Prediction of good method of working out!
Fabricio Dujardin
10/17/2017
Background of the data
Six young health participants were asked to perform one set of 10 repetitions of the Unilateral Dumbbell Biceps Curl in five different fashions: exactly according to the specification (Class A), throwing the elbows to the front (Class B), lifting the dumbbell only halfway (Class C), lowering the dumbbell only halfway (Class D) and throwing the hips to the front (Class E). The data for this project come from this source: http://groupware.les.inf.puc-rio.br/har. Class A corresponds to the specified execution of the exercise, while the other 4 classes correspond to common mistakes. Participants were supervised by an experienced weight lifter to make sure the execution complied to the manner they were supposed to simulate. The exercises were performed by six male participants aged between 20-28 years, with little weight lifting experience. We made sure that all participants could easily simulate the mistakes in a safe and controlled manner by using a relatively light dumbbell (1.25kg).
Read more: http://web.archive.org/web/20161224072740/http:/groupware.les.inf.puc-rio.br/har#ixzz4p9pxiYPa
Read more: http://web.archive.org/web/20161224072740/http:/groupware.les.inf.puc-rio.br/har#ixzz4p9pXE5b7
Loading the data
The required packages are mainly below but others are shown in the code afterwards when required. There data has been divided into 70% training and 30% testing for cross validation. The validation data is for prediction at the end of the paper.
library(caret)
library(ggplot2)
library(data.table)
library(cowplot)
library(knitr)
library(rpart)
library(rpart.plot)
library(pander)
library(kableExtra)
options(knitr.tableformat="html")
Testing_forprediction <- data.table(read.csv("pml-testing.csv", na.strings=c("NA","#DIV/0!","")))
Data <- data.table(read.csv("pml-training.csv",na.strings=c("NA","#DIV/0!","")))
set.seed(123)
#Partitioning the training set into 2
inTrain <- createDataPartition(Data$classe,p=0.70,list=FALSE)
Training <- Data[inTrain,]
Testing <- Data[-inTrain,]Exploring and cleaning the data
We will focus on the training data. The following steps are used to clean and adjust the data.
- Drop out variables that are near zero variability
- Drop out variables that are nearly collinear
- Drop out variables that should not be predictors out of logic
- Drop out variables that have too many NAs & have complese cases of the predictors
The aim is to have predictors that matter for the final prediction. Afterwards we need to check if the validation data has the proper classes and names as the training data.
Near Zero Variability
Many variables have been cut off as their variability does not meet the standards required.
cols <- nearZeroVar(Training)
nearZeroVar(Training, saveMetrics=T)## freqRatio percentUnique zeroVar nzv
## X 1.000000 100.00000000 FALSE FALSE
## user_name 1.110114 0.04367766 FALSE FALSE
## raw_timestamp_part_1 1.000000 6.09303341 FALSE FALSE
## raw_timestamp_part_2 1.000000 89.48096382 FALSE FALSE
## cvtd_timestamp 1.014409 0.14559220 FALSE FALSE
## new_window 46.532872 0.01455922 FALSE TRUE
## num_window 1.000000 6.24590522 FALSE FALSE
## roll_belt 1.034375 8.08764650 FALSE FALSE
## pitch_belt 1.204918 12.17150761 FALSE FALSE
## yaw_belt 1.077348 13.15425493 FALSE FALSE
## total_accel_belt 1.077358 0.21110868 FALSE FALSE
## kurtosis_roll_belt 2.000000 2.03829075 FALSE FALSE
## kurtosis_picth_belt 1.000000 1.70342870 FALSE FALSE
## kurtosis_yaw_belt 0.000000 0.00000000 TRUE TRUE
## skewness_roll_belt 1.000000 2.03829075 FALSE FALSE
## skewness_roll_belt.1 1.000000 1.79806362 FALSE FALSE
## skewness_yaw_belt 0.000000 0.00000000 TRUE TRUE
## max_roll_belt 1.142857 1.15745796 FALSE FALSE
## max_picth_belt 1.625000 0.15287181 FALSE FALSE
## max_yaw_belt 1.181818 0.39309893 FALSE FALSE
## min_roll_belt 1.125000 1.12105991 FALSE FALSE
## min_pitch_belt 2.157895 0.10919415 FALSE FALSE
## min_yaw_belt 1.181818 0.39309893 FALSE FALSE
## amplitude_roll_belt 1.304348 0.85899396 FALSE FALSE
## amplitude_pitch_belt 3.276596 0.09463493 FALSE FALSE
## amplitude_yaw_belt 0.000000 0.00727961 TRUE TRUE
## var_total_accel_belt 1.482143 0.40765815 FALSE FALSE
## avg_roll_belt 1.090909 1.13561913 FALSE FALSE
## stddev_roll_belt 1.000000 0.45861542 FALSE FALSE
## var_roll_belt 1.648148 0.56780957 FALSE FALSE
## avg_pitch_belt 1.000000 1.26665211 FALSE FALSE
## stddev_pitch_belt 1.086957 0.28390478 FALSE FALSE
## var_pitch_belt 1.159420 0.40765815 FALSE FALSE
## avg_yaw_belt 1.125000 1.37584625 FALSE FALSE
## stddev_yaw_belt 1.875000 0.37126010 FALSE FALSE
## var_yaw_belt 1.354839 0.87355318 FALSE FALSE
## gyros_belt_x 1.072034 0.92451045 FALSE FALSE
## gyros_belt_y 1.153819 0.46589503 FALSE FALSE
## gyros_belt_z 1.064205 1.20113562 FALSE FALSE
## accel_belt_x 1.068519 1.17201718 FALSE FALSE
## accel_belt_y 1.122109 0.99730654 FALSE FALSE
## accel_belt_z 1.055921 2.11836646 FALSE FALSE
## magnet_belt_x 1.108871 2.21300138 FALSE FALSE
## magnet_belt_y 1.103604 2.08196841 FALSE FALSE
## magnet_belt_z 1.002924 3.15207105 FALSE FALSE
## roll_arm 47.560000 17.36186940 FALSE FALSE
## pitch_arm 76.741935 20.28827255 FALSE FALSE
## yaw_arm 30.487179 19.10897576 FALSE FALSE
## total_accel_arm 1.079872 0.48045425 FALSE FALSE
## var_accel_arm 7.000000 2.06012958 FALSE FALSE
## avg_roll_arm 49.000000 1.75438596 FALSE TRUE
## stddev_roll_arm 49.000000 1.75438596 FALSE TRUE
## var_roll_arm 49.000000 1.75438596 FALSE TRUE
## avg_pitch_arm 49.000000 1.75438596 FALSE TRUE
## stddev_pitch_arm 49.000000 1.75438596 FALSE TRUE
## var_pitch_arm 49.000000 1.75438596 FALSE TRUE
## avg_yaw_arm 49.000000 1.75438596 FALSE TRUE
## stddev_yaw_arm 51.000000 1.73982675 FALSE TRUE
## var_yaw_arm 51.000000 1.73982675 FALSE TRUE
## gyros_arm_x 1.010753 4.61527262 FALSE FALSE
## gyros_arm_y 1.490411 2.66433719 FALSE FALSE
## gyros_arm_z 1.056848 1.70342870 FALSE FALSE
## accel_arm_x 1.133929 5.57618112 FALSE FALSE
## accel_arm_y 1.165605 3.79995632 FALSE FALSE
## accel_arm_z 1.068182 5.60529956 FALSE FALSE
## magnet_arm_x 1.101695 9.65276261 FALSE FALSE
## magnet_arm_y 1.016129 6.22406639 FALSE FALSE
## magnet_arm_z 1.012987 9.11407149 FALSE FALSE
## kurtosis_roll_arm 1.000000 1.73982675 FALSE FALSE
## kurtosis_picth_arm 1.000000 1.73254714 FALSE FALSE
## kurtosis_yaw_arm 2.000000 2.04557036 FALSE FALSE
## skewness_roll_arm 1.000000 1.74710636 FALSE FALSE
## skewness_pitch_arm 1.000000 1.73254714 FALSE FALSE
## skewness_yaw_arm 1.000000 2.05284997 FALSE FALSE
## max_roll_arm 16.333333 1.60151416 FALSE FALSE
## max_picth_arm 8.166667 1.50687923 FALSE FALSE
## max_yaw_arm 1.058824 0.36398049 FALSE FALSE
## min_roll_arm 16.333333 1.55783650 FALSE FALSE
## min_pitch_arm 12.250000 1.55783650 FALSE FALSE
## min_yaw_arm 1.052632 0.26206595 FALSE FALSE
## amplitude_roll_arm 24.500000 1.66703065 FALSE TRUE
## amplitude_pitch_arm 17.000000 1.63791221 FALSE FALSE
## amplitude_yaw_arm 1.187500 0.36398049 FALSE FALSE
## roll_dumbbell 1.009804 86.31433355 FALSE FALSE
## pitch_dumbbell 2.000000 84.32700007 FALSE FALSE
## yaw_dumbbell 1.133333 85.69556672 FALSE FALSE
## kurtosis_roll_dumbbell 1.000000 2.05284997 FALSE FALSE
## kurtosis_picth_dumbbell 1.000000 2.06740919 FALSE FALSE
## kurtosis_yaw_dumbbell 0.000000 0.00000000 TRUE TRUE
## skewness_roll_dumbbell 2.000000 2.07468880 FALSE FALSE
## skewness_pitch_dumbbell 1.000000 2.06740919 FALSE FALSE
## skewness_yaw_dumbbell 0.000000 0.00000000 TRUE TRUE
## max_roll_dumbbell 1.333333 1.78350440 FALSE FALSE
## max_picth_dumbbell 1.000000 1.82718206 FALSE FALSE
## max_yaw_dumbbell 1.000000 0.45133581 FALSE FALSE
## min_roll_dumbbell 1.000000 1.79806362 FALSE FALSE
## min_pitch_dumbbell 1.000000 1.91453738 FALSE FALSE
## min_yaw_dumbbell 1.000000 0.45133581 FALSE FALSE
## amplitude_roll_dumbbell 7.000000 1.99461309 FALSE FALSE
## amplitude_pitch_dumbbell 7.000000 1.96549465 FALSE FALSE
## amplitude_yaw_dumbbell 0.000000 0.00727961 TRUE TRUE
## total_accel_dumbbell 1.074816 0.30574361 FALSE FALSE
## var_accel_dumbbell 5.000000 1.97277426 FALSE FALSE
## avg_roll_dumbbell 1.000000 2.05284997 FALSE FALSE
## stddev_roll_dumbbell 14.000000 2.00917231 FALSE FALSE
## var_roll_dumbbell 14.000000 2.00917231 FALSE FALSE
## avg_pitch_dumbbell 1.000000 2.05284997 FALSE FALSE
## stddev_pitch_dumbbell 14.000000 2.00917231 FALSE FALSE
## var_pitch_dumbbell 14.000000 2.00917231 FALSE FALSE
## avg_yaw_dumbbell 1.000000 2.05284997 FALSE FALSE
## stddev_yaw_dumbbell 14.000000 2.00917231 FALSE FALSE
## var_yaw_dumbbell 14.000000 2.00917231 FALSE FALSE
## gyros_dumbbell_x 1.006961 1.71070831 FALSE FALSE
## gyros_dumbbell_y 1.286064 1.92181699 FALSE FALSE
## gyros_dumbbell_z 1.058962 1.43408313 FALSE FALSE
## accel_dumbbell_x 1.031111 2.95552158 FALSE FALSE
## accel_dumbbell_y 1.052023 3.27582442 FALSE FALSE
## accel_dumbbell_z 1.159509 2.89728471 FALSE FALSE
## magnet_dumbbell_x 1.068376 7.78918250 FALSE FALSE
## magnet_dumbbell_y 1.257812 6.02023732 FALSE FALSE
## magnet_dumbbell_z 1.021429 4.79726287 FALSE FALSE
## roll_forearm 11.118367 13.62742957 FALSE FALSE
## pitch_forearm 61.886364 18.99978161 FALSE FALSE
## yaw_forearm 16.106509 12.90674820 FALSE FALSE
## kurtosis_roll_forearm 1.000000 1.62335299 FALSE FALSE
## kurtosis_picth_forearm 1.000000 1.61607338 FALSE FALSE
## kurtosis_yaw_forearm 0.000000 0.00000000 TRUE TRUE
## skewness_roll_forearm 1.000000 1.63063260 FALSE FALSE
## skewness_pitch_forearm 2.000000 1.60879377 FALSE FALSE
## skewness_yaw_forearm 0.000000 0.00000000 TRUE TRUE
## max_roll_forearm 21.666667 1.40496469 FALSE TRUE
## max_picth_forearm 2.708333 0.88083279 FALSE FALSE
## max_yaw_forearm 1.277778 0.26934556 FALSE FALSE
## min_roll_forearm 21.666667 1.46320157 FALSE TRUE
## min_pitch_forearm 4.062500 0.98274732 FALSE FALSE
## min_yaw_forearm 1.277778 0.26934556 FALSE FALSE
## amplitude_roll_forearm 21.666667 1.53599767 FALSE TRUE
## amplitude_pitch_forearm 4.785714 1.01914537 FALSE FALSE
## amplitude_yaw_forearm 0.000000 0.00727961 TRUE TRUE
## total_accel_forearm 1.088664 0.50229308 FALSE FALSE
## var_accel_forearm 3.000000 2.08924802 FALSE FALSE
## avg_roll_forearm 32.500000 1.63063260 FALSE TRUE
## stddev_roll_forearm 68.000000 1.61607338 FALSE TRUE
## var_roll_forearm 68.000000 1.61607338 FALSE TRUE
## avg_pitch_forearm 65.000000 1.63791221 FALSE TRUE
## stddev_pitch_forearm 65.000000 1.63791221 FALSE TRUE
## var_pitch_forearm 65.000000 1.63791221 FALSE TRUE
## avg_yaw_forearm 65.000000 1.63791221 FALSE TRUE
## stddev_yaw_forearm 67.000000 1.62335299 FALSE TRUE
## var_yaw_forearm 67.000000 1.62335299 FALSE TRUE
## gyros_forearm_x 1.074792 2.06012958 FALSE FALSE
## gyros_forearm_y 1.029412 5.24859868 FALSE FALSE
## gyros_forearm_z 1.137313 2.14020528 FALSE FALSE
## accel_forearm_x 1.047619 5.67809565 FALSE FALSE
## accel_forearm_y 1.000000 7.11217879 FALSE FALSE
## accel_forearm_z 1.185185 4.04746306 FALSE FALSE
## magnet_forearm_x 1.000000 10.61367111 FALSE FALSE
## magnet_forearm_y 1.163934 13.37264323 FALSE FALSE
## magnet_forearm_z 1.000000 11.84392517 FALSE FALSE
## classe 1.469526 0.03639805 FALSE FALSElength(cols)# number of variables dropped## [1] 32head(cols,10)## [1] 6 14 17 26 51 52 53 54 55 56dropped1 <- Training[,.SD,.SDcols=cols]
Training1 <- Training[,.SD,.SDcols=-cols]Collinear Variables
I have selected
#code for ggheatmap has been hidden because it takes too much space for this assignment. Kindly check github for it.
# Print the heatmap
ggheatmap
melted_cormat <- data.table(melted_cormat)
ggplot(data=melted_cormat[value!=1,],aes(value)) + geom_histogram(bins=100) 
above_0.9 <- melted_cormat[value!=1,][value>0.9|value< -0.9,]
above_0.9 <- above_0.9[order(-abs(value),Var1), ]
kable(head(above_0.9,5))| Var1 | Var2 | value |
|---|---|---|
| kurtosis_roll_dumbbell | max_yaw_dumbbell | 0.9999717 |
| kurtosis_roll_dumbbell | min_yaw_dumbbell | 0.9999717 |
| kurtosis_roll_forearm | max_yaw_forearm | 0.9999501 |
| kurtosis_roll_forearm | min_yaw_forearm | 0.9999501 |
| kurtosis_roll_belt | max_yaw_belt | 0.9999291 |
I decided to drop the following variables from the Training set due to the high correlations above 0.9 and below -0.9.
name_todrop2<- above_0.9[,unique(Var1)]
Training2 <- Training1[,.SD,.SDcols=-as.character(name_todrop2)]We have left the following amount of observations and variables.
dim(Training2)## [1] 13737 98Interprettable predictors
The response is the variable class with 5 levels: A, B, C, D, E as mentioned in the background section of this assignment. The
Training2[,levels(classe)]## [1] "A" "B" "C" "D" "E"descr <- Training[,.N,by=c("classe","user_name")]
kable(dcast(descr,user_name ~ classe), caption="amount of observations per user by class")| user_name | A | B | C | D | E |
|---|---|---|---|---|---|
| adelmo | 808 | 544 | 514 | 364 | 492 |
| carlitos | 576 | 485 | 349 | 339 | 429 |
| charles | 616 | 513 | 377 | 459 | 487 |
| eurico | 619 | 426 | 352 | 404 | 376 |
| jeremy | 836 | 331 | 456 | 369 | 386 |
| pedro | 451 | 359 | 348 | 317 | 355 |
| All predicto | rs see | m to h | ave an | effec | t on the classe however the time stamp is repeated in different format and therefore I discard both parts of the raw time stamp. |
Training2 <- Training2[,.SD,.SDcols= -c("raw_timestamp_part_1","raw_timestamp_part_2","user_name","cvtd_timestamp","X","num_window")]Missing values
The missing values per variable are as follows:
missing <-Training2[,lapply(.SD,is.na)][,lapply(.SD,sum)][,lapply(.SD,function(x){if(x>0) x})]
length(missing)## [1] 50missing[,1]/dim(Training2)[1]## kurtosis_picth_belt
## 1: 0.9803451Most of the variables have the same amount of NAs which is about 98% of the data. I further looked into it because I found it weird that the near zero variance did not discard this variables. Therefore I supposed these variables are relevant to a particular classe only. Apparently all classes have the same number of missing values per classe for hte 24 variables that have 98% of missing values. I therefore drop these variables.
missing## kurtosis_picth_belt skewness_roll_belt skewness_roll_belt.1
## 1: 13467 13455 13467
## max_yaw_belt min_yaw_belt var_total_accel_belt var_roll_belt
## 1: 13456 13456 13448 13448
## avg_pitch_belt var_pitch_belt avg_yaw_belt var_yaw_belt var_accel_arm
## 1: 13448 13448 13448 13448 13448
## kurtosis_roll_arm kurtosis_picth_arm kurtosis_yaw_arm skewness_roll_arm
## 1: 13498 13499 13455 13497
## skewness_pitch_arm skewness_yaw_arm max_roll_arm max_picth_arm
## 1: 13499 13455 13448 13448
## max_yaw_arm min_roll_arm min_pitch_arm min_yaw_arm amplitude_pitch_arm
## 1: 13448 13448 13448 13448 13448
## amplitude_yaw_arm kurtosis_picth_dumbbell skewness_roll_dumbbell
## 1: 13448 13450 13451
## skewness_pitch_dumbbell max_roll_dumbbell max_yaw_dumbbell
## 1: 13449 13448 13452
## min_roll_dumbbell min_pitch_dumbbell min_yaw_dumbbell
## 1: 13448 13448 13452
## var_accel_dumbbell avg_roll_dumbbell var_roll_dumbbell
## 1: 13448 13448 13448
## avg_pitch_dumbbell stddev_pitch_dumbbell avg_yaw_dumbbell
## 1: 13448 13448 13448
## stddev_yaw_dumbbell kurtosis_picth_forearm skewness_roll_forearm
## 1: 13448 13515 13513
## skewness_pitch_forearm max_picth_forearm max_yaw_forearm
## 1: 13515 13448 13514
## min_pitch_forearm min_yaw_forearm amplitude_pitch_forearm
## 1: 13448 13514 13448
## var_accel_forearm
## 1: 13448M<-Training2[,.SD,.SDcols=c("classe",names(missing))]
kable(M[,lapply(.SD,is.na),by=classe][,lapply(.SD,sum,na.rm=T),by=classe][,1:2])| classe | kurtosis_picth_belt |
|---|---|
| A | 3838 |
| B | 2604 |
| C | 2348 |
| D | 2209 |
| E | 2468 |
Selected variables to use as predictors.
We are left with fewer variables in the training data.
Training3 <- Training2[,.SD,.SDcols= -names(missing)]
dim(Training3)## [1] 13737 42dim(Training3) == dim(na.omit(Training3))## [1] TRUE TRUEModels used with adjusted Training data
- Decision tree
We fit a predictive model for activity recognition using the decision tree algorithm.
tree_ <- rpart(classe ~ ., data=Training3, method="class")
prp(tree_)
The performance of the model with the validation data is as follows:
tree_out <- predict(tree_, Testing, type = "class")
tree_ct <- confusionMatrix(Testing$classe, tree_out)
tree_ct## Confusion Matrix and Statistics
##
## Reference
## Prediction A B C D E
## A 1478 61 83 30 22
## B 201 589 198 124 27
## C 40 105 843 31 7
## D 52 146 203 517 46
## E 61 200 180 112 529
##
## Overall Statistics
##
## Accuracy : 0.6722
## 95% CI : (0.6601, 0.6842)
## No Information Rate : 0.3113
## P-Value [Acc > NIR] : < 2.2e-16
##
## Kappa : 0.5842
## Mcnemar's Test P-Value : < 2.2e-16
##
## Statistics by Class:
##
## Class: A Class: B Class: C Class: D Class: E
## Sensitivity 0.8068 0.5350 0.5594 0.63514 0.83835
## Specificity 0.9516 0.8850 0.9582 0.91185 0.89475
## Pos Pred Value 0.8829 0.5171 0.8216 0.53631 0.48891
## Neg Pred Value 0.9159 0.8921 0.8633 0.93965 0.97876
## Prevalence 0.3113 0.1871 0.2561 0.13832 0.10722
## Detection Rate 0.2511 0.1001 0.1432 0.08785 0.08989
## Detection Prevalence 0.2845 0.1935 0.1743 0.16381 0.18386
## Balanced Accuracy 0.8792 0.7100 0.7588 0.77349 0.86655accuracy <- postResample(tree_out, Testing$classe)
#show table
tab <- tree_ct
kable(tab[2],caption="confusion table of the tree model")
|
rm(tree_out)The Accuracy is:
kable(tab$overall)| Accuracy | 0.6722175 |
| Kappa | 0.5841515 |
| AccuracyLower | 0.6600565 |
| AccuracyUpper | 0.6842075 |
| AccuracyNull | 0.3112999 |
| AccuracyPValue | 0.0000000 |
| McnemarPValue | 0.0000000 |
- Random Forest
It is quite accurate since at each split it has bootstrap variables. It grows multiple trees and vote. We will use 4 fold cross validation when applying the algorithm.
#rf - random forest
rf_ <- train(classe ~ ., data=Training3, method="rf", verbose=FALSE, trControl=trainControl(method ="cv",4), ntree = 250)
#predict
rf.out <- predict(rf_,newdata=Testing)
#contigency table
rf.ct <- confusionMatrix(rf.out,Testing$classe)
#show table
tab <- rf.ct
kable(tab[2],caption="confusion table of the Random Forest model")
|
rm(rf_out)
rm(rf_ct)The Accuracy is:
kable(tab$overall)| Accuracy | 0.9870858 |
| Kappa | 0.9836595 |
| AccuracyLower | 0.9838623 |
| AccuracyUpper | 0.9898120 |
| AccuracyNull | 0.2844520 |
| AccuracyPValue | 0.0000000 |
| McnemarPValue | NaN |
Prediction/ Forecasting of the 20 classes
We use the validation data from the first section and predict the 20 classes with all the models. As they were all equally good. But before we make sure that the predicted data has the same format as the training and testing. We therefore need to coerce it into the same type of data.
Model.tree <- predict(tree_,Testing_forprediction)
Model.rf <- predict(rf_,Testing_forprediction)
result_predictions = data.frame(Model.tree)
kable(data.frame(result_predictions), caption=" results for the final quiz")| A | B | C | D | E |
|---|---|---|---|---|
| 0.0298063 | 0.1445604 | 0.5176354 | 0.1500248 | 0.1579732 |
| 0.7664234 | 0.1690998 | 0.0121655 | 0.0237226 | 0.0285888 |
| 0.9636511 | 0.0363489 | 0.0000000 | 0.0000000 | 0.0000000 |
| 0.9754098 | 0.0245902 | 0.0000000 | 0.0000000 | 0.0000000 |
| 0.7330097 | 0.0194175 | 0.0436893 | 0.0291262 | 0.1747573 |
| 0.0298063 | 0.1445604 | 0.5176354 | 0.1500248 | 0.1579732 |
| 0.0639854 | 0.1371115 | 0.0383912 | 0.6910420 | 0.0694698 |
| 0.0496032 | 0.1666667 | 0.0337302 | 0.6369048 | 0.1130952 |
| 0.9636511 | 0.0363489 | 0.0000000 | 0.0000000 | 0.0000000 |
| 0.7664234 | 0.1690998 | 0.0121655 | 0.0237226 | 0.0285888 |
| 0.0298063 | 0.1445604 | 0.5176354 | 0.1500248 | 0.1579732 |
| 0.0000000 | 0.5921053 | 0.1348684 | 0.1217105 | 0.1513158 |
| 0.0298063 | 0.1445604 | 0.5176354 | 0.1500248 | 0.1579732 |
| 0.9636511 | 0.0363489 | 0.0000000 | 0.0000000 | 0.0000000 |
| 0.0766284 | 0.1417625 | 0.0421456 | 0.2030651 | 0.5363985 |
| 0.0170455 | 0.0000000 | 0.0000000 | 0.0681818 | 0.9147727 |
| 0.6575342 | 0.0958904 | 0.0834371 | 0.1145704 | 0.0485679 |
| 0.0997067 | 0.4076246 | 0.0058651 | 0.3167155 | 0.1700880 |
| 0.0997067 | 0.4076246 | 0.0058651 | 0.3167155 | 0.1700880 |
| 0.0000000 | 0.5921053 | 0.1348684 | 0.1217105 | 0.1513158 |
result_predictions = data.frame(Model.rf)
kable(data.frame(result_predictions), caption=" results for the final quiz")| Model.rf |
|---|
| B |
| A |
| B |
| A |
| A |
| E |
| D |
| B |
| A |
| A |
| B |
| C |
| B |
| A |
| E |
| E |
| A |
| B |
| B |
| B |
write.table(result_predictions, "results.csv")