Start matter

Load and clean data

data <- read.csv2(here::here("data", "sakulatordata2.csv"))

# Make categorical
data$case_subtype <- factor(data$case_subtype)
data$case_court <- factor(data$case_court)
data$case_date_start <- ymd(data$case_date_start)
data$case_month_start <- as.character(data$case_date_start, format="%m")

data$case_time_court_hearing_log <- log1p(data$case_time_court_hearing)

Create training and test datasets

# Set seed
set.seed(1234)

# Shuffle data
rows <- sample(nrow(data))
data <- data[rows, ]

# Get row numbers for the training data
trainRowNumbers <- createDataPartition(data$case_time_court_hearing_log, p=0.80, list=FALSE) 

# Create the training dataset
trainData <- data[trainRowNumbers,]

# Create the test dataset
testData <- data[-trainRowNumbers,]

# Store X and Y for later use.
y = trainData$case_time_court_hearing_log
y2 = testData$case_time_court_hearing_log

Train data

One-hot encoding of categorical data (if needed)

dummies_model <-
  dummyVars(
    case_time_court_hearing_log ~  case_priority + case_n_trans + case_subtype + case_n_part +
      case_n_witnesses + case_time_lowercourt + case_court,
    data = trainData
  )
trainData_mat <- predict(dummies_model, newdata = trainData)
trainData <- data.frame(trainData_mat)
str(trainData)
## 'data.frame':    9646 obs. of  17 variables:
##  $ case_priority                                            : num  0 0 0 0 0 0 0 1 0 0 ...
##  $ case_n_trans                                             : num  0 0 0 0 0 4 0 1 0 0 ...
##  $ case_subtype.Fagdommersak                                : num  0 0 0 0 1 0 0 1 0 0 ...
##  $ case_subtype.Lagrettesak                                 : num  0 0 1 1 0 0 0 0 0 0 ...
##  $ case_subtype.Meddomsrettssak...begrenset.anke            : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ case_subtype.Meddomsrettssak...bevisanke..gammel.ordning.: num  1 1 0 0 0 0 1 0 1 0 ...
##  $ case_subtype.Meddomsrettssak...bevisanke.over.6.Ã¥r       : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ case_subtype.Meddomsrettssak...bevisanke.under.6.Ã¥r      : num  0 0 0 0 0 1 0 0 0 1 ...
##  $ case_n_part                                              : num  2 2 3 2 2 2 2 2 2 3 ...
##  $ case_n_witnesses                                         : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ case_time_lowercourt                                     : num  99 137 152 295 69 64 59 29 110 81 ...
##  $ case_court.Agder.Lagmannsrett                            : num  1 0 0 1 0 0 0 0 0 0 ...
##  $ case_court.Borgarting.Lagmannsrett                       : num  0 0 0 0 1 0 0 1 0 0 ...
##  $ case_court.Eidsivating.Lagmannsrett                      : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ case_court.Frostating.Lagmannsrett                       : num  0 0 0 0 0 1 0 0 0 1 ...
##  $ case_court.Gulating.Lagmannsrett                         : num  0 1 0 0 0 0 0 0 1 0 ...
##  $ case_court.HÃ¥logaland.Lagmannsrett                       : num  0 0 1 0 0 0 1 0 0 0 ...

Pre-processing (if needed)

#preProcess_range_model <- preProcess(trainData, method='range')
#trainData <- predict(preProcess_range_model, newdata = trainData)

# Append Y variable
trainData$case_time_court_hearing_log <- y

Train model

fitControl <- trainControl(
  method = "repeatedcv",
  number = 10,
  repeats = 5)

set.seed(1234)
model = train(
  case_time_court_hearing_log ~ .,
  data = trainData,
  method = 'ranger',
  trControl = fitControl,
  metric = "RMSE",
  importance = 'impurity',
  na.action = na.omit
)

model
## Random Forest 
## 
## 9646 samples
##   17 predictor
## 
## No pre-processing
## Resampling: Cross-Validated (10 fold, repeated 5 times) 
## Summary of sample sizes: 8658, 8658, 8656, 8658, 8656, 8656, ... 
## Resampling results across tuning parameters:
## 
##   mtry  splitrule   RMSE       Rsquared   MAE      
##    2    variance    0.4802062  0.6909144  0.3698157
##    2    extratrees  0.5168724  0.6452251  0.4063584
##    9    variance    0.4579669  0.6987067  0.3408681
##    9    extratrees  0.4530770  0.7048395  0.3366680
##   17    variance    0.4770204  0.6754078  0.3563168
##   17    extratrees  0.4710280  0.6825491  0.3506846
## 
## Tuning parameter 'min.node.size' was held constant at a value of 5
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were mtry = 9, splitrule = extratrees
##  and min.node.size = 5.

Plot model

plot(model, main="Model Accuracies")

Variable importance

varimp <- varImp(model)
plot(varimp, main="Variable Importance")

Test data

One-hot dummy coding

dummies_model2 <-
  dummyVars(
    case_time_court_hearing_log ~  case_priority + case_n_trans + case_subtype + case_n_part +
      case_n_witnesses + case_time_lowercourt + case_court,
    data = testData
  )
testData_mat <- predict(dummies_model2, newdata = testData)
testData <- data.frame(testData_mat)
str(testData)
## 'data.frame':    2410 obs. of  17 variables:
##  $ case_priority                                            : num  0 0 1 0 0 0 0 0 0 0 ...
##  $ case_n_trans                                             : num  2 1 0 0 1 0 0 0 0 1 ...
##  $ case_subtype.Fagdommersak                                : num  0 0 1 0 1 0 1 0 0 0 ...
##  $ case_subtype.Lagrettesak                                 : num  0 1 0 0 0 0 0 0 0 1 ...
##  $ case_subtype.Meddomsrettssak...begrenset.anke            : num  0 0 0 1 0 0 0 1 0 0 ...
##  $ case_subtype.Meddomsrettssak...bevisanke..gammel.ordning.: num  1 0 0 0 0 1 0 0 1 0 ...
##  $ case_subtype.Meddomsrettssak...bevisanke.over.6.Ã¥r       : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ case_subtype.Meddomsrettssak...bevisanke.under.6.Ã¥r      : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ case_n_part                                              : num  2 2 2 2 2 2 2 2 2 2 ...
##  $ case_n_witnesses                                         : num  0 5 1 0 0 6 0 0 0 0 ...
##  $ case_time_lowercourt                                     : num  192 43 115 92 88 71 44 70 50 70 ...
##  $ case_court.Agder.Lagmannsrett                            : num  0 0 0 0 0 0 1 0 0 0 ...
##  $ case_court.Borgarting.Lagmannsrett                       : num  1 1 1 0 1 0 0 0 0 0 ...
##  $ case_court.Eidsivating.Lagmannsrett                      : num  0 0 0 0 0 1 0 0 0 0 ...
##  $ case_court.Frostating.Lagmannsrett                       : num  0 0 0 0 0 0 0 1 0 0 ...
##  $ case_court.Gulating.Lagmannsrett                         : num  0 0 0 1 0 0 0 0 1 1 ...
##  $ case_court.HÃ¥logaland.Lagmannsrett                       : num  0 0 0 0 0 0 0 0 0 0 ...

Pre-processing (whenever needed)

#preProcess_range_model2 <- preProcess(testData, method='range')
#testData <- predict(preProcess_range_model2, newdata = testData)

# Append Y variable
testData$case_time_court_hearing_log <- y2

Predict on testData

predicted <- predict(model, testData)
head(predicted)
## [1] 2.379718 2.770529 1.577985 1.448289 1.173735 2.258025

Actual and predicted values

modelEval <- cbind(testData$case_time_court_hearing_log, predicted)
colnames(modelEval) <- c('Actual', 'Predicted')
modelEval <- as.data.frame(modelEval)

# inverse log transformation for predicted and actual values
modelEval$Actual <- expm1(modelEval$Actual)
modelEval$Predicted <- expm1(modelEval$Predicted)
modelEval
##      Actual Predicted
## 1      32.5  9.801855
## 2      15.0 14.967079
## 3       5.5  3.845183
## 4       6.0  3.255825
## 5       2.0  2.234050
## 6       4.5  8.564178
## 7       4.5  1.976181
## 8       8.5  3.965892
## 9       7.0  5.886072
## 10      9.0 13.657918
## 11      2.0  2.080594
## 12      3.0  2.479168
## 13      9.5  6.301180
## 14      3.0  3.797674
## 15      1.5  2.620903
## 16      6.5  9.919042
## 17      6.0  4.906865
## 18      3.0  2.312593
## 19     56.5 31.470215
## 20     16.0 21.680819
## 21      0.5  1.743132
## 22      3.0  3.918610
## 23      6.0  3.052504
## 24     32.5 24.785988
## 25      5.0  9.140646
## 26      5.5 12.587296
## 27      5.5  5.675292
## 28      1.5  1.957907
## 29     11.5 13.269082
## 30     17.5 13.176682
## 31      1.5  2.910751
## 32      2.0  2.334560
## 33      2.0  2.416585
## 34     31.0  5.697695
## 35      3.0 11.119581
## 36      1.0  2.078343
## 37      1.5  2.047773
## 38      7.5  9.550895
## 39     31.5  7.570438
## 40      2.5  2.038603
## 41      6.5 12.218163
## 42     43.5 15.406495
## 43     35.0 28.571031
## 44     12.5 14.947420
## 45     16.5 22.745800
## 46     23.5 10.241052
## 47      4.0 13.946450
## 48     13.5 16.783660
## 49     12.5 13.735778
## 50     10.5 10.950728
## 51      2.0  2.149927
## 52      1.5  4.377719
## 53     30.5 12.202874
## 54      5.5  3.089051
## 55      1.5  1.761577
## 56     12.0 17.330758
## 57     10.0 11.722836
## 58      5.5  5.311247
## 59      3.5  4.344745
## 60      9.0  5.780397
## 61      3.0  2.135857
## 62      7.0  3.321013
## 63     17.5 22.149833
## 64     19.5 13.302578
## 65      2.5  2.927933
## 66      2.5  6.049258
## 67     18.5 12.302897
## 68      3.0  6.015622
## 69      3.0  2.371663
## 70     10.5 11.240187
## 71     54.0  8.127350
## 72      2.5  4.956411
## 73     23.0 18.236068
## 74      6.0  2.917686
## 75      1.5  2.001991
## 76      3.5  2.963362
## 77      1.0  1.904601
## 78      5.0  7.814761
## 79      5.5  6.934888
## 80     36.0 16.674944
## 81      2.5  8.402838
## 82     21.0 20.296096
## 83      5.0  3.037055
## 84      1.0  1.957826
## 85      5.0  5.562400
## 86     27.0 11.780438
## 87     16.0 13.901275
## 88      2.5  2.338641
## 89      3.5  3.919971
## 90      7.5  7.582818
## 91      2.5  3.055253
## 92     14.0 16.092783
## 93      2.0  2.060468
## 94      7.0  4.953532
## 95      3.0  2.830361
## 96      9.5  4.745252
## 97      2.5  5.206139
## 98     10.0 15.656477
## 99      9.0 12.956833
## 100     6.0  6.198434
## 101     8.5  7.027594
## 102     8.0  5.968648
## 103    40.0 37.153754
## 104    34.5 32.924591
## 105     4.5  5.759707
## 106     2.0  1.881321
## 107    20.5  8.525233
## 108     9.5  9.833870
## 109     1.5  3.480927
## 110     4.0  5.006520
## 111     2.5  3.198675
## 112     2.5  1.993141
## 113     4.0  3.027345
## 114    14.0 14.349937
## 115    11.0 13.771098
## 116     6.5  7.980467
## 117    11.5 13.773073
## 118     1.0  2.249815
## 119     3.0  3.502138
## 120     9.0 15.980758
## 121     2.0  2.111925
## 122     4.5  2.841071
## 123    16.5 15.035536
## 124     3.0  2.238103
## 125     4.5 13.467887
## 126     5.0  6.999613
## 127    16.0 18.146726
## 128     3.0  3.117573
## 129     5.0  6.880459
## 130     1.5  1.785789
## 131     3.0  2.392914
## 132     7.0  6.047879
## 133     5.5 11.764948
## 134    16.5 17.833340
## 135     5.0  5.730093
## 136    13.5 14.118523
## 137     2.5  2.834582
## 138     4.5  5.010974
## 139    13.5 13.747940
## 140     8.0  7.343981
## 141    36.0 30.111934
## 142     4.5  4.578805
## 143     2.5  6.806067
## 144     2.0  2.052602
## 145    14.0  8.203301
## 146     1.5  1.457591
## 147     3.0  2.860163
## 148    10.5 12.919479
## 149    13.0  2.563148
## 150     2.5  3.136453
## 151     5.0  6.416198
## 152     6.5 11.841430
## 153    15.0 22.423131
## 154     3.0  2.527563
## 155     2.0  1.986803
## 156     1.5  1.907454
## 157     5.5  4.842353
## 158     5.0  5.328775
## 159     1.5  3.679000
## 160     5.5  8.457347
## 161    25.0 23.983709
## 162     1.5  2.448686
## 163     3.5  4.354347
## 164     2.0  3.058149
## 165     1.0  3.103406
## 166     2.5  2.155180
## 167     8.0  3.036132
## 168     3.0  2.092647
## 169     8.0 12.015892
## 170     2.5  3.090766
## 171    27.0 16.025577
## 172    17.0 18.552864
## 173    29.5 25.994332
## 174    14.0 15.963514
## 175     2.5  2.066190
## 176     6.5  5.845233
## 177     1.0  2.127928
## 178    29.0 14.834907
## 179    39.0 35.406126
## 180     2.0  2.963142
## 181     2.0  4.007792
## 182    10.5 13.182172
## 183     1.5  2.090506
## 184     4.5  3.117688
## 185     2.5  2.944307
## 186     7.5 10.177997
## 187     3.0  2.008526
## 188     5.5  8.890323
## 189     2.0  2.422911
## 190     8.0 15.996983
## 191    40.5 26.594476
## 192     3.5  2.157815
## 193    14.0  8.030507
## 194    10.0  6.117588
## 195     5.0 11.847736
## 196    15.0 25.118108
## 197     3.5  6.301205
## 198     8.0  9.096922
## 199    18.0  8.431677
## 200     4.5  6.206807
## 201    24.0  7.479632
## 202     6.0  7.641730
## 203    20.5 16.795353
## 204     3.5  7.062271
## 205     2.5  2.916933
## 206    10.5 12.275808
## 207     5.0  4.338497
## 208    23.0 24.961889
## 209    10.0 15.407458
## 210     3.5  2.459422
## 211    17.5 21.050702
## 212    32.5 15.755898
## 213    12.5  5.913585
## 214     2.5  2.074283
## 215     2.0  2.060468
## 216    24.5  9.641590
## 217     3.0  1.730131
## 218     1.0  2.654337
## 219    10.5  9.689636
## 220     5.0  8.501885
## 221     5.0  2.341584
## 222    10.5 18.435980
## 223     0.5  1.836035
## 224     1.5  1.800463
## 225     4.0  3.084020
## 226    46.5  8.460749
## 227    15.0 11.721601
## 228     3.5  2.539090
## 229     2.5  3.276294
## 230     7.0  7.610693
## 231    34.5 25.230543
## 232    34.0 23.996505
## 233     8.5 12.833156
## 234     5.5  8.766554
## 235    12.5 17.241276
## 236    13.5 11.634948
## 237     7.5  9.147057
## 238     6.0  9.771588
## 239     3.0  2.341517
## 240     3.0  4.157016
## 241     7.0  3.885091
## 242    14.5 14.201141
## 243     1.5  2.366496
## 244     2.0  3.009693
## 245    11.5 14.986865
## 246    14.0 19.933559
## 247     2.0  2.685137
## 248    10.0  9.612160
## 249     5.5  3.540682
## 250     1.5  1.722250
## 251     9.5 12.748893
## 252    10.5  5.728225
## 253     7.0  6.854038
## 254    15.0  6.917394
## 255     3.0  6.159221
## 256     5.0  5.355513
## 257     1.5  2.938039
## 258     7.0  8.893047
## 259     1.0  1.972959
## 260    45.0 39.980259
## 261    17.0 15.692067
## 262     2.0  3.824062
## 263     1.5  4.281948
## 264     2.0  2.656193
## 265    12.5  8.219618
## 266     1.0  2.387566
## 267    24.5  8.108773
## 268     5.5 11.100363
## 269     3.0  1.987050
## 270     1.5  2.878247
## 271    47.0  8.475321
## 272     6.0  6.258975
## 273     3.0  2.940263
## 274    32.0 14.450861
## 275     6.0  5.688729
## 276    12.0  9.074571
## 277     2.0  2.610890
## 278    10.0 10.408043
## 279    25.0 23.531472
## 280     6.5  6.105197
## 281     1.5  2.436861
## 282     9.0 10.215544
## 283    31.5 30.293831
## 284     2.0  1.957231
## 285     3.0  4.296783
## 286    22.0 18.099823
## 287     6.5 12.120644
## 288     5.5 10.023485
## 289    29.0  5.730500
## 290     4.0  3.827762
## 291    13.0 13.420543
## 292     4.5  5.601657
## 293    11.0  4.696517
## 294    13.5  5.845233
## 295     2.0  3.207982
## 296     2.5  2.075300
## 297    16.5  4.907865
## 298     2.0 12.578446
## 299    25.5  3.144562
## 300    12.5 14.460061
## 301    16.0  2.922151
## 302     2.5  3.370368
## 303     4.5  7.306449
## 304     8.5 14.394116
## 305    11.5  3.326629
## 306     4.5  6.007553
## 307     4.5  4.378824
## 308     2.0 37.067666
## 309    21.0  7.756537
## 310     7.0 14.280265
## 311    14.0 19.781283
## 312    16.0  3.431035
## 313     2.0 15.355419
## 314    12.0 32.035404
## 315    33.0 10.885618
## 316     5.5  3.183392
## 317     2.5  2.863022
## 318     3.0  2.424708
## 319     2.5 28.469524
## 320    42.0 22.887708
## 321    18.0  7.107201
## 322     6.0 11.226252
## 323     9.5 13.820854
## 324     8.5  5.889701
## 325     2.5 23.333766
## 326    20.5 11.246557
## 327    15.5  7.347945
## 328    44.0  3.923634
## 329     5.5  6.307280
## 330    10.5 17.276295
## 331    19.5  2.098822
## 332     1.0  1.986803
## 333     1.5 13.897993
## 334    36.0 15.172238
## 335    22.5 10.154669
## 336    13.0  8.188412
## 337    11.5  3.360402
## 338     1.5  2.296623
## 339     1.0  2.087990
## 340     1.0  3.657966
## 341     2.5 16.639299
## 342    14.0 13.611803
## 343     6.0  2.447664
## 344     4.0 10.495308
## 345    10.0 11.469526
## 346    12.5  1.976218
## 347     2.0  2.328065
## 348     1.0 12.206322
## 349     6.0 13.166590
## 350    17.0 12.229155
## 351    12.0  7.685748
## 352     9.0 18.403973
## 353    20.0 12.474632
## 354    36.0  2.863275
## 355     2.0  2.826029
## 356     2.0 19.943442
## 357    16.0 18.054769
## 358    21.5 23.246140
## 359    25.5  8.122041
## 360     5.5  2.301533
## 361     2.5  7.526358
## 362     5.5 21.149964
## 363    24.0  2.427175
## 364     3.0  2.520976
## 365     1.0 18.163700
## 366    14.0  4.255309
## 367    13.0  5.359929
## 368     5.0 12.206322
## 369    19.5  2.097415
## 370     1.0  2.130955
## 371     2.0  3.682602
## 372     8.0 18.961498
## 373    26.0  2.158827
## 374     1.5  9.410836
## 375    12.5 31.126402
## 376    38.0  2.168624
## 377     1.0  2.431344
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## 379    16.5  2.063246
## 380     1.5 13.512233
## 381    17.5 13.636936
## 382    17.5 16.973804
## 383    19.5  3.893945
## 384     5.5 29.107194
## 385    51.0  3.912266
## 386     2.5  2.656193
## 387     2.0  2.359669
## 388     6.5  5.925895
## 389     4.0  6.705116
## 390     7.0 13.002274
## 391    10.0  5.272685
## 392     7.5  3.479486
## 393     3.5  8.853498
## 394    10.5  4.351796
## 395     3.5 17.438285
## 396    29.5 13.361007
## 397     3.5 14.999700
## 398    19.0  9.526573
## 399     8.0 20.745354
## 400    21.0  6.372446
## 401    12.5 17.249366
## 402    14.0  2.288619
## 403     1.5  2.486737
## 404     6.0 10.863059
## 405     6.0  4.321059
## 406     5.5  6.485339
## 407     2.5 20.890301
## 408    33.5  1.723442
## 409     2.0  7.596589
## 410     7.5  2.376254
## 411     2.0 17.346084
## 412    26.5 20.441614
## 413    20.5 11.787878
## 414    26.5 13.882038
## 415    19.5  6.863994
## 416     5.5  8.259779
## 417    41.5  6.042850
## 418     3.5 15.636003
## 419     9.5  4.669908
## 420     4.0 17.549200
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## 1581    7.5  6.135654
## 1582    5.5 14.661422
## 1583   14.0 14.479293
## 1584    5.0  5.689041
## 1585   25.5  2.048186
## 1586   12.0  2.102514
## 1587    7.0  7.293475
## 1588    2.0 26.464796
## 1589    5.0  6.766806
## 1590    8.0  6.272575
## 1591   49.5  4.021350
## 1592    5.0  1.942901
## 1593    7.0 14.306558
## 1594    6.5 16.504904
## 1595    1.5 17.677324
## 1596   13.0  3.976280
## 1597   12.0 16.168679
## 1598   16.0  2.841932
## 1599    1.0 18.346259
## 1600   28.5 24.501646
## 1601    3.0 11.818958
## 1602   19.0  4.450819
## 1603   32.0 14.010044
## 1604    9.0 14.652841
## 1605    3.0 13.455442
## 1606   15.0  4.015248
## 1607   21.5  2.311305
## 1608   13.5  2.941328
## 1609    3.0  7.629967
## 1610    2.0  1.950864
## 1611    1.5  8.437344
## 1612    5.5  6.643568
## 1613    2.5  3.631010
## 1614   12.0  3.079347
## 1615    6.0  2.546407
## 1616    7.0  7.283203
## 1617    3.0 20.766734
## 1618    0.5  1.775032
## 1619    6.0  1.864179
## 1620   33.5  9.353916
## 1621    1.0 17.688459
## 1622    1.5  8.437099
## 1623   17.0  2.019173
## 1624    9.5  5.060830
## 1625    8.5  2.268270
## 1626    2.5  4.840067
## 1627   10.5 14.039186
## 1628    2.5 14.082433
## 1629    8.5 29.929769
## 1630   12.0 15.029294
## 1631   15.5 13.993912
## 1632   55.0 23.650954
## 1633   14.5 33.846520
## 1634    9.0  1.921944
## 1635   42.0  4.072565
## 1636   54.5  1.837095
## 1637    1.0  7.192768
## 1638    5.5  8.636503
## 1639    2.0  3.833220
## 1640    5.5 13.813586
## 1641    7.5  8.770811
## 1642    7.0  2.913880
## 1643    9.0  3.175306
## 1644   10.0  3.563301
## 1645    7.0 13.534378
## 1646    3.0  1.957826
## 1647    2.0  5.863272
## 1648    7.5  2.113742
## 1649    1.0  2.572308
## 1650    7.5 11.066718
## 1651    1.5  6.986189
## 1652    2.0 19.897635
## 1653   36.0 13.591309
## 1654    5.0  2.583840
## 1655    6.0  7.678701
## 1656   14.0  2.089019
## 1657    5.0 11.712587
## 1658    9.0 16.635949
## 1659    2.0 15.980758
## 1660   10.5 12.377004
## 1661   22.0  5.719516
## 1662   14.0  7.303886
## 1663   28.0  2.019514
## 1664    7.5  7.978355
## 1665    9.0  5.889701
## 1666    2.0  1.960593
## 1667    7.0 18.334754
## 1668    6.5 12.634995
## 1669    2.0  5.791007
## 1670   21.0  8.891301
## 1671   12.5  4.061963
## 1672    3.0 23.590205
## 1673    4.0 15.027789
## 1674    3.0  8.406965
## 1675   20.5  2.277017
## 1676   10.0 14.816485
## 1677    8.0  2.255962
## 1678    4.5  9.754789
## 1679   10.5 10.978370
## 1680    1.5  5.311247
## 1681    6.0  6.198434
## 1682   23.0 19.321034
## 1683    3.5 11.442676
## 1684    3.5  6.274357
## 1685   22.0 10.265911
## 1686   25.0  7.913365
## 1687   15.5 27.803549
## 1688    4.5  2.909439
## 1689   21.5 17.229202
## 1690   55.0  3.643594
## 1691    1.5 13.177545
## 1692   14.5  8.206795
## 1693    2.0  1.958137
## 1694   18.0  2.374398
## 1695    4.5  8.567753
## 1696    1.0  5.159339
## 1697    3.5  6.949873
## 1698    8.0  2.995047
## 1699    5.0  1.729485
## 1700    2.5  2.094223
## 1701    5.5  9.633805
## 1702    2.0  2.095735
## 1703    2.5  2.031827
## 1704    5.5 19.473551
## 1705   13.0 12.848283
## 1706    1.5  6.017816
## 1707   36.5  2.855268
## 1708    7.0 17.025057
## 1709    4.5  2.459422
## 1710    3.0 11.490693
## 1711   31.5  1.969595
## 1712    1.5 13.251518
## 1713    7.0  5.510875
## 1714    1.0  2.306094
## 1715   15.5  5.938686
## 1716    3.5  5.701098
## 1717    2.5  9.424408
## 1718    4.5  3.863316
## 1719    6.5  2.415420
## 1720    6.0  2.958937
## 1721    4.5  9.342524
## 1722    1.5 18.013401
## 1723    2.5  5.813852
## 1724   12.0 20.230840
## 1725   45.0  2.864035
## 1726    5.0  3.685272
## 1727   24.5 18.204097
## 1728    2.0 15.498278
## 1729    3.5  7.154219
## 1730   28.0 11.511909
## 1731   13.5  2.039008
## 1732    8.5  1.910248
## 1733   10.0 10.427139
## 1734    1.5  6.421508
## 1735    1.5  9.368689
## 1736    8.5  2.404619
## 1737    3.5  1.690551
## 1738    7.0 13.979078
## 1739    2.5 23.902630
## 1740    1.5  5.984160
## 1741   15.5 14.191551
## 1742   38.0 11.867616
## 1743    3.0  5.352788
## 1744   10.0 14.796761
## 1745   33.5  9.163382
## 1746    6.5  5.783165
## 1747    8.5 33.542533
## 1748   18.5  9.700006
## 1749    2.5 28.059283
## 1750   54.5 11.726703
## 1751    7.0  6.199534
## 1752   36.5  2.188238
## 1753   11.5  6.155933
## 1754    2.0  2.167544
## 1755    6.5  4.922882
## 1756    5.5 13.136626
## 1757    1.5  7.385675
## 1758   19.0  3.408284
## 1759   11.5  6.693284
## 1760   10.5  2.215847
## 1761    4.0  8.675425
## 1762    6.5  5.280064
## 1763    1.0  2.107713
## 1764    9.5 17.424154
## 1765    3.5  3.360826
## 1766    2.5  2.737915
## 1767   12.5  2.000710
## 1768    1.5 24.270706
## 1769    2.5  2.003358
## 1770    3.5  5.976608
## 1771   28.5 14.429180
## 1772    0.5 14.523499
## 1773   13.5 22.183349
## 1774    6.0  1.899132
## 1775   24.0  3.666378
## 1776   18.0  2.216155
## 1777    2.0 17.295745
## 1778    2.5  2.341584
## 1779    2.0  1.765224
## 1780   18.5  7.413398
## 1781    3.5 10.974974
## 1782    1.5  6.999613
## 1783    4.0 11.517227
## 1784    5.0 12.233463
## 1785    8.5  3.029473
## 1786   20.5  6.169554
## 1787   28.0  2.196845
## 1788    3.0 15.104380
## 1789    2.5  5.984924
## 1790    1.5 21.945073
## 1791   12.5 13.923902
## 1792   11.5  1.981350
## 1793   40.5  2.120453
## 1794   21.0  4.523299
## 1795    1.0  2.486737
## 1796    3.5  7.811391
## 1797    4.5  8.439018
## 1798    1.5 25.299205
## 1799    2.0 25.234526
## 1800   44.0  5.886550
## 1801   51.5 19.065221
## 1802   38.5 10.602922
## 1803    6.5 15.007818
## 1804   49.0  9.867150
## 1805   11.5  1.690483
## 1806   16.0 16.796570
## 1807    7.0  8.520886
## 1808    2.5 30.952554
## 1809   21.0 19.354050
## 1810    2.5  9.125539
## 1811   18.0 23.770831
## 1812   16.0  2.910658
## 1813   10.0 31.795617
## 1814   19.5  2.214165
## 1815    5.5 11.931536
## 1816   16.5  2.447363
## 1817    1.5  9.564830
## 1818   13.5  6.977573
## 1819    2.0  6.499311
## 1820   12.0  3.123405
## 1821    5.5  2.036928
## 1822    7.0  2.938649
## 1823    3.0  8.679219
## 1824    2.0 28.243072
## 1825    3.0  2.087579
## 1826    4.5 13.708595
## 1827   49.0  3.120622
## 1828    1.0  5.431947
## 1829    6.0  2.301548
## 1830    3.0 18.804738
## 1831    2.5  2.228722
## 1832    2.0  6.330134
## 1833   14.5  6.320523
## 1834    1.0  5.367103
## 1835   16.5 12.347426
## 1836   11.0 25.236192
## 1837    5.5  2.488939
## 1838   33.0 13.327519
## 1839   25.0  7.070772
## 1840    2.5 10.692914
## 1841    6.0 33.195370
## 1842   27.0 17.121304
## 1843   10.5  2.167558
## 1844   39.5  3.439098
## 1845   40.5 11.817197
## 1846    2.0 15.228232
## 1847    2.5  2.598222
## 1848   15.0 11.693691
## 1849   15.0  5.939499
## 1850    3.0 24.782976
## 1851   15.5  9.938718
## 1852    5.0  5.730093
## 1853   27.0 14.174044
## 1854   41.0 13.746063
## 1855    3.0  2.358005
## 1856   15.0  2.327575
## 1857    0.5 16.140192
## 1858    5.5  2.063612
## 1859    2.5 14.544865
## 1860   16.0  3.774766
## 1861    2.5 11.286341
## 1862   14.0  3.928414
## 1863    2.0  3.043457
## 1864   34.5 21.325790
## 1865    3.0  9.587956
## 1866    4.5  6.822150
## 1867   23.0  1.902191
## 1868    4.5  1.682458
## 1869    7.5  3.652983
## 1870    2.0  1.722760
## 1871    1.0  2.301533
## 1872    4.0  3.459032
## 1873    2.5  3.452481
## 1874    1.5 12.797622
## 1875    1.5  7.662223
## 1876    2.5 10.534856
## 1877   11.5  5.465974
## 1878    5.0  2.861993
## 1879   14.0 17.337528
## 1880    7.5  5.692868
## 1881    2.5  2.782293
## 1882   41.0 11.592491
## 1883    6.5  2.287246
## 1884    3.5  8.455228
## 1885    6.0  6.147373
## 1886    1.0  4.917301
## 1887    8.0  3.759904
## 1888    7.0  2.588875
## 1889    5.0 11.165410
## 1890   22.0  2.914044
## 1891    2.5  2.833095
## 1892    5.0 14.961023
## 1893    3.0  4.123365
## 1894    2.5  4.021591
## 1895   11.0  5.854671
## 1896   12.0  5.292329
## 1897    2.5 21.002628
## 1898    4.5 19.112110
## 1899    5.5  8.826440
## 1900   23.0  2.015918
## 1901   13.0 14.755018
## 1902   12.5  2.341584
## 1903    3.0 14.640940
## 1904   10.5 10.707811
## 1905    1.0  7.084936
## 1906   15.0  3.180848
## 1907   44.0 17.576617
## 1908    5.5  6.601413
## 1909    5.0  9.361771
## 1910   17.0 17.690890
## 1911    4.5  7.557755
## 1912    6.5  6.089483
## 1913   47.0  2.894466
## 1914    7.5 30.720061
## 1915    8.5 25.784442
## 1916    3.0  1.715460
## 1917   34.0  2.091647
## 1918   23.5  4.436109
## 1919    3.0  2.521037
## 1920    3.0  4.849652
## 1921    5.0 14.791298
## 1922    1.5 12.636958
## 1923    2.5 15.780860
## 1924   16.5  2.207632
## 1925   11.0 14.756642
## 1926   15.5 13.488724
## 1927    1.0  1.881321
## 1928   12.5  3.303843
## 1929   11.0  2.706873
## 1930    2.0 10.301776
## 1931    2.5  7.437984
## 1932    2.0 22.754463
## 1933   13.0 12.535253
## 1934    2.5  6.090476
## 1935   50.5  3.346135
## 1936   45.0  3.135258
## 1937   28.0  4.633563
## 1938    2.0  2.917849
## 1939    2.0  5.562400
## 1940    7.0 15.365699
## 1941    3.5 15.323509
## 1942    4.5  2.812642
## 1943    9.5  5.794221
## 1944   20.5  2.453315
## 1945    4.0 23.179973
## 1946    1.5 15.258226
## 1947    2.5 26.670429
## 1948   47.0  2.208598
## 1949   10.0  6.599128
## 1950   43.5  2.814378
## 1951    3.5 18.391568
## 1952    3.5 21.287385
## 1953    1.5 14.933671
## 1954   24.5  5.487929
## 1955   14.5  2.055242
## 1956   18.0 10.667225
## 1957    2.5  2.277271
## 1958    1.5 16.144883
## 1959   10.0 16.371168
## 1960    2.0 16.777299
## 1961   16.5 16.371674
## 1962    9.5  9.718422
## 1963    6.0  6.359482
## 1964   10.5  3.176731
## 1965   16.5  5.503521
## 1966    8.0 28.108184
## 1967    3.5  2.455905
## 1968    6.0  8.833262
## 1969   11.0  3.715739
## 1970    2.5  2.456606
## 1971   16.5 29.627081
## 1972    1.5  4.176347
## 1973    2.5  5.770451
## 1974   14.0  1.784631
## 1975    4.5 18.455535
## 1976    4.5 15.580677
## 1977    2.5 12.546996
## 1978   18.0  9.403919
## 1979   18.5  5.270371
## 1980   16.0 12.310444
## 1981   12.5  2.257740
## 1982    5.0  2.018404
## 1983   15.5  3.607872
## 1984    1.5  4.796774
## 1985    1.5  1.836035
## 1986    4.0  2.442211
## 1987    8.0  2.419619
## 1988    2.0 16.855046
## 1989    1.5  4.750676
## 1990    2.5  9.103145
## 1991    9.0  5.938686
## 1992    5.5 36.618917
## 1993    8.0  2.710938
## 1994    5.5 12.890886
## 1995   26.0 13.682473
## 1996    7.5  6.330017
## 1997   19.0 18.696259
## 1998   10.0 19.635985
## 1999   10.5 19.875968
## 2000   23.5  2.066352
## 2001   27.5 15.737107
## 2002   15.5  2.351747
## 2003    2.0 21.672656
## 2004   13.5  6.156068
## 2005    1.5  2.029305
## 2006   12.0 13.674533
## 2007    6.5  5.594930
## 2008    2.0  9.300295
## 2009    8.5  8.154755
## 2010   23.0 16.439281
## 2011    7.0 12.811943
## 2012   13.0 13.569843
## 2013   17.0 10.416074
## 2014    6.0  1.738504
## 2015    9.5  2.118218
## 2016    6.0 12.458489
## 2017    1.0 26.557875
## 2018    2.0  1.740809
## 2019   20.5  5.160099
## 2020   22.5  3.625919
## 2021    1.5 16.739518
## 2022   11.0 12.281064
## 2023    3.0  2.060864
## 2024    2.0  9.601799
## 2025    9.5 16.051618
## 2026   12.0 12.781393
## 2027    2.0 10.250099
## 2028    7.0  5.794221
## 2029   20.5 20.304041
## 2030   15.0  2.085525
## 2031    6.0 14.824874
## 2032   12.0 21.310600
## 2033   28.0  2.474588
## 2034    2.0 10.726742
## 2035    7.0  4.058731
## 2036   10.0  6.301205
## 2037    1.5  2.119297
## 2038   11.0 17.843801
## 2039    3.5 11.266308
## 2040    4.0  3.350261
## 2041    1.5 13.873831
## 2042   22.0 12.000856
## 2043   11.0  8.042913
## 2044    5.0  6.334618
## 2045   17.5 14.308354
## 2046   12.5  3.082065
## 2047   20.0  4.515901
## 2048   16.5  2.004961
## 2049   17.5  5.159479
## 2050    1.5  2.327575
## 2051    5.5  4.342588
## 2052    2.5  2.931406
## 2053    2.0  6.046074
## 2054    2.5  5.081245
## 2055    5.5  6.806422
## 2056    4.5 25.611265
## 2057    7.5 16.025528
## 2058    5.0 15.416538
## 2059    9.0  7.240996
## 2060   26.5  2.835357
## 2061   10.5  5.238062
## 2062   11.5  3.630034
## 2063    5.0  9.316299
## 2064    2.0  6.766806
## 2065    3.0 14.264248
## 2066    3.0  3.120622
## 2067    3.0  1.534870
## 2068    6.5  2.066297
## 2069   15.0  5.968467
## 2070    1.5  2.833330
## 2071    3.0 12.797047
## 2072    4.5  4.231635
## 2073    2.5 20.258978
## 2074    2.5  9.414610
## 2075    2.0 12.490143
## 2076    4.0 16.094585
## 2077   31.5  4.315550
## 2078   18.5 14.622314
## 2079   32.5  4.564378
## 2080   14.5  8.829114
## 2081   28.5 13.648374
## 2082    8.5  5.074905
## 2083    4.5  2.318504
## 2084   12.0 16.080487
## 2085   26.0  3.995004
## 2086   12.0  4.253236
## 2087    1.0  7.839979
## 2088   11.5  4.366383
## 2089    2.5  2.593578
## 2090    9.5  7.737375
## 2091    6.0  2.098271
## 2092    6.0  4.717337
## 2093    1.5  2.077510
## 2094    7.0 10.118579
## 2095    2.5  3.371063
## 2096    9.5  7.830021
## 2097    5.5  1.984219
## 2098   11.0  3.419382
## 2099    5.5  5.688729
## 2100    5.5  1.715460
## 2101    1.0  2.073077
## 2102    3.0 17.813580
## 2103    5.5 29.681382
## 2104    1.5 10.891393
## 2105    1.5  5.189040
## 2106   13.0 15.199384
## 2107   59.0  4.451159
## 2108    7.5  2.671286
## 2109    5.5  4.952671
## 2110   24.0 10.029560
## 2111    3.5  4.844089
## 2112    3.0 36.369381
## 2113    4.5 14.040261
## 2114    8.0  2.670464
## 2115    3.0  6.258896
## 2116   21.5 13.368616
## 2117   13.5  6.979357
## 2118    1.0 30.272791
## 2119    7.0 21.058698
## 2120   33.5  2.036928
## 2121    7.0  2.269582
## 2122   18.0  2.000710
## 2123   33.0  1.692775
## 2124    2.0  5.393749
## 2125    2.0  6.625899
## 2126    1.5  9.768594
## 2127    2.5  2.156651
## 2128   13.5  5.272276
## 2129    2.0 21.324816
## 2130    6.0 15.599980
## 2131    2.5  2.094223
## 2132    6.0 12.886571
## 2133   15.5  2.106231
## 2134   23.0  3.700654
## 2135    2.0 12.076147
## 2136   10.0  7.888298
## 2137    1.5 25.515002
## 2138    2.0  5.286031
## 2139    9.0  2.631074
## 2140    5.5  2.094219
## 2141   26.0 12.248726
## 2142   24.5 11.845435
## 2143    2.0  5.577652
## 2144    1.5  3.135258
## 2145   11.0  2.003358
## 2146   12.5 10.626436
## 2147    4.0 16.473721
## 2148    7.0  3.584217
## 2149    1.5 10.577063
## 2150    6.0 14.757720
## 2151   24.0  2.079772
## 2152    4.0  6.498299
## 2153    6.5  3.278566
## 2154   38.5 20.763767
## 2155    4.0  7.335450
## 2156    5.5  7.908286
## 2157    7.0  4.450819
## 2158   15.0  2.590692
## 2159    5.5  5.868502
## 2160    5.0  8.108311
## 2161    5.0  5.495520
## 2162    1.5  2.352291
## 2163    7.0  2.829197
## 2164    5.5 12.798559
## 2165    1.5  7.158076
## 2166    1.0 17.442482
## 2167    4.5 14.790711
## 2168   22.5  3.960975
## 2169    3.5  6.381509
## 2170   15.5 18.419123
## 2171    9.5  2.455744
## 2172    5.0  3.366677
## 2173    8.0  5.728829
## 2174   11.0  4.873532
## 2175    2.5  1.995009
## 2176   14.5 31.297060
## 2177    3.5 16.700177
## 2178    6.0  1.981350
## 2179    3.0  1.991695
## 2180   35.0 14.314326
## 2181   27.0 17.161697
## 2182    2.0  4.886608
## 2183    1.5 22.572533
## 2184    8.5  3.976829
## 2185   23.0 12.953541
## 2186    6.5  3.140759
## 2187   14.0 13.064970
## 2188    6.0  6.363610
## 2189   44.0 11.893886
## 2190    2.5 18.214220
## 2191   11.0 17.178768
## 2192    7.0  2.696532
## 2193    6.0  1.962816
## 2194   22.0  7.883574
## 2195   37.5  1.702396
## 2196    2.5 11.579972
## 2197    1.5 13.802979
## 2198   57.5 13.150030
## 2199    3.0  2.162209
## 2200   23.5  3.538508
## 2201   27.5  2.807326
## 2202    7.0  8.128733
## 2203    1.0 18.213201
## 2204    1.0  2.320246
## 2205    1.5  4.820557
## 2206    9.5 19.296650
## 2207   16.5  5.889701
## 2208    6.0  2.746694
## 2209    4.5 10.675794
## 2210   18.0  3.252116
## 2211    5.5 11.463748
## 2212    2.5  3.440783
## 2213   13.5  2.334077
## 2214    3.0  3.069761
## 2215   13.5  6.761791
## 2216    4.0  2.036882
## 2217    1.5  4.292009
## 2218    1.5  2.986284
## 2219    8.0  2.467307
## 2220    1.5  5.937237
## 2221    6.0 11.225176
## 2222    1.0 13.703239
## 2223    2.5  3.024645
## 2224    3.5  2.192189
## 2225    8.0  2.101654
## 2226   12.0 19.766298
## 2227   15.0  2.594191
## 2228    4.5 18.062979
## 2229    1.5 14.221720
## 2230   24.5 10.746515
## 2231    2.0  3.025790
## 2232   25.5 16.859588
## 2233   16.0  2.161392
## 2234   12.5  2.891433
## 2235    1.0  8.563771
## 2236   14.5  2.181462
## 2237    1.5  1.971978
## 2238    3.0 12.490150
## 2239   12.5 17.271910
## 2240    3.0 26.541162
## 2241    2.0  2.747387
## 2242   17.5  7.830438
## 2243   14.5  9.365382
## 2244   25.5 18.315745
## 2245    3.0  1.784631
## 2246   10.5  7.790457
## 2247   14.5 17.445654
## 2248   21.0 23.354709
## 2249    1.0 12.498300
## 2250    5.0  9.565033
## 2251   18.5  8.311991
## 2252   34.5  7.711959
## 2253    7.5 14.248198
## 2254    9.5  2.138097
## 2255    7.0  1.775032
## 2256   13.5  4.469910
## 2257   18.0 13.749800
## 2258    2.5  1.854207
## 2259    1.0  7.420547
## 2260    5.5  7.385675
## 2261    2.5 12.009968
## 2262    2.5  5.926374
## 2263    3.0  6.140213
## 2264   10.5  5.196612
## 2265    9.0  6.165837
## 2266    7.5 17.912303
## 2267    7.0  5.474496
## 2268    5.5  2.593346
## 2269    4.5 12.718311
## 2270   31.5  3.822520
## 2271    8.5  5.758480
## 2272    1.0  5.322854
## 2273   16.5  2.056759
## 2274    3.0  4.017727
## 2275    3.5 25.866283
## 2276    3.5  2.458901
## 2277    3.5  7.437519
## 2278    5.0  1.836035
## 2279   28.0  5.768371
## 2280    2.5 11.606106
## 2281    5.5  2.479168
## 2282    4.5 12.463481
## 2283    9.0  7.624946
## 2284    9.5 12.898685
## 2285    2.0  3.535302
## 2286    2.0  4.715806
## 2287    6.0  6.979939
## 2288    9.5  2.109883
## 2289    2.0  9.346036
## 2290    3.5 15.693400
## 2291    6.0  4.810491
## 2292    3.0 13.777660
## 2293    7.0 30.557521
## 2294   17.5 13.489521
## 2295    5.0  1.907454
## 2296   20.5  2.073694
## 2297   33.0 13.666858
## 2298   12.0  2.090964
## 2299    2.0  5.968648
## 2300    2.0 17.249005
## 2301   10.5  2.060864
## 2302    2.5 12.359879
## 2303   11.0 13.469426
## 2304   12.0  7.351954
## 2305    2.0  2.193417
## 2306   12.5 13.658820
## 2307    8.5  4.687687
## 2308   12.5  1.996195
## 2309    1.0  6.753095
## 2310   10.5 12.481680
## 2311    2.5  2.415487
## 2312    1.5  1.708108
## 2313    6.0 21.008821
## 2314    5.5 14.364033
## 2315    2.0 38.936766
## 2316    2.5  1.854207
## 2317   27.0  7.326398
## 2318    7.5 25.103479
## 2319   50.5  1.708108
## 2320    2.5 13.590575
## 2321   10.0  4.454884
## 2322   33.5  3.141534
## 2323    2.0  2.768131
## 2324   12.5 22.752893
## 2325    3.0  3.999008
## 2326    1.0 10.842402
## 2327    2.5  7.481580
## 2328   19.0  2.129907
## 2329    1.5 16.862995
## 2330    6.5  2.960691
## 2331    7.5  2.006917
## 2332    4.0 12.843147
## 2333   20.0  2.171212
## 2334    6.5  2.048186
## 2335    2.0 13.061116
## 2336    7.0 15.788135
## 2337    0.5  2.109883
## 2338    6.0 14.038834
## 2339   15.5  2.056877
## 2340    7.0  4.213463
## 2341    1.5  8.888590
## 2342   11.5  5.886072
## 2343    1.0  2.016493
## 2344    3.5 18.235429
## 2345    7.5  2.073077
## 2346    5.5 12.518248
## 2347    3.5  5.311247
## 2348   33.0  2.856594
## 2349    2.0  3.931540
## 2350   15.0 13.247244
## 2351    4.5 10.521232
## 2352    1.5 14.448298
## 2353    3.0  3.204467
## 2354   28.0  5.623380
## 2355    4.0  2.934555
## 2356    6.5  6.234063
## 2357    3.0 18.938501
## 2358    4.0 10.123381
## 2359    2.5  2.467560
## 2360   13.5  3.772136
## 2361   10.0  3.393691
## 2362   17.0 18.187365
## 2363    2.0  2.267813
## 2364    6.0  2.894627
## 2365    4.5  2.875784
## 2366   24.5 17.304180
## 2367    2.0  7.314060
## 2368    2.0 12.271914
## 2369    2.5  5.585438
## 2370   16.0 10.857376
## 2371    7.0  2.188101
## 2372   13.5 14.004698
## 2373    4.5 15.224282
## 2374   33.0  2.068362
## 2375    1.5 17.352873
## 2376   21.5  9.393020
## 2377    7.5 11.551410
## 2378    1.5  2.673043
## 2379   27.5  2.419725
## 2380    9.0  7.855634
## 2381   13.0 18.271335
## 2382    2.0 18.460922
## 2383    3.5 13.311900
## 2384    6.5  2.475671
## 2385   20.5  3.166390
## 2386   12.5  2.068305
## 2387    9.5  2.470336
## 2388    5.5 13.083399
## 2389    3.5  2.451836
## 2390    1.5  6.507920
## 2391    2.0  4.607328
## 2392   44.5  2.063615
## 2393    2.0  7.946302
## 2394    8.0 10.847948
## 2395    4.5 16.247326
## 2396    1.5  1.904601
## 2397    7.0  2.067865
## 2398    9.5  6.037172
## 2399   19.0 30.806543
## 2400    1.5  3.645831
## 2401    1.5  3.127318
## 2402   16.5  7.255031
## 2403   21.5 21.055071
## 2404    5.0  8.586621
## 2405    3.5 30.038558
## 2406   10.5 11.755471
## 2407   19.0  9.801855
## 2408   21.0 14.967079
## 2409   18.5  3.845183
## 2410   13.0  3.255825

A plot: Actual versus predicted

ggplot(modelEval, aes(x = Actual, y = Predicted)) +
  geom_point(alpha = 0.6, color = "cadetblue") +
  geom_smooth(method = "loess", formula = "y ~ x") +
  geom_abline(intercept = 0, slope = 1, linetype = 2) +
  labs(title = "Predicted vs Actual")

Model evaluation

evaluation <- postResample(pred = modelEval$Predicted, obs = modelEval$Actual)
knitr::kable(evaluation, digits = 2) # Still a relatively large RMSE after predicting on the test data
x
RMSE 12.02
Rsquared 0.01
MAE 8.36