## [2961]  2.00000000  4.42285714  0.28235294  6.43200000  1.56000000
## [2966]  4.76000000 -2.40000000  2.43200000  2.92500000 18.06666667
## [2971]  6.92682927  4.53600000  3.99130435  3.60000000  5.48000000
## [2976]  5.13882353  2.59200000  6.48000000  6.67200000  4.16000000
## [2981]  3.67883212 -2.04000000  0.10000000  2.20500000  0.54000000
## [2986]  8.95204263  2.44800000  3.33000000  0.42000000  4.49142857
## [2991]  2.76000000  1.70823529 -1.05000000  1.48800000  9.25000000
## [2996]  1.95000000  1.77230769  2.15000000  4.04444444 11.88000000
## [3001]  0.27567568  3.16455696  4.72000000  0.54000000  9.74769231
## [3006]  1.36800000  5.80000000  1.23000000 13.47692308  5.44615385
## [3011]  2.96842105  2.24000000  1.09411765  1.32000000  3.96000000
## [3016] -1.33714286  1.54285714  5.40000000 -0.64285714  4.53333333
## [3021]  5.40000000  0.82800000  4.50000000  4.26000000 15.84000000
## [3026]  4.64000000  2.36220472  3.12000000  0.62526316  2.62285714
## [3031]  7.10400000  0.54000000  8.88000000  2.01600000 14.40000000
## [3036]  6.22222222 18.00000000  4.14000000  4.97142857  7.92857143
## [3041]  2.49230769  9.69600000  2.45647059  0.93913044  2.93333333
## [3046] 15.60000000  2.35714286  9.23076923  2.00000000  0.18000000
## [3051]  5.34857143  2.04000000  1.71974522  2.40000000  4.48363636
## [3056]  3.30000000  4.14000000  1.14545454 16.60800000  1.93043478
## [3061]  2.22000000  8.56800000 13.27058824  9.31578947 -0.20571429
## [3066]  0.67200000  3.37500000  4.08000000  2.85000000  3.54000000
## [3071] 10.44000000  4.32000000  8.18823529  5.16000000 -0.43500000
## [3076]  6.08571429  2.40875912  4.15384615  8.10000000  3.36923077
## [3081]  2.50000000  2.16000000  2.40000000  2.30000000 11.57142857
## [3086] 13.10000000  1.53846154  7.58400000  1.60000000  2.60455267
## [3091]  5.40000000  5.00000000  4.93714286  3.60000000  1.99800000
## [3096]  3.49090909  0.88500000  1.52307692  1.36363636  1.51714286
## [3101]  6.73846154 11.95200000  0.09600000 -2.13000000  1.02857143
## [3106]  5.10000000  1.34400000  1.50000000 13.50000000  0.69600000
## [3111]  7.85454546  2.80534351  5.19272727  3.65454546  0.69120000
## [3116]  6.03000000  3.98400000  5.48000000  1.57241379  1.92000000
## [3121]  4.93333333  4.08000000  3.30000000  0.95575221  1.08000000
## [3126]  3.78181818  6.86666667  2.72000000  2.60000000  3.60000000
## [3131]  1.92000000  1.18800000 11.91428571  2.59200000  1.20000000
## [3136]  4.32000000  5.72307692  6.32571429  6.61333333  6.69230769
## [3141]  4.88135593  2.22000000  7.68000000  2.17600000  3.93600000
## [3146]  3.05000000 -0.16000000  6.84444444  6.81931034  5.47826087
## [3151]  2.14020619 10.20000000  1.08000000  1.44000000  1.89000000
## [3156]  5.58720000  4.73142857  2.49600000  3.55200000  3.84000000
## [3161]  1.66386555 -0.60923077  1.10769231  1.64210526  4.46153846
## [3166]  2.07000000  6.85236769  2.67428571  4.80000000  3.69600000
## [3171]  6.90909091  8.76279070  1.28000000  0.40800000  5.66666667
## [3176]  3.74400000 -1.62000000  1.38600000  4.01760000  2.12000000
## [3181]  5.67000000  1.47692308  0.93600000  2.79529412  2.82000000
## [3186]  6.25714286  1.92000000  9.62613333 10.98000000  2.93647059
## [3191]  8.58000000  3.39428571 -0.41400000  5.23800000  5.20000000
## [3196]  2.03076923  1.80000000  7.32000000  3.96000000  1.22181818
## [3201]  4.80000000  2.58461539  2.44800000  1.50857143  1.51200000
## [3206]  1.41428571  2.38267148  0.60000000  1.92000000  1.09714286
## [3211]  1.33662857  0.62222222 -0.81818182 15.68000000  7.20000000
## [3216]  1.51578947  1.00000000  1.35000000  3.95076923  5.41894737
## [3221] -0.27272727  6.00000000 -0.42352941  7.50545455  4.50000000
## [3226]  1.35000000  0.40000000  3.98048781  1.82857143 -0.01411765
## [3231]  0.50400000  4.30000000  2.05714286  1.47000000  1.62000000
## [3236]  5.20000000  6.94285714  0.28800000  4.49523810 18.46153846
## [3241]  2.31428571  3.15000000  6.00000000  3.52000000  3.57230769
## [3246] -0.38400000  0.92000000  2.20800000  2.43750000  2.88000000
## [3251]  4.56000000  3.54000000 18.00000000  6.48000000  3.09836066
## [3256]  6.05538462  3.45857143  0.95172414 -0.58500000 -0.46153846
## [3261]  3.42000000 12.30000000  2.27586207  9.14594595  2.04000000
## [3266]  2.81538462  1.80000000  1.96363636  2.98832685  1.85000000
## [3271]  5.18823529  0.87272727  5.81538462  3.38181818  0.75000000
## [3276]  5.68695652  0.69176471 -0.19200000  5.64963504  3.02400000
## [3281]  0.50400000  6.43200000  3.32307692  4.37538461  1.77230769
## [3286]  3.02400000  2.74285714  2.43750000  2.80000000  8.18181818
## [3291]  6.04800000  2.10240000  2.14857143  1.07500000  4.08888889
## [3296]  0.69333333  1.72000000  1.64749536  0.86400000  3.45600000
## [3301] 13.92000000  1.80000000  1.80253165  3.81308411  5.23076923
## [3306]  0.36000000  2.25000000  2.22857143  1.20000000  5.85882353
## [3311]  2.19272727 16.64516129 13.72500000  3.18000000  3.95000000
## [3316]  9.45000000  3.93333333 15.21600000 -1.87058824  1.96363636
## [3321]  5.86285714 12.00000000  3.20000000  1.99384615  2.11500000
## [3326]  1.36800000  4.63636364  1.18153846  0.63529412  0.48800000
## [3331]  3.89333333  1.45548387  1.68224299 11.46666667  0.30857143
## [3336] 10.28571429  1.81980000  1.46666667  0.76000000  5.73600000
## [3341]  3.20000000  8.40000000  1.20000000  6.22105263  5.30769231
## [3346]  4.69894737  6.30000000  6.93333333  6.73333333  4.77000000
## [3351]  3.54545455  4.75636364  2.82000000  6.91200000  3.25000000
## [3356]  6.88941177  4.50461539  2.20000000  1.26000000  2.40000000
## [3361]  3.02400000  2.16000000  0.86400000  2.45581395  0.00000000
## [3366]  0.25560000  4.98113207  0.92800000  6.64285714  2.82352941
## [3371]  1.56000000  0.54193548  1.72000000  3.33750000  2.62956522
## [3376]  6.36521739  5.07272727  3.45454545  0.16000000  2.53846154
## [3381]  4.21565217  1.80000000  5.22857143 -0.11294118  4.82926829
## [3386] 15.60000000  1.64000000  0.57600000  2.11200000  3.36000000
## [3391]  1.50000000  9.35840000  8.00000000  3.75000000  4.17777778
## [3396] 10.44000000  7.10933333  3.60000000  2.40000000  3.90000000
## [3401]  5.00869565 -1.01818182  7.20000000  3.88800000  2.49000000
## [3406]  9.00000000  5.40000000  2.23578947  4.95000000  3.86250000
## [3411]  1.37142857 12.96000000  4.92000000  3.84000000  0.98181818
## [3416]  6.00000000  1.76000000 13.60000000  6.72000000  2.07692308
## [3421]  4.53333333  3.48631579  3.07200000  3.71454546  1.83157895
## [3426]  1.80000000  4.81500000  5.42400000  4.00000000 21.20000000
## [3431]  1.16000000  5.17714286  2.48888889  3.64800000  1.82410424
## [3436]  4.71428571 -0.80000000  0.60000000  8.70000000  2.30625000
## [3441] 15.84000000  3.14285714 -0.93600000  5.34000000  2.80800000
## [3446]  6.42000000  3.88363636  3.55200000  1.56521739  4.52000000
## [3451]  7.08571429  5.86666667  1.24615385  0.14400000  3.14285714
## [3456]  4.55172414  2.32258064 -0.26666667  2.77200000  3.17538462
## [3461]  1.10769231  5.40000000  9.92920354  4.06416000  5.34000000
## [3466]  3.30000000  2.40000000  2.28000000  2.45454545  5.22000000
## [3471]  3.24000000  1.54285714  7.77600000  1.52727273  5.16000000
## [3476]  4.25454545  6.88000000  4.10526316 -0.48000000  3.37500000
## [3481]  4.34000000  3.93442623  2.55000000  4.34482759  2.09600000
## [3486]  4.84800000  0.67200000  1.66153846  4.96551724  0.38400000
## [3491] -0.33333333  1.71000000  2.28785455  3.35000000  3.12000000
## [3496]  0.07272727  0.84000000  4.38941539  0.32307692  2.26415094
## [3501]  3.44000000  3.50000000  1.37454546  3.48000000  4.80000000
## [3506]  6.86746988  4.56470588  4.98857143  0.83076923  7.68000000
## [3511]  3.51000000  6.84000000 -0.50000000  0.90000000  3.20000000
## [3516]  3.52800000  4.20000000  0.11520000  1.80000000  6.57672850
## [3521]  0.65217391  5.09538462  2.98800000  4.63636364  2.28000000
## [3526]  3.38400000  1.98000000  7.12500000  2.32000000  9.37500000
## [3531] 10.00000000  7.83333333  2.96000000  0.26400000  3.55555556
## [3536]  7.90909091  4.99200000 10.24000000  6.00000000  4.80000000
## [3541]  2.11111111  2.25000000  4.11891892  0.45000000  3.68000000
## [3546]  1.92000000  4.62857143  0.67200000  1.93846154  1.55076923
## [3551]  5.76000000  2.85333333  1.87200000 -0.30000000 -0.69230769
## [3556]  2.67096774  2.84210526  4.26000000  1.73333333  3.28000000
## [3561]  2.35223160  2.08941176  4.94400000  9.32000000  1.84000000
## [3566]  1.10000000  5.32500000  5.78571429  3.94285714  6.92307692
## [3571]  2.93538461  2.29090909 -0.60000000  3.15555556 11.77500000
## [3576] 10.27200000  5.76000000  2.33333333  4.30000000 14.28000000
## [3581]  0.96000000  0.20000000  6.18000000  4.65000000  4.48000000
## [3586] 17.00000000  1.50000000  4.91428571  6.46363636  7.20000000
## [3591]  9.51428571  1.70526316 25.08000000  3.40000000  4.88571429
## [3596]  2.50485437 12.24000000  3.12000000  3.85920000  4.56000000
## [3601]  3.43636364  9.45000000  2.98666667  2.40000000  9.52500000
## [3606]  3.20000000  4.48000000  2.44800000  4.02000000 11.00000000
## [3611]  3.40000000  4.84615385  2.40000000  3.43636364  2.07692308
## [3616]  4.81500000  5.31428571  7.20000000  3.79636364  4.02000000
## [3621]  3.30882353  2.07000000  5.04000000  2.58461539 -0.18000000
## [3626]  7.32000000  0.36923077  7.20000000  1.57241379  2.03076923
## [3631]  2.25600000 -0.73333333  0.28800000  2.47500000  7.80000000
## [3636]  0.04000000  5.14433881  7.87500000  5.40000000  4.05000000
## [3641]  2.18947368  4.74000000 15.12000000  1.44303797  2.46000000
## [3646]  3.33333333  5.12000000  4.10526316  1.58769231  2.44000000
## [3651]  4.74000000  6.20307692 -0.18000000  3.15000000  3.09333333
## [3656]  2.48000000  2.67000000  3.37500000  2.07692308  3.66666667
## [3661]  2.40000000  2.52000000  5.75000000 12.48000000  3.36000000
## [3666]  1.68000000  9.72000000 17.54666667  2.34240000  1.68000000
## [3671]  0.42461539  9.25714286  3.46666667  1.43076923  1.72800000
## [3676] 12.30000000  5.68421053  2.83200000 12.66000000  1.50000000
## [3681]  1.76250000  3.88800000 -0.72000000  1.17000000  0.95000000
## [3686]  5.57333333  5.44500000  3.72000000 -1.32000000  8.48000000
## [3691]  3.03750000  4.53333333  3.56250000  2.51250000  1.71000000
## [3696]  0.36000000  3.24000000  3.00000000  2.29090909  4.42285714
## [3701]  5.98153846  6.28915663  8.60000000  4.00000000  5.10000000
## [3706]  2.66250000  3.60000000  4.40625000  6.84000000  7.96800000
## [3711]  2.88000000  1.48800000  4.99200000  0.10285714  0.32914286
## [3716]  0.78750000  2.24307692  5.55130435  6.03947368  0.36000000
## [3721] 19.80000000  3.34285714  2.18181818  1.20000000  3.78000000
## [3726] -0.37500000  6.72000000  1.99500000  0.38181818  0.98181818
## [3731]  3.20000000  0.93600000  9.27818182  4.62857143  4.14246575
## [3736]  0.86400000  3.52000000  3.96000000  1.70526316  4.05709091
## [3741]  2.40000000  6.67826087  0.33600000 -1.30909091  3.85714286
## [3746]  4.68000000  3.20000000  6.75555556  3.30000000  3.46666667
## [3751]  5.96571429  2.60000000  4.96695652  9.69230769  3.16000000
## [3756]  2.20000000  1.70847458  2.05714286  3.60000000  0.54000000
## [3761]  5.16000000  4.55625000  1.74545455 12.36923077  1.21200000
## [3766]  3.12000000  2.92800000  4.23333333  1.61538461  6.24000000
## [3771]  1.74857143  7.62616822  5.73913043  2.85569620  3.27272727
## [3776]  1.18588235  8.29090909  3.64285714  0.37894737  3.26400000
## [3781]  2.10000000  3.83076923  2.25000000  5.60000000  7.17913044
## [3786]  0.00000000  4.57142857  9.90000000  2.88000000  4.92000000
## [3791]  3.71250000 -0.19200000  1.98750000  2.13428571  2.64000000
## [3796]  3.35000000  7.24137931  3.60000000  3.81818182  4.39200000
## [3801]  2.00000000  1.92000000  0.98823529  3.36000000  3.00000000
## [3806]  6.85984252  1.89928058  1.50857143  1.01538462  4.17600000
## [3811]  0.08727273  4.51764706  6.72000000  4.68571429  2.76000000
## [3816]  3.96000000 -1.40000000 -0.11162791  2.35200000  0.86400000
## [3821]  4.01142857  2.82898551  0.33729730  1.47272727  1.60000000
## [3826]  7.20000000  1.29230769  4.62461539  1.54285714  2.25882353
## [3831]  8.60000000  1.98620690  5.28000000  5.04000000  1.58571429
## [3836]  3.86666667  3.36923077 -0.12000000 13.56000000 11.40000000
## [3841]  2.66666667  4.27200000  3.07200000  4.38000000  9.12000000
## [3846] -1.52000000  1.10769231  0.33600000  3.42000000  4.90909091
## [3851]  1.61538461  3.06000000  2.13818182  1.97169231 -0.48000000
## [3856]  2.83333333  3.86363636  5.40000000 12.33962264  4.16000000
## [3861]  5.36470588  3.78000000  4.27659574  2.18181818  7.20000000
## [3866]  1.98000000  0.99692308  0.60000000 16.10769231  2.68800000
## [3871]  5.29090909  2.12121212  5.94000000  6.12000000 -0.06857143
## [3876]  1.86000000  2.70000000  2.64000000 -0.41333333  8.25000000
## [3881]  0.49070632  1.80000000 11.95384615  2.16000000  2.70000000
## [3886]  3.08000000  2.90322581  3.20000000  0.23261539  9.00000000
## [3891]  3.74400000  0.62400000  0.32842105 -1.63200000  4.47337278
## [3896]  0.48000000  5.64480000  3.76000000 12.50000000  1.84000000
## [3901]  2.33142857  4.80000000  2.60625000  3.65000000 -0.60000000
## [3906]  0.32914286  2.80000000  3.00000000  1.63636364  1.92413793
## [3911]  1.92558140  4.96800000  4.02000000  5.65000000  1.13406593
## [3916]  5.76000000  4.05000000  3.45454545  1.49538462  1.06800000
## [3921]  1.33714286  8.40000000  3.55263158  0.50086957  9.00000000
## [3926]  9.98400000  4.80000000  0.45600000 10.67586207  1.08000000
## [3931]  4.80000000  2.92500000  3.00000000  1.55076923  3.31200000
## [3936]  4.88000000  0.32000000  1.46666667  6.16000000  0.40000000
## [3941]  3.42000000  8.85714286  2.11200000  0.68571429  2.52000000
## [3946]  2.45454545  1.89230769  5.47826087  2.84210526  2.54400000
## [3951]  5.62500000  5.45454545  0.84000000  3.29032258  1.12941176
## [3956]  6.14400000  1.80000000  5.04000000  0.53333333  6.00000000
## [3961]  6.57142857  0.56727273  3.18857143  2.07000000  2.01818182
## [3966]  2.64000000  6.63333333  2.76923077  2.50000000  2.20800000
## [3971]  1.41176471  4.32000000  3.06666667  3.89333333  5.94000000
## [3976]  6.60000000  4.05000000  0.96923077  6.20571429  3.90857143
## [3981]  2.33333333  2.86956522  2.61818182  0.64000000  6.13846154
## [3986]  1.71360000  1.38461539  0.13090909  4.56000000 11.68888889
## [3991]  1.36119403  4.45935484  5.40000000  2.50909091  2.52000000
## [3996]  8.40000000  3.39130435  2.48759124  1.80000000  8.26285714
## [4001]  2.89655172  0.32727273  6.08000000  7.32000000  0.15000000
## [4006]  0.97411765  2.30000000  1.97818182  8.40000000  2.48914286
## [4011]  4.83840000  1.89600000  1.83050848  2.40000000  5.91818182
## [4016]  5.40000000  0.21000000  2.45454545  2.25000000  1.84000000
## [4021]  4.01739130  2.24000000  2.00000000  4.58181818  3.90000000
## [4026]  4.80000000  8.30769231  1.29600000  0.68807339  6.26086957
## [4031]  0.76000000  1.03448276  1.75714286  2.61000000  1.96969697
## [4036]  1.72800000  3.12000000  0.00000000  2.84210526  2.78709677
## [4041]  1.12000000  3.33750000 13.39200000  5.72160000  4.12500000
## [4046]  5.13600000  6.64285714  1.13785714  0.93333333  8.70000000
## [4051]  0.00000000  0.48000000  2.55600000  1.15862069  5.28000000
## [4056]  2.78400000  6.48000000  2.54117647  7.11428571  1.82000000
## [4061]  3.10000000  5.01333333  0.12000000  5.16363636 12.60000000
## [4066]  1.61445910  3.08571429  4.16842105  0.72000000  2.34000000
## [4071]  2.95500000  3.28205128  7.44000000  3.02400000  9.05000000
## [4076]  6.33333333  0.09600000  2.40000000  1.58571429 30.48000000
## [4081]  6.05000000  4.87500000  0.03130435  5.74680000  0.66666667
## [4086]  3.53936842  1.66666667  3.58800000 10.62222222  2.64827586
## [4091]  6.25090909  0.23076923  4.38000000  3.33333333  3.20000000
## [4096]  7.25000000  5.70000000  2.70000000  2.95200000  5.32000000
## [4101]  2.94315790  4.28571429  2.52000000 15.60000000 -1.11428571
## [4106] -1.61280000  2.93142857  3.21428571 -0.48000000 10.92000000
## [4111]  9.85000000  5.83727034  7.96800000  1.34400000 10.36800000
## [4116]  4.27500000  5.40000000  1.61454546  3.26400000  2.92173913
## [4121]  6.19354839  8.33333333  8.41121495  7.32352941  2.64000000
## [4126]  3.16800000  2.44000000  9.50400000  1.65600000  9.97500000
## [4131]  3.13846154 13.65900000  3.90000000  9.33333333  6.93333333
## [4136]  5.18181818  5.35000000  4.12800000  5.00000000  5.60000000
## [4141]  4.86000000  5.16923077  0.72000000  3.64800000  2.44800000
## [4146]  3.36000000  4.54545455  4.14000000  3.24324324  2.01600000
## [4151]  0.60000000  0.40000000  1.20000000  2.46000000  1.14000000
## [4156]  0.10285714  0.28800000  7.08000000  3.65454546  7.66285714
## [4161]  2.92800000 -1.80000000  4.23529412  7.61142857  2.59200000
## [4166]  3.92307692  1.00000000  2.27142857 11.23636364  3.66000000
## [4171]  3.75000000  9.51272727  8.34000000  1.40000000  6.86400000
## [4176]  5.94000000  1.27659575  1.42080000  1.98461538  3.72000000
## [4181]  4.68000000  9.30000000  8.48000000 -1.37142857  8.82000000
## [4186]  1.80000000  2.49600000  3.63529412  2.85000000  5.25333333
## [4191] -0.28800000  1.89000000  1.80000000  5.40000000  3.84000000
## [4196]  5.63076923  1.90000000  6.90000000  2.34000000  2.97931035
## [4201]  9.36000000  1.08000000  2.12571429  7.62666667  1.12500000
## [4206] 15.08571429  2.11764706  2.78181818  2.00000000  2.16000000
## [4211]  2.49000000  2.02105263  4.06956522  1.80923077  8.54400000
## [4216]  0.96000000  0.51428571  2.40000000  2.06896552  2.40000000
## [4221]  5.17500000  1.77777778  3.64285714  3.54461539  2.01600000
## [4226] -0.72000000  1.57377049  1.66153846  5.46352941  5.01818182
## [4231]  3.12857143  2.77333333  0.00000000  1.05000000  0.98526316
## [4236]  4.27826087  3.15000000  7.80000000  2.88000000  6.28235294
## [4241]  6.00000000  3.56250000 -0.20000000  5.02500000  2.16000000
## [4246]  0.37090909  2.00000000  6.46451613  5.46923077  4.68000000
## [4251]  5.06250000  2.34000000  3.86666667  0.31500000  7.52727273
## [4256]  1.80000000 13.30000000  0.99082569  0.68571429  2.25000000
## [4261]  4.28571429  3.78000000  2.11200000 -0.13333333  5.89714286
## [4266]  4.01538462  2.37857143  0.04363636  1.51578947  6.10285714
## [4271]  2.76923077  4.14545454  6.00000000  3.86915888  3.10153846
## [4276]  1.40000000  9.12000000  7.20000000  3.83551402  0.71928000
## [4281]  1.86782609  4.07142857 -1.72800000  1.50000000  3.79200000
## [4286]  2.40000000  3.16000000  5.00400000  3.12000000  3.12857143
## [4291]  4.44444444  1.97142857  3.80000000  1.94400000  5.81538462
## [4296]  3.42000000  4.26666667  1.08000000  2.02500000  2.72307692
## [4301]  9.27272727  3.38095238  3.02857143  2.66086957  0.66666667
## [4306]  2.10000000  0.80000000  1.74545455  2.88000000  6.33750000
## [4311]  2.91428571  3.24000000  1.97183099  1.32000000  3.85263158
## [4316]  2.05714286  3.12857143  1.90909091  2.63225806  2.40000000
## [4321] 10.73684211  0.39600000  4.67478261  1.41000000  2.88000000
## [4326]  0.76800000  1.17000000  1.79104478  3.31914894  3.57818182
## [4331]  1.92000000  8.32500000  5.65714286 10.66666667  7.69090909
## [4336]  4.32000000  2.88000000  1.28571429  0.82285714  5.54400000
## [4341] -0.16800000  3.16000000  4.80000000  3.60000000  4.02857143
## [4346]  2.21052632  0.45176471  3.72000000  7.72363636  1.38000000
## [4351]  3.00000000  0.66000000  6.80492547  3.33434483 11.70000000
## [4356]  7.66222222  4.41000000  0.62400000  6.72000000  7.61538461
## [4361]  1.10400000 -0.53333333  2.92173913  1.28571429  5.35500000
## [4366]  3.68000000  2.48727273  2.40000000  2.11200000  2.62800000
## [4371]  2.84000000  6.13333333  1.17000000  4.93333333  7.99200000
## [4376]  6.63272727  2.77894737  1.03200000  1.29600000  4.56000000
## [4381]  2.06222222  3.21391304  1.70666667  2.37142857 31.00000000
## [4386] 11.25000000  7.20000000  0.85714286  4.53488372  2.62285714
## [4391]  0.90000000  2.55652174  4.67368421  1.69714286  2.14000000
## [4396]  1.49791956  3.42857143  2.56000000  3.35000000  2.56000000
## [4401]  5.53846154  6.60000000  0.14400000  3.73333333 -0.50400000
## [4406]  1.48800000  2.05714286 11.00000000 10.40000000  9.60000000
## [4411]  4.34482759 -1.14000000  2.66086957  3.65000000 -0.24000000
## [4416]  4.33333333  2.59090909  2.62285714  4.15384615  5.48571429
## [4421]  8.76923077  4.43076923  7.62000000  3.00000000  1.88000000
## [4426]  2.34514286  7.70000000  0.85714286  3.33750000  6.97500000
## [4431] -1.07142857  7.44000000  1.17945206 10.98947368  1.68000000
## [4436]  8.28000000  3.25000000 -0.86896552  4.64000000  8.33333333
## [4441]  0.08000000  1.53333333  0.56842105  1.44000000  7.94181818
## [4446]  3.11111111

1B) Compute the mean and standard deviation of the assigned features (columns)

  • Commands: mean() sd()
  • Use the mean() function on feature to calculate the average
  • Name the result mean and the feature name. For example meanChecking
# Calculate the feature averate
meanexpenses = mean(expenses)

# Inspect the variable with the calculated mean
meanexpenses
## [1] 55.60144

Repeat the same procedure for the other feature

# Calculate the feature average
meansavings = mean(savings)
# Inspect the variable with the calculated mean
meansavings
## [1] 3.860083

1C) Compute the standard deviation or spread of the two features

  • Commands: sd()

Compute the standard deviation for the first feature

#Computing the standard deviation
spreadexpenses = sd(expenses)

# Inspect the variable with the calculated sd
spreadexpenses
## [1] 19.52084

Compute the standard deviation for the second feature

# Calculate the feature standard deviation
spreadsavings = sd(savings)
# Inspect the variable with the calculated standard deviation
spreadsavings
## [1] 3.726292

1D) Compute the signal to noise ratio (SNR) using the given formula:

  • SNR: Is the average (mean) divided by the spread (sd).
#Compute the snr of Checking and name it snr_Checking
snr_expenses = meanexpenses/spreadexpenses

#Call snr_Checking
snr_expenses
## [1] 2.848312
# Find the SNR of the second feature
snr_savings = meansavings/spreadsavings

# Inspect the variable with the calculated SNR
snr_savings
## [1] 1.035905

Of the two features which has a higher SNR? Why do you think that is? Write your answer below.

The higher signal to noise ratio (SNR) is expenses, which is mean income over the spread of the income. I think that is because the data points are more spread out. Larger standard deviation and higher mean than the savings data.


Task 2

2A) Examine the content of the csv file ‘Scoring.csv’ by opening the file in RStudio and display the first rows of the dataset.

mydatastar = read_csv("data/data - Scoring.csv")
## Parsed with column specification:
## cols(
##   Status = col_character(),
##   Seniority = col_integer(),
##   Home = col_character(),
##   Time = col_integer(),
##   Age = col_integer(),
##   Marital = col_character(),
##   Records = col_character(),
##   Job = col_character(),
##   Expenses = col_integer(),
##   Income = col_integer(),
##   Assets = col_integer(),
##   Debt = col_integer(),
##   Amount = col_character(),
##   Price = col_character(),
##   Finrat = col_double(),
##   Savings = col_double()
## )
head(mydatastar)
## # A tibble: 6 x 16
##   Status Seniority Home   Time   Age Marital Records Job   Expenses Income
##   <chr>      <int> <chr> <int> <int> <chr>   <chr>   <chr>    <int>  <int>
## 1 good           9 rent     60    30 married no_rec  free…       73    129
## 2 good          17 rent     60    58 widow   no_rec  fixed       48    131
## 3 bad           10 owner    36    46 married yes_rec free…       90    200
## 4 good           0 rent     60    24 single  no_rec  fixed       63    182
## 5 good           0 rent     36    26 single  no_rec  fixed       46    107
## 6 good           1 owner    60    36 married no_rec  fixed       75    214
## # ... with 6 more variables: Assets <int>, Debt <int>, Amount <chr>,
## #   Price <chr>, Finrat <dbl>, Savings <dbl>

2B) Create a star schema using the website erdplus stanalone feature: https://erdplus.com/#/standalone

Do an ER Scheme save to images and then insert into the RStudio lab

Below is an example of what the simple star relational schema should look like.

Example of how to create an start schema using erdplus

Example of how to export the final start schema on erdplus

Completed Star Schema Example

2C) Create a code chunk and display the star schema diagram


Task 3

Here we are going to familiarize with watson analytics, you should have access to the portal below.

https://watson.analytics.ibmcloud.com

3A) Login into Watson Analytics and upload the assigned dataset. Take an screenshot of watson’s Data section showing the quality of the dataset

3B) Use Watson Discovery capabilities to find insights in the dataset

3C) Save your work and upload a screenshot of your finding below.

3D) Thank you for reading!