library(reshape2)
library(ggplot2)
library(dplyr)
## 
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
library(caret)
## Loading required package: lattice
## Warning in as.POSIXlt.POSIXct(Sys.time()): unknown timezone 'zone/tz/2017c.
## 1.0/zoneinfo/America/Fortaleza'
library(lattice)
library(corrplot)
## corrplot 0.84 loaded
library(tidyr)
## 
## Attaching package: 'tidyr'
## The following object is masked from 'package:reshape2':
## 
##     smiths
library(magrittr)
## 
## Attaching package: 'magrittr'
## The following object is masked from 'package:tidyr':
## 
##     extract
train <- read.csv("train.csv", encoding="UTF-8")
test <- read.csv("test.csv", encoding="UTF-8")
submission <- read.csv("sample_submission.csv")

#Alterando valores de NA para zero
train[is.na(train)] <- 0
test[is.na(test)] <- 0
  1. Usando todas as variáveis disponíveis, tune (usando validação cruzada): (i) um modelo de regressão Ridge, (ii) um modelo de regressão Lasso e (iii) um modelo KNN. Para os modelos de regressão linear, o parâmetro a ser tunado é o lambda (penalização dos coeficientes) e o KNN o número de vizinhos.
fitControl <- trainControl(method = "cv",
                    number = 5,
                    search= "random")
lambdaGrid <- expand.grid(lambda = seq(0, 0.50, by=0.01))

fractionGrid <-  expand.grid(fraction = seq(0, 0.50, by=0.01))

neighborsGrid <- expand.grid(k = seq(1, 50, length=50))

train_dadosFiltrados <- train %>% select(-nome, -cargo, -setor_economico_receita, -setor_economico_despesa, -numero_cadidato)
test_dadosFiltrados <- test %>% select(-nome, -cargo, -setor_economico_receita, -setor_economico_despesa, -numero_cadidato)
model_ridge <- train(votos ~ .,
          data = train_dadosFiltrados,
          method = "ridge", 
          metric="RMSE",
          trControl = fitControl,
          tuneGrid = lambdaGrid,
          na.action = na.omit)
## Loading required package: lars
## Loaded lars 1.2
model_ridge
## Ridge Regression 
## 
## 4152 samples
##   20 predictor
## 
## No pre-processing
## Resampling: Cross-Validated (5 fold) 
## Summary of sample sizes: 3322, 3323, 3323, 3320, 3320 
## Resampling results across tuning parameters:
## 
##   lambda  RMSE      Rsquared   MAE     
##   0.00    33287.53  0.4588502  13014.19
##   0.01    32838.58  0.4726824  12925.79
##   0.02    32892.23  0.4717896  12937.41
##   0.03    32936.37  0.4712676  12949.15
##   0.04    32974.99  0.4709778  12961.97
##   0.05    33010.14  0.4708496  12975.19
##   0.06    33043.16  0.4708376  12989.14
##   0.07    33074.98  0.4709105  13002.69
##   0.08    33106.28  0.4710460  13017.24
##   0.09    33137.57  0.4712277  13033.81
##   0.10    33169.22  0.4714435  13052.84
##   0.11    33201.50  0.4716844  13073.04
##   0.12    33234.63  0.4719435  13094.75
##   0.13    33268.76  0.4722156  13118.38
##   0.14    33304.03  0.4724964  13143.82
##   0.15    33340.52  0.4727828  13170.54
##   0.16    33378.30  0.4730724  13198.45
##   0.17    33417.43  0.4733632  13228.37
##   0.18    33457.95  0.4736536  13258.97
##   0.19    33499.89  0.4739425  13290.71
##   0.20    33543.27  0.4742289  13323.65
##   0.21    33588.09  0.4745121  13357.25
##   0.22    33634.36  0.4747914  13392.29
##   0.23    33682.10  0.4750665  13427.92
##   0.24    33731.29  0.4753369  13465.17
##   0.25    33781.93  0.4756025  13503.11
##   0.26    33834.01  0.4758630  13541.51
##   0.27    33887.52  0.4761184  13580.53
##   0.28    33942.45  0.4763685  13620.46
##   0.29    33998.80  0.4766133  13661.67
##   0.30    34056.53  0.4768528  13703.59
##   0.31    34115.64  0.4770870  13746.36
##   0.32    34176.12  0.4773159  13789.53
##   0.33    34237.93  0.4775396  13833.16
##   0.34    34301.08  0.4777581  13877.32
##   0.35    34365.53  0.4779715  13922.05
##   0.36    34431.27  0.4781799  13967.34
##   0.37    34498.28  0.4783833  14013.35
##   0.38    34566.54  0.4785820  14060.30
##   0.39    34636.04  0.4787759  14107.87
##   0.40    34706.75  0.4789651  14156.61
##   0.41    34778.65  0.4791498  14206.32
##   0.42    34851.72  0.4793300  14257.28
##   0.43    34925.95  0.4795059  14308.97
##   0.44    35001.32  0.4796776  14361.22
##   0.45    35077.80  0.4798451  14414.63
##   0.46    35155.37  0.4800085  14469.34
##   0.47    35234.03  0.4801680  14524.56
##   0.48    35313.74  0.4803237  14580.34
##   0.49    35394.48  0.4804756  14636.52
##   0.50    35476.25  0.4806238  14693.43
## 
## RMSE was used to select the optimal model using  the smallest value.
## The final value used for the model was lambda = 0.01.
model_lasso <- train(votos ~ ., 
                    data = train_dadosFiltrados, 
                    method = "lasso", 
                    metric="RMSE",
                    trControl = fitControl,
                    tuneGrid = fractionGrid,
                    na.action = na.omit)
## Warning in nominalTrainWorkflow(x = x, y = y, wts = weights, info =
## trainInfo, : There were missing values in resampled performance measures.
model_lasso
## The lasso 
## 
## 4152 samples
##   20 predictor
## 
## No pre-processing
## Resampling: Cross-Validated (5 fold) 
## Summary of sample sizes: 3324, 3321, 3321, 3322, 3320 
## Resampling results across tuning parameters:
## 
##   fraction  RMSE      Rsquared   MAE     
##   0.00      44262.05        NaN  23678.65
##   0.01      39861.55  0.4326927  19835.51
##   0.02      38024.71  0.4321895  18250.12
##   0.03      36605.06  0.4324688  16931.50
##   0.04      35627.17  0.4322762  15944.01
##   0.05      34953.58  0.4329998  15154.01
##   0.06      34475.10  0.4337543  14454.12
##   0.07      34126.72  0.4380605  13816.86
##   0.08      33864.16  0.4440089  13315.78
##   0.09      33740.44  0.4470121  12929.54
##   0.10      33636.70  0.4505693  12614.18
##   0.11      33463.22  0.4562352  12390.86
##   0.12      33348.98  0.4600737  12254.25
##   0.13      33291.56  0.4621587  12218.23
##   0.14      33256.38  0.4636589  12219.76
##   0.15      33233.49  0.4648081  12243.85
##   0.16      33214.00  0.4659311  12268.41
##   0.17      33200.93  0.4668531  12294.15
##   0.18      33193.92  0.4676046  12321.18
##   0.19      33189.67  0.4683144  12344.07
##   0.20      33189.48  0.4689201  12372.60
##   0.21      33192.50  0.4694309  12409.30
##   0.22      33197.04  0.4698920  12448.65
##   0.23      33201.88  0.4703105  12489.46
##   0.24      33214.52  0.4705152  12528.62
##   0.25      33230.74  0.4706418  12569.09
##   0.26      33251.14  0.4706457  12612.30
##   0.27      33274.39  0.4705690  12651.15
##   0.28      33292.30  0.4705451  12689.19
##   0.29      33302.72  0.4706039  12714.09
##   0.30      33317.41  0.4705991  12737.40
##   0.31      33330.85  0.4705541  12753.97
##   0.32      33328.10  0.4706414  12761.20
##   0.33      33326.96  0.4706898  12767.54
##   0.34      33327.41  0.4706998  12775.17
##   0.35      33329.98  0.4706583  12781.58
##   0.36      33333.74  0.4705908  12786.90
##   0.37      33338.18  0.4705089  12792.68
##   0.38      33343.61  0.4704074  12802.09
##   0.39      33349.31  0.4703070  12812.28
##   0.40      33355.73  0.4701955  12821.06
##   0.41      33362.99  0.4700557  12829.15
##   0.42      33370.94  0.4699008  12837.49
##   0.43      33379.03  0.4697457  12845.76
##   0.44      33385.40  0.4696410  12853.41
##   0.45      33392.66  0.4695174  12861.38
##   0.46      33401.30  0.4693611  12869.57
##   0.47      33409.95  0.4692059  12877.34
##   0.48      33418.73  0.4690422  12886.15
##   0.49      33427.28  0.4688846  12893.83
##   0.50      33435.57  0.4687417  12901.06
## 
## RMSE was used to select the optimal model using  the smallest value.
## The final value used for the model was fraction = 0.2.
model_knn <- train(votos ~ ., 
                    data = train_dadosFiltrados, 
                    method = "knn", 
                    trControl = fitControl,
                    metric="RMSE",
                    tuneGrid = neighborsGrid,
                    na.action = na.omit)

model_knn
## k-Nearest Neighbors 
## 
## 4152 samples
##   20 predictor
## 
## No pre-processing
## Resampling: Cross-Validated (5 fold) 
## Summary of sample sizes: 3320, 3323, 3322, 3322, 3321 
## Resampling results across tuning parameters:
## 
##   k   RMSE      Rsquared   MAE      
##    1  45000.33  0.2984028  12541.129
##    2  36805.63  0.3947152  11195.860
##    3  35455.14  0.4210384  10638.849
##    4  33638.05  0.4602105  10291.003
##    5  32686.06  0.4842035  10032.135
##    6  32070.14  0.4996445   9834.942
##    7  31571.26  0.5134598   9717.635
##    8  31274.55  0.5221542   9572.166
##    9  31165.35  0.5261203   9548.937
##   10  31130.62  0.5284789   9540.523
##   11  31191.30  0.5281649   9525.329
##   12  31297.11  0.5265621   9554.005
##   13  31397.50  0.5252761   9571.069
##   14  31479.14  0.5242604   9581.016
##   15  31587.43  0.5222294   9629.574
##   16  31679.39  0.5209630   9664.323
##   17  31816.64  0.5178349   9704.614
##   18  31914.66  0.5162465   9740.209
##   19  32088.89  0.5126799   9798.518
##   20  32278.75  0.5078774   9898.734
##   21  32386.73  0.5065080   9916.330
##   22  32498.59  0.5048991   9947.007
##   23  32678.11  0.5012297   9987.142
##   24  32771.69  0.5005528  10041.270
##   25  32902.17  0.4989694  10091.203
##   26  33036.69  0.4964468  10150.523
##   27  33146.08  0.4948580  10208.842
##   28  33292.98  0.4923134  10270.280
##   29  33386.13  0.4914368  10324.532
##   30  33457.61  0.4899846  10415.411
##   31  33635.42  0.4855535  10503.050
##   32  33769.44  0.4815729  10587.224
##   33  33942.95  0.4757426  10707.367
##   34  34087.85  0.4707664  10805.174
##   35  34150.55  0.4682550  10891.524
##   36  34290.04  0.4637500  10991.153
##   37  34442.71  0.4585107  11112.860
##   38  34571.89  0.4549212  11219.385
##   39  34614.49  0.4541245  11310.113
##   40  34750.63  0.4492696  11413.144
##   41  34883.21  0.4455749  11530.939
##   42  34985.33  0.4429846  11652.822
##   43  35052.25  0.4406334  11764.515
##   44  35132.92  0.4380784  11892.296
##   45  35235.66  0.4346891  12016.561
##   46  35339.53  0.4308994  12136.621
##   47  35415.29  0.4268220  12263.319
##   48  35491.35  0.4259987  12272.700
##   49  35625.55  0.4217408  12348.454
##   50  35679.49  0.4205959  12373.602
## 
## RMSE was used to select the optimal model using  the smallest value.
## The final value used for the model was k = 10.
  1. Compare os três modelos em termos do erro RMSE de validação cruzada. Temos os seguintes resultados:

Modelo de regressão ridge: Menor RMSE é 32260.19 quando lambda = 0.02

Modelo de regressão lasso: Menor RMSE é 32072.43 quando fração = 0.16

Modelo KNN: Menor RMSE é 30596.60 quando k = 10

plot(model_ridge)

plot(model_lasso)

plot(model_knn)

Método Ridge: O gráfico nos mostra uma curva crescente que tem início quando o parâmetro “lambda” é 0. Isso pode ser explicado pelo filtro que fizemos na fase Pré-Lab.

Podemos observar que a fração usada no modelo é 0.16, que é onde encontramos o menor RMSE:

Método KNN: Temos para este modelo que com K próximo de 0 tem um RMSE muito alto e um ponto de inflexão com k = 10.

  1. Quais as variáveis mais importantes segundo o modelo de regressão Ridge e Lasso? Variáveis foram descartadas pelo Lasso? Quais?
plot(varImp(model_ridge))

plot(varImp(model_lasso))

As mesmas variáveis tem a mesma importância. Por não ter importância as variáveis: UF, Recursos_proprios e recursos_de_outros_candidatos, foram descartadas do modelo.

  1. Re-treine o melhor modelo (usando os melhores valores de parâmetros encontrados em todos os dados, sem usar validação cruzada).

O melhor modelo foi o KNN com k=10.

bestK <- expand.grid(k = seq(10, 10, length=1))

best_model <- train(votos ~ ., 
                    data = train_dadosFiltrados, 
                    method = "knn",
                    metric="RMSE",
                    tuneGrid = bestK,
                    na.action = na.omit)
  1. Use esse último modelo treinado para prever os dados de teste disponíveis no challenge que criamos na plataforma Kaggle.
submission_predict <- predict(best_model, test_dadosFiltrados)

for(i in 1:length(submission_predict)){
  print(submission_predict[i])
  submission$votos[i] = abs(submission_predict[i])
}
## [1] 1333.2
## [1] 1346.2
## [1] 969.2
## [1] 473.8
## [1] 737.7
## [1] 32618
## [1] 981.7273
## [1] 62157.7
## [1] 44919.8
## [1] 72077.3
## [1] 6420.7
## [1] 941.6
## [1] 75979.8
## [1] 4307.5
## [1] 12944.3
## [1] 556.7
## [1] 64654.7
## [1] 707.8
## [1] 765.6
## [1] 828
## [1] 1082.7
## [1] 5873
## [1] 826.7
## [1] 5741
## [1] 1082.7
## [1] 851.8
## [1] 491.1
## [1] 657.2
## [1] 657.2
## [1] 13634.2
## [1] 13990.4
## [1] 12857.7
## [1] 2091.7
## [1] 680.9
## [1] 657.2
## [1] 2413.7
## [1] 657.2
## [1] 12847.5
## [1] 28971.9
## [1] 57321
## [1] 11286.2
## [1] 1188.7
## [1] 10711
## [1] 1354
## [1] 38872.4
## [1] 4281
## [1] 400.9
## [1] 12486.2
## [1] 43553.2
## [1] 57321
## [1] 3694
## [1] 400.9
## [1] 1353
## [1] 2383.1
## [1] 22591.3
## [1] 1270.5
## [1] 42376.9
## [1] 3937.3
## [1] 1188.7
## [1] 400.9
## [1] 57321
## [1] 7345.1
## [1] 8650
## [1] 2596.7
## [1] 67773.7
## [1] 1344.3
## [1] 2119.8
## [1] 64730.7
## [1] 6486.9
## [1] 686.2
## [1] 711.4
## [1] 489.7
## [1] 1815.3
## [1] 931.2
## [1] 2452.8
## [1] 2594.9
## [1] 2689.5
## [1] 489.7
## [1] 1358.5
## [1] 11492
## [1] 50186.4
## [1] 11784.2
## [1] 924.6
## [1] 565.4
## [1] 1831
## [1] 433.6
## [1] 7548.9
## [1] 1662.7
## [1] 8278.5
## [1] 300.9
## [1] 300.9
## [1] 232.3
## [1] 50264.6
## [1] 611.2
## [1] 4037.4
## [1] 1135.1
## [1] 902.3
## [1] 1199.1
## [1] 130338.9
## [1] 8619.1
## [1] 1887
## [1] 2013.9
## [1] 300.9
## [1] 300.9
## [1] 13133.8
## [1] 66247.8
## [1] 960.5
## [1] 78112.1
## [1] 703.5
## [1] 412.5
## [1] 1317.7
## [1] 88033.2
## [1] 1474.2
## [1] 126853.8
## [1] 148.6
## [1] 1955.3
## [1] 4114.7
## [1] 960.5
## [1] 114667.5
## [1] 61212.1
## [1] 960.5
## [1] 148.6
## [1] 960.5
## [1] 151532.4
## [1] 26366.9
## [1] 2189.5
## [1] 4966.5
## [1] 153941.6
## [1] 9117.9
## [1] 72372.4
## [1] 65762.5
## [1] 132373.8
## [1] 64618.2
## [1] 1256.2
## [1] 65762.5
## [1] 30861.9
## [1] 1657.3
## [1] 5957.2
## [1] 54691.6
## [1] 1201.4
## [1] 2241.9
## [1] 1656.7
## [1] 1225.5
## [1] 1002.3
## [1] 2377.7
## [1] 1159.1
## [1] 7641.3
## [1] 1205.1
## [1] 426.6
## [1] 8727.8
## [1] 78358.4
## [1] 8500
## [1] 652.7
## [1] 2423.6
## [1] 1605.4
## [1] 108928.4
## [1] 3464.9
## [1] 2265.1
## [1] 1546.3
## [1] 10769.6
## [1] 446.6
## [1] 1479.5
## [1] 1324.5
## [1] 834.8
## [1] 2328.4
## [1] 5795.5
## [1] 4301.3
## [1] 299.7
## [1] 711.8
## [1] 1128.5
## [1] 81930.8
## [1] 293.1
## [1] 7009
## [1] 299.7
## [1] 1053.4
## [1] 116110
## [1] 360.3
## [1] 910.5
## [1] 2621.2
## [1] 326.8
## [1] 874.1
## [1] 793.6
## [1] 1053.6
## [1] 672.9
## [1] 655.1
## [1] 572.8
## [1] 20296.5
## [1] 36571.6
## [1] 985.7
## [1] 9994.7
## [1] 2723.9
## [1] 5544.1
## [1] 1112.3
## [1] 1071.7
## [1] 84373.1
## [1] 5167.5
## [1] 84213.2
## [1] 1565.1
## [1] 61131
## [1] 1419.4
## [1] 43884.2
## [1] 5178
## [1] 3347.4
## [1] 10913.2
## [1] 49688.2
## [1] 1107.2
## [1] 996.1
## [1] 2603.2
## [1] 7020.2
## [1] 91681.5
## [1] 63777
## [1] 996.1
## [1] 5841.6
## [1] 7067.2
## [1] 3043.1
## [1] 323.7
## [1] 827.9
## [1] 5011.6
## [1] 323.7
## [1] 323.7
## [1] 7215.8
## [1] 7377.8
## [1] 39068.2
## [1] 7735.8
## [1] 827.9
## [1] 2436.9
## [1] 323.7
## [1] 4853.3
## [1] 4714.6
## [1] 335.2
## [1] 323.7
## [1] 962.9
## [1] 513.8
## [1] 9594.5
## [1] 32935.3
## [1] 29821.8
## [1] 738.8
## [1] 15858.4
## [1] 639.4
## [1] 640.2
## [1] 768.2
## [1] 52190
## [1] 44679.1
## [1] 1518.6
## [1] 765.3636
## [1] 10254.3
## [1] 546.1
## [1] 632.7
## [1] 1310.3
## [1] 7326.5
## [1] 7454.1
## [1] 13499.1
## [1] 593.2
## [1] 11249.2
## [1] 569.5
## [1] 12569.3
## [1] 783.6
## [1] 10609.5
## [1] 8249.9
## [1] 697.8
## [1] 623.6
## [1] 122946.7
## [1] 60089.8
## [1] 52115.9
## [1] 715
## [1] 59490.3
## [1] 902.8
## [1] 759.6
## [1] 25515.6
## [1] 6744.4
## [1] 542.5
## [1] 1799.3
## [1] 789
## [1] 709.7
## [1] 783
## [1] 679.4
## [1] 757.2
## [1] 424.6
## [1] 889
## [1] 7454.1
## [1] 11146.6
## [1] 8240.1
## [1] 531.1
## [1] 1055
## [1] 66614.3
## [1] 74206.5
## [1] 95608.6
## [1] 122350.4
## [1] 77109.4
## [1] 2363.1
## [1] 12216
## [1] 12293.1
## [1] 1198.9
## [1] 1198.9
## [1] 1083.7
## [1] 1014.8
## [1] 1442.8
## [1] 1599
## [1] 4415.1
## [1] 10200.7
## [1] 685
## [1] 75905.1
## [1] 106760.4
## [1] 135644.6
## [1] 83708.1
## [1] 941.7
## [1] 601.3636
## [1] 1301.7
## [1] 91580
## [1] 1295.1
## [1] 35189.6
## [1] 544.5
## [1] 1185.6
## [1] 1135.2
## [1] 1295.1
## [1] 15779.4
## [1] 91580
## [1] 5849.7
## [1] 91580
## [1] 497.2
## [1] 544.5
## [1] 532.6
## [1] 501.9
## [1] 2575.4
## [1] 903.4
## [1] 2990.9
## [1] 6093.9
## [1] 1890.1
## [1] 1225.5
## [1] 518.4
## [1] 16437.3
## [1] 1069.2
## [1] 851.9
## [1] 462.8
## [1] 666.6
## [1] 755.5
## [1] 770
## [1] 1404.1
## [1] 521.3
## [1] 793.1
## [1] 375.5
## [1] 1448.8
## [1] 3100.9
## [1] 912
## [1] 2063.5
## [1] 2184.8
## [1] 2450
## [1] 8966.8
## [1] 293.2
## [1] 311.2
## [1] 3671.1
## [1] 3127
## [1] 2450
## [1] 1353
## [1] 888.3
## [1] 2104.5
## [1] 880.4
## [1] 880.4
## [1] 880.4
## [1] 241.9
## [1] 5110.9
## [1] 8350.4
## [1] 907.4
## [1] 951.5
## [1] 654.6
## [1] 1541
## [1] 22355.4
## [1] 701.8
## [1] 1111.7
## [1] 691.2
## [1] 436.8
## [1] 385.9
## [1] 691.2
## [1] 691.2
## [1] 365.4
## [1] 37760.3
## [1] 2384.5
## [1] 844
## [1] 2653.8
## [1] 1034
## [1] 2274.2
## [1] 814.2
## [1] 630.5
## [1] 5923.7
## [1] 1500.5
## [1] 564.7
## [1] 2477.8
## [1] 1353.4
## [1] 638.3
## [1] 3849.9
## [1] 1250
## [1] 521.1
## [1] 239.6
## [1] 2603.2
## [1] 57936.3
## [1] 26561.3
## [1] 2365.5
## [1] 81544.1
## [1] 49325.6
## [1] 68184.8
## [1] 44840.8
## [1] 4422
## [1] 564.6
## [1] 52098.6
## [1] 1375.6
## [1] 52416.2
## [1] 74470.3
## [1] 821.5
## [1] 5549.3
## [1] 58889.4
## [1] 76754
## [1] 324.6
## [1] 1084.3
## [1] 1509
## [1] 526.2
## [1] 1343.4
## [1] 6860
## [1] 776.1818
## [1] 565.9
## [1] 1237.7
## [1] 1687
## [1] 880.6
## [1] 971.7
## [1] 5394.2
## [1] 1260
## [1] 2791
## [1] 396.6
## [1] 16877
## [1] 5329.5
## [1] 930.2
## [1] 5224.1
## [1] 34269.6
## [1] 721.5
## [1] 1701.4
## [1] 2253.9
## [1] 728.3
## [1] 1344.9
## [1] 1896.7
## [1] 8728.5
## [1] 2689.1
## [1] 5781.7
## [1] 700.1
## [1] 1894.8
## [1] 1088.7
## [1] 13928.4
## [1] 1391.3
## [1] 463.3
## [1] 377.3
## [1] 247.9
## [1] 1905
## [1] 1893
## [1] 440.8
## [1] 10298.8
## [1] 17897.5
## [1] 618.1
## [1] 1440.9
## [1] 395
## [1] 30521.9
## [1] 1730.7
## [1] 2060.1
## [1] 1111.5
## [1] 1109.4
## [1] 2304.5
## [1] 1476.8
## [1] 1032.2
## [1] 1203.4
## [1] 84651
## [1] 980.1
## [1] 4734
## [1] 3267.2
## [1] 674.4
## [1] 2595.3
## [1] 2595.3
## [1] 7132
## [1] 21241.7
## [1] 2276.5
## [1] 68988.3
## [1] 6772.1
## [1] 2411.5
## [1] 68988.3
## [1] 70849.4
## [1] 1050.4
## [1] 540.3
## [1] 6569
## [1] 6569
## [1] 68988.3
## [1] 453.7
## [1] 687
## [1] 1599.9
## [1] 787.3
## [1] 787.3
## [1] 770.5
## [1] 787.3
## [1] 1599.9
## [1] 1452.6
## [1] 552.2
## [1] 1187.1
## [1] 2240.8
## [1] 4993.4
## [1] 876.2
## [1] 5548.1
## [1] 6765
## [1] 117305.3
## [1] 436.5
## [1] 670.1
## [1] 2902.9
## [1] 6441.8
## [1] 1036
## [1] 4915.1
## [1] 4755.4
## [1] 2035.8
## [1] 82042
## [1] 70930.5
## [1] 1842.9
## [1] 124043.8
## [1] 71707.2
## [1] 427.7
## [1] 466.5
## [1] 415.8
## [1] 2993.4
## [1] 7351.6
## [1] 4128
## [1] 21299.5
## [1] 1232.1
## [1] 5580.7
## [1] 81692.5
## [1] 1459.9
## [1] 2030.1
## [1] 69693.5
## [1] 2138.8
## [1] 20075.8
## [1] 74090.2
## [1] 1017.9
## [1] 1082.2
## [1] 4260.9
## [1] 6537
## [1] 965.3
## [1] 1342.8
## [1] 74203.7
## [1] 838
## [1] 6760.4
## [1] 81447.4
## [1] 4042.8
## [1] 1133.9
## [1] 872.9
## [1] 791.3
## [1] 5301.6
## [1] 3446
## [1] 18724.4
## [1] 24450.8
## [1] 6014
## [1] 24450.8
## [1] 19756.2
## [1] 10932.8
## [1] 18890.8
## [1] 1211.2
## [1] 1320
## [1] 159.7
## [1] 159.7
## [1] 241.7
## [1] 203.5
## [1] 238.6
## [1] 238.6
## [1] 5589.8
## [1] 11646.2
## [1] 1288.9
## [1] 1265.8
## [1] 238.6
## [1] 484.8
## [1] 991.4
## [1] 3056.4
## [1] 7780.3
## [1] 5900.1
## [1] 7780.3
## [1] 2518.5
## [1] 66352.4
## [1] 112923.7
## [1] 109586
## [1] 96728
## [1] 30312
## [1] 942.8
## [1] 126271
## [1] 2318.8
## [1] 3473.2
## [1] 2425.4
## [1] 10341.7
## [1] 41346.3
## [1] 7115.3
## [1] 3229.6
## [1] 7663
## [1] 760.1
## [1] 760.1
## [1] 942.8
## [1] 3343.8
## [1] 2629.1
## [1] 3072.2
## [1] 942.8
## [1] 742.1
## [1] 789.2
## [1] 2465.8
## [1] 998.2
## [1] 902.6
## [1] 949.7
## [1] 2001.4
## [1] 522
## [1] 592.8
## [1] 878.3
## [1] 616.2
## [1] 6959
## [1] 868.7
## [1] 2952.4
## [1] 3705.9
## [1] 3326.8
## [1] 821.8
## [1] 15652.1
## [1] 5723
## [1] 337.4
## [1] 4748.1
## [1] 94892
## [1] 80655.9
## [1] 61013
## [1] 6992.8
## [1] 82738
## [1] 1013.3
## [1] 68024.9
## [1] 6475
## [1] 4577.9
## [1] 125963.2
## [1] 39948.4
## [1] 108838.1
## [1] 6037.6
## [1] 655.4
## [1] 104769.8
## [1] 48725.1
## [1] 23785.1
## [1] 7982.6
## [1] 1843.9
## [1] 17740.8
## [1] 36054.6
## [1] 23887.8
## [1] 88309.6
## [1] 53780.8
## [1] 24545.7
## [1] 82522.5
## [1] 27762.7
## [1] 1455.1
## [1] 62917.4
## [1] 9029.3
## [1] 1076.3
## [1] 1031.8
## [1] 3887
## [1] 10261
## [1] 1403.1
## [1] 57473.5
## [1] 6256.8
## [1] 1380.5
## [1] 27053.4
## [1] 4118.3
## [1] 2360.7
## [1] 51329.2
## [1] 894.4
## [1] 1297.7
## [1] 1210.8
## [1] 346.5
## [1] 3049.7
## [1] 718
## [1] 2001.4
## [1] 2732.8
## [1] 3202.9
## [1] 272.5
## [1] 6624
## [1] 55820
## [1] 13389.2
## [1] 1978
## [1] 7151.5
## [1] 2709.9
## [1] 750.7
## [1] 269300.6
## [1] 2360.7
## [1] 2328.9
## [1] 23480.5
## [1] 875.3
## [1] 7277.9
## [1] 3397.1
## [1] 9355.4
## [1] 5018.3
## [1] 655.4
## [1] 3297.4
## [1] 6347
## [1] 5453.8
## [1] 1210.4
## [1] 2396.3
## [1] 1208.5
## [1] 1362.2
## [1] 4138.2
## [1] 91267.9
## [1] 873.3
## [1] 959.2
## [1] 446.4
## [1] 75513.5
## [1] 48881.7
## [1] 1570.3
## [1] 969.4
## [1] 15872.6
## [1] 2772.1
## [1] 22303.3
## [1] 2279.5
## [1] 707.1
## [1] 1367.9
## [1] 1369
## [1] 40527
## [1] 1296.4
## [1] 349.5
## [1] 552.4
## [1] 1805.2
## [1] 949.3
## [1] 371.9
## [1] 2262.6
## [1] 726.5
## [1] 1500.6
## [1] 1434.7
## [1] 2581.1
## [1] 2059.6
## [1] 2664.3
## [1] 2195.6
## [1] 1479.2
## [1] 2129.4
## [1] 961.9
## [1] 875.4
## [1] 3211.9
## [1] 292
## [1] 481.2
## [1] 1823.6
## [1] 556.2
## [1] 732.3
## [1] 1238
## [1] 885.7
## [1] 510.9
## [1] 513.2
## [1] 2053.7
## [1] 579.1
## [1] 26264.8
## [1] 2865.4
## [1] 655.4
## [1] 19617.9
## [1] 3023.8
## [1] 5416.2
## [1] 246.2
## [1] 1089.3
## [1] 30712.2
## [1] 20461.6
## [1] 719.7
## [1] 696
## [1] 861.7
## [1] 18182.6
## [1] 1048.8
## [1] 177378.9
## [1] 3449.7
## [1] 16566.1
## [1] 3106.4
## [1] 179674.6
## [1] 121192.2
## [1] 162145.8
## [1] 1141.2
## [1] 2935.3
## [1] 181.3
## [1] 3776.7
## [1] 181.3
## [1] 610.4
## [1] 4717.1
## [1] 181.3
## [1] 1349.9
## [1] 10099.8
## [1] 1424.9
## [1] 58364.5
## [1] 1112.3
## [1] 614.5
## [1] 243.5
## [1] 181.3
## [1] 8466
## [1] 29566.3
## [1] 1285.4
## [1] 3602.9
## [1] 1197.7
## [1] 727.2
## [1] 2821
## [1] 4067.2
## [1] 1382.2
## [1] 602.7
## [1] 760.4
## [1] 6521.3
## [1] 1639.4
## [1] 947.2
## [1] 751.3
## [1] 2069.1
## [1] 622.6
## [1] 779.1
## [1] 5216.9
## [1] 272.4
## [1] 370.1
## [1] 294
## [1] 3449.5
## [1] 748.6
## [1] 652.7
## [1] 1592.1
## [1] 1966.7
## [1] 1632.5
## [1] 1491.5
## [1] 682.8
## [1] 815.2
## [1] 550.8
## [1] 47403.5
## [1] 595.3
## [1] 7151.5
## [1] 717.4
## [1] 1558.7
## [1] 2424
## [1] 492.6
## [1] 27949.6
## [1] 7139.5
## [1] 683.2
## [1] 813
## [1] 3035.2
## [1] 654.9
## [1] 669.1
## [1] 10998
## [1] 751.4
## [1] 1292.6
## [1] 630.1
## [1] 1008.5
## [1] 362.6
## [1] 426.7
## [1] 1248.5
## [1] 1255.4
## [1] 1251.9
## [1] 1138.3
## [1] 622.6
## [1] 999
## [1] 1286.9
## [1] 17551.3
## [1] 17551.3
## [1] 41713.9
## [1] 17551.3
## [1] 339.9
## [1] 999
## [1] 1394.4
## [1] 333.4
## [1] 333.4
## [1] 7966
## [1] 11636.4
## [1] 1810.6
## [1] 9800.8
## [1] 2125.4
## [1] 635.7
## [1] 495.4
## [1] 774
## [1] 1845.8
## [1] 719
## [1] 2114.8
## [1] 719
## [1] 11598.2
## [1] 719
## [1] 2043.9
## [1] 719
## [1] 719
## [1] 1685.7
## [1] 2242.5
## [1] 10324.4
## [1] 1601.5
## [1] 75925.3
## [1] 18620.5
## [1] 759.7
## [1] 8218.2
## [1] 7741.4
## [1] 1032.2
## [1] 8220.9
## [1] 7313.4
## [1] 57580.8
## [1] 542.1
## [1] 542.1
## [1] 542.1
## [1] 542.1
## [1] 542.1
## [1] 542.1
## [1] 8352.6
## [1] 137.2
## [1] 361.4
## [1] 137.2
## [1] 1104.2
## [1] 1750.6
## [1] 137.2
## [1] 4157.7
## [1] 2815.7
## [1] 2388.5
## [1] 74231.3
## [1] 1104.2
## [1] 108191.9
## [1] 72246.8
## [1] 39448.5
## [1] 167.1
## [1] 108191.9
## [1] 10733.5
## [1] 5922.8
## [1] 5922.8
## [1] 964.6364
## [1] 675.5
## [1] 137.2
## [1] 8786.3
## [1] 885.3
## [1] 818.7
## [1] 8371.9
## [1] 8786.3
## [1] 42159.7
## [1] 4176.2
## [1] 1102.7
## [1] 1452.8
## [1] 187.6
## [1] 73531.1
## [1] 137.2
## [1] 73531.1
## [1] 89618.5
## [1] 16420
## [1] 1634.8
## [1] 18311.1
## [1] 119133.7
## [1] 569.3
## [1] 1158.3
## [1] 32829.6
## [1] 27629.6
## [1] 63760.1
## [1] 4731.2
## [1] 53343.1
## [1] 4310.1
## [1] 12349.3
## [1] 3096.9
## [1] 2420.7
## [1] 716
## [1] 67674.3
## [1] 2163.9
## [1] 1391.4
## [1] 449.7
## [1] 105891.5
## [1] 10435.2
## [1] 1647.7
## [1] 74930.7
## [1] 716
## [1] 1086
## [1] 5034.7
## [1] 6313.7
## [1] 879.7
## [1] 6313.7
## [1] 51580.5
## [1] 60005.2
## [1] 111458.8
## [1] 56654.4
## [1] 71221
## [1] 2172.7
## [1] 6040.7
## [1] 2845.7
## [1] 1424.9
## [1] 1031
## [1] 595.9
## [1] 111371.2
## [1] 6313.7
## [1] 423.3
## [1] 9987.7
## [1] 3938.8
## [1] 786.5
## [1] 3457.7
## [1] 4103
## [1] 4585.6
## [1] 49202.6
## [1] 1096.3
## [1] 53335
## [1] 52574.9
## [1] 811
## [1] 22642.6
## [1] 20065.9
## [1] 5832.7
## [1] 13671
## [1] 67611.4
## [1] 15300.2
## [1] 362.5
## [1] 633.6
## [1] 423.3
## [1] 891.7
## [1] 1347.1
## [1] 423.3
## [1] 566.3
## [1] 29111.2
## [1] 1043.3
## [1] 51719.9
## [1] 3489
## [1] 44361
## [1] 14932.3
## [1] 5294.1
## [1] 568.3
## [1] 4491.2
## [1] 69167.5
## [1] 1056.9
## [1] 2703.9
## [1] 1545.091
## [1] 9162.6
## [1] 1071.6
## [1] 7159
## [1] 12227.5
## [1] 3408.2
## [1] 9511
## [1] 1043.3
## [1] 69167.5
## [1] 69167.5
## [1] 12227.5
## [1] 580
## [1] 70426.9
## [1] 44361
## [1] 34795.5
## [1] 928.6
## [1] 894.9
## [1] 1086.3
## [1] 762.7
## [1] 666.8
## [1] 47890.4
## [1] 2708.8
## [1] 2947.1
## [1] 2912.9
## [1] 1909.3
## [1] 1937.5
## [1] 1860.5
## [1] 94453.8
## [1] 3184.7
## [1] 3060.6
## [1] 78470.5
## [1] 78470.5
## [1] 80072.9
## [1] 69349.7
## [1] 817.4545
## [1] 817.4545
## [1] 756.2
## [1] 74564.8
write.csv(submission, file = "MarcosArruda.csv", row.names = FALSE)