Predicting Earnings Manipulation by Indian Firms Using Machine Learning Algorithms (IMB577) and supporting Excel file shared.

IIMK ADSM 2020-21 Batch-2, Group 6: Ramana, Venugopal, Siju, Vikesh, Abdul

Load the required libraries

library(readxl)
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)

## Warning: package 'caret' was built under R version 4.0.4

## Loading required package: lattice

## Loading required package: ggplot2

library(ROSE)

## Warning: package 'ROSE' was built under R version 4.0.4

## Loaded ROSE 0.0-3

library(knitr)

Load the data

setwd("C:/_MyData_/IIMK/Assignment 4_Predictive Earnings")
earningsData <- read_excel ("Predicting earnings excel IMB579-XLS-ENG.xlsx", sheet = "Sample for Model Development")

names (earningsData)

##  [1] "Company ID"    "DSRI"          "GMI"           "AQI"          
##  [5] "SGI"           "DEPI"          "SGAI"          "ACCR"         
##  [9] "LEVI"          "Manipulator"   "C-MANIPULATOR"

# Delete the Company ID and Manipulator columns
earningsData <- earningsData[c(-1, -10)]

names (earningsData)

## [1] "DSRI"          "GMI"           "AQI"           "SGI"          
## [5] "DEPI"          "SGAI"          "ACCR"          "LEVI"         
## [9] "C-MANIPULATOR"

# Rename C-MANIPULATOR column as just MANIPULATOR and make it categorical
names (earningsData) [names(earningsData) == "C-MANIPULATOR"] <- "MANIPULATOR"
earningsData$MANIPULATOR <- as.factor(earningsData$MANIPULATOR)

str (earningsData)

## tibble [220 x 9] (S3: tbl_df/tbl/data.frame)
##  $ DSRI       : num [1:220] 1.62 1 1 1.49 1 ...
##  $ GMI        : num [1:220] 1.13 1.61 1.02 1 1.37 ...
##  $ AQI        : num [1:220] 7.185 1.005 1.241 0.466 0.637 ...
##  $ SGI        : num [1:220] 0.366 13.081 1.475 0.673 0.861 ...
##  $ DEPI       : num [1:220] 1.38 0.4 1.17 2 1.45 ...
##  $ SGAI       : num [1:220] 1.6241 5.1982 0.6477 0.0929 1.7415 ...
##  $ ACCR       : num [1:220] -0.1668 0.0605 0.0367 0.2734 0.123 ...
##  $ LEVI       : num [1:220] 1.161 0.987 1.264 0.681 0.939 ...
##  $ MANIPULATOR: Factor w/ 2 levels "0","1": 2 2 2 2 2 2 2 2 2 2 ...

# Split the data into Train & Test

set.seed(1234)
myindex <- createDataPartition(earningsData$MANIPULATOR, p = .60, list = FALSE)
trainData <- earningsData[myindex,]

## Warning: The `i` argument of ``[`()` can't be a matrix as of tibble 3.0.0.
## Convert to a vector.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_warnings()` to see where this warning was generated.

testData <- earningsData[-myindex,]

Construct the basic model (without resampling)

set.seed(1234)
reg1 <- glm (MANIPULATOR~., family = binomial, data = trainData)

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

summary(reg1)

## 
## Call:
## glm(formula = MANIPULATOR ~ ., family = binomial, data = trainData)
## 
## Deviance Residuals: 
##      Min        1Q    Median        3Q       Max  
## -1.75098  -0.33344  -0.21620  -0.08278   2.76568  
## 
## Coefficients:
##              Estimate Std. Error z value Pr(>|z|)    
## (Intercept) -11.49626    2.77748  -4.139 3.49e-05 ***
## DSRI          1.04452    0.47734   2.188 0.028656 *  
## GMI           3.26900    0.90837   3.599 0.000320 ***
## AQI           0.36645    0.20192   1.815 0.069550 .  
## SGI           3.25939    0.98407   3.312 0.000926 ***
## DEPI         -0.14376    0.93801  -0.153 0.878196    
## SGAI          0.09423    0.22055   0.427 0.669184    
## ACCR         10.39373    3.06203   3.394 0.000688 ***
## LEVI          0.08068    0.42236   0.191 0.848502    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 125.572  on 132  degrees of freedom
## Residual deviance:  60.231  on 124  degrees of freedom
## AIC: 78.231
## 
## Number of Fisher Scoring iterations: 8

Findings

This model suggests that ACCR, SGI, GMI, DSRI and AQI indices are significant for predicting manipulator

# Run the stepwise regression and see the results

reg2 <- step(reg1, trace = 0)

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

summary (reg2)

## 
## Call:
## glm(formula = MANIPULATOR ~ DSRI + GMI + AQI + SGI + ACCR, family = binomial, 
##     data = trainData)
## 
## Deviance Residuals: 
##      Min        1Q    Median        3Q       Max  
## -1.74331  -0.35222  -0.21735  -0.07719   2.71990  
## 
## Coefficients:
##             Estimate Std. Error z value Pr(>|z|)    
## (Intercept) -11.5329     2.3601  -4.887 1.03e-06 ***
## DSRI          1.2343     0.3018   4.089 4.32e-05 ***
## GMI           3.1516     0.8252   3.819 0.000134 ***
## AQI           0.3717     0.2009   1.850 0.064315 .  
## SGI           3.2334     0.9429   3.429 0.000605 ***
## ACCR         10.4393     3.0836   3.385 0.000711 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 125.572  on 132  degrees of freedom
## Residual deviance:  60.552  on 127  degrees of freedom
## AIC: 72.552
## 
## Number of Fisher Scoring iterations: 8

exp(coef(reg2))

##  (Intercept)         DSRI          GMI          AQI          SGI         ACCR 
## 9.801979e-06 3.435813e+00 2.337297e+01 1.450170e+00 2.536652e+01 3.417672e+04

Findings

This model also indicates the same indices as the basic model

Predict the test data set and interpret the Confusion Matrix

# Predict the values for test data set
testData$prob <- predict(reg2, newdata = testData, type = "response")
testData$predicted <- ifelse (testData$prob >0.50, 1,0)

# Detailed Confusion Matrix for test data
str(testData)

## tibble [87 x 11] (S3: tbl_df/tbl/data.frame)
##  $ DSRI       : num [1:87] 1.62 1 1.49 1 7.66 ...
##  $ GMI        : num [1:87] 1.13 1.02 1 1.37 0.58 ...
##  $ AQI        : num [1:87] 7.185 1.241 0.466 0.637 1.036 ...
##  $ SGI        : num [1:87] 0.366 1.475 0.673 0.861 1.485 ...
##  $ DEPI       : num [1:87] 1.382 1.169 2 1.455 0.679 ...
##  $ SGAI       : num [1:87] 1.6241 0.6477 0.0929 1.7415 0.6537 ...
##  $ ACCR       : num [1:87] -0.16681 0.03673 0.27343 0.12305 0.00365 ...
##  $ LEVI       : num [1:87] 1.161 1.264 0.681 0.939 1.102 ...
##  $ MANIPULATOR: Factor w/ 2 levels "0","1": 2 2 2 2 2 2 2 2 2 2 ...
##  $ prob       : Named num [1:87] 0.0207 0.1849 0.2069 0.1574 0.9931 ...
##   ..- attr(*, "names")= chr [1:87] "1" "2" "3" "4" ...
##  $ predicted  : Named num [1:87] 0 0 0 0 1 1 0 1 0 1 ...
##   ..- attr(*, "names")= chr [1:87] "1" "2" "3" "4" ...

testData$predicted <- as.factor (testData$predicted)
confusionMatrix(testData$predicted, testData$MANIPULATOR, positive = '1')

## Confusion Matrix and Statistics
## 
##           Reference
## Prediction  0  1
##          0 66  9
##          1  6  6
##                                           
##                Accuracy : 0.8276          
##                  95% CI : (0.7316, 0.9002)
##     No Information Rate : 0.8276          
##     P-Value [Acc > NIR] : 0.5684          
##                                           
##                   Kappa : 0.3439          
##                                           
##  Mcnemar's Test P-Value : 0.6056          
##                                           
##             Sensitivity : 0.40000         
##             Specificity : 0.91667         
##          Pos Pred Value : 0.50000         
##          Neg Pred Value : 0.88000         
##              Prevalence : 0.17241         
##          Detection Rate : 0.06897         
##    Detection Prevalence : 0.13793         
##       Balanced Accuracy : 0.65833         
##                                           
##        'Positive' Class : 1               
##

Findings

Classification Accuracy = 0.8276 which means this model is accurate 83% of the time
In the non-manipulator category:
- 66 were predicted correctly (True Negative)
- 6 were predicted incorrectly (Type I Error - False Positive)
In the manipulator category:
- 9 were predicted incorrectly (Type II Error - False Negative)
- 6 were predicted correctly (True Positive)
With 95% CI, one can say that this accuracy value is likely to be between 73% and 90%
No Information Rate is 83%
- This means that 83% will be the classification accuracy when we do not use any modeling
- This is same as the Overall Classification Accuracy which indicates that the model which we developed is inferior than that of the random prediction. We need Accuracy > NIR
P-Value (Ha: Accuracy > NIR, H0: Accuracy <= NIR)
- From the result, p-value shown is > 0.05, which means we accept H0 (reject Ha) and indicates that the test is insignificant
Sensitivity (Recall) is 40%
- This means, out of all the manipulator cases, the model predicted only 40% of them correctly.
- We need this to be high
Specificity is 91%
- This means, out of all the non-manipulator cases, the model predicted 91% of them correctly.
- This is higher than Sensitivity. But for a good model, we need Sensitivity > Specificity
Positive Predicted Value (Precision) is 50%
- This is out of all the predicted manipulator cases, the model predicted only 50% of them correctly.
- This needs to be even higher.
Negative Predicted Value is 88%
- This means, out of all the non-manipulator cases, the model predicted 88% of them correctly.
Prevalence is only 17% which means that the data is highly imbalanced.

Conclusion

As the data is highly imbalanced, which means we have far lesser data of manipulators than non-manipulators.
Let us apply data balancing techniques - Over Sampling, Under Sampling and Both and then create the models again

OVER SAMPLING

Data of Non-manipulators and Manipulators before and after over sampling.

table(trainData$MANIPULATOR)

## 
##   0   1 
## 109  24

overSampledData <- ovun.sample(MANIPULATOR~., data = trainData, method = "over", N = 218, seed = 1234)$data

table(overSampledData$MANIPULATOR)

## 
##   0   1 
## 109 109

Construct the basic model, run step wise regression and then build the confusion matrix with over sampled data

# Construct basic model
set.seed(1234)
reg_over <- glm (MANIPULATOR~., family = binomial, data = overSampledData)

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

summary(reg_over)

## 
## Call:
## glm(formula = MANIPULATOR ~ ., family = binomial, data = overSampledData)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -3.0914  -0.4741   0.0000   0.3921   2.0569  
## 
## Coefficients:
##             Estimate Std. Error z value Pr(>|z|)    
## (Intercept)  -9.9732     1.6512  -6.040 1.54e-09 ***
## DSRI          1.8404     0.4935   3.729 0.000192 ***
## GMI           3.1342     0.6200   5.055 4.30e-07 ***
## AQI           0.3591     0.1522   2.360 0.018278 *  
## SGI           3.5438     0.6955   5.095 3.48e-07 ***
## DEPI         -0.5371     0.6556  -0.819 0.412635    
## SGAI         -0.1402     0.1878  -0.747 0.455153    
## ACCR         12.1239     2.2449   5.401 6.64e-08 ***
## LEVI         -0.5062     0.3056  -1.656 0.097658 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 302.21  on 217  degrees of freedom
## Residual deviance: 137.27  on 209  degrees of freedom
## AIC: 155.27
## 
## Number of Fisher Scoring iterations: 8

# Run the step wise regression and see the results

step_over <- step(reg_over, trace = 0)

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

summary (step_over)

## 
## Call:
## glm(formula = MANIPULATOR ~ DSRI + GMI + AQI + SGI + ACCR + LEVI, 
##     family = binomial, data = overSampledData)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.7919  -0.4798   0.0000   0.4114   2.1123  
## 
## Coefficients:
##             Estimate Std. Error z value Pr(>|z|)    
## (Intercept) -10.7305     1.4805  -7.248 4.24e-13 ***
## DSRI          1.6322     0.4265   3.827  0.00013 ***
## GMI           3.3378     0.5967   5.594 2.22e-08 ***
## AQI           0.3525     0.1511   2.333  0.01966 *  
## SGI           3.5155     0.6848   5.134 2.84e-07 ***
## ACCR         12.0507     2.1879   5.508 3.63e-08 ***
## LEVI         -0.3836     0.2695  -1.423  0.15470    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 302.21  on 217  degrees of freedom
## Residual deviance: 138.20  on 211  degrees of freedom
## AIC: 152.2
## 
## Number of Fisher Scoring iterations: 9

# Predict test data
testData <- testData [c(-10,-11)] # Remove the last two columns prob and predicted

testData$prob <- predict(step_over, newdata = testData, type = "response")
testData$predicted <- ifelse (testData$prob >0.50, 1,0)
testData$predicted <- as.factor (testData$predicted)
confusionMatrix(testData$predicted, testData$MANIPULATOR, positive = '1')

## Confusion Matrix and Statistics
## 
##           Reference
## Prediction  0  1
##          0 63  5
##          1  9 10
##                                           
##                Accuracy : 0.8391          
##                  95% CI : (0.7448, 0.9091)
##     No Information Rate : 0.8276          
##     P-Value [Acc > NIR] : 0.4558          
##                                           
##                   Kappa : 0.4899          
##                                           
##  Mcnemar's Test P-Value : 0.4227          
##                                           
##             Sensitivity : 0.6667          
##             Specificity : 0.8750          
##          Pos Pred Value : 0.5263          
##          Neg Pred Value : 0.9265          
##              Prevalence : 0.1724          
##          Detection Rate : 0.1149          
##    Detection Prevalence : 0.2184          
##       Balanced Accuracy : 0.7708          
##                                           
##        'Positive' Class : 1               
##

Findings

Basic model: DSRI, GMI, SGI, ACCR, AQI, LEVI
Stepwise model: DSRI, GMI, SGI, ACCR, AQI, LEVI
Overall Classification Accuracy is 84% which is better than the initial model without data balancing
In Non-Manipulator
- 63 predicted correctly
- 19 predicted incorrectly
In Manipulator
- 10 predicted correctly
- 5 predicted incorrectly
With 95% CI, this accuracy value is likely to be between 75% to 91%
No Information Rate is 83% which is less than Accuracy, but closer to it. This indicates that the model which we developed is better (not superior) than that of the random precition.
P-Value is > 0.05 which means we accept H0 (Acc <= NIR) which means, the test is insignificant.
Sensitivity (Recall) is 66%
- This means, out of all the manipulator cases, the model predicted 66% of them correctly, whis is better than the model with imbalanced data
- We need this to be still high anyway
Specificity is 88%
- This means, out of all the non-manipulator cases, the model predicted 88% of them correctly.
- But this is higher than Sensitivity and for a good model, we need Sensitivity > Specificity
Positive Predicted Value (Precision) is 53%
- This is out of all the predicted manipulator cases, the model predicted only 53% of them correctly.
- This needs to be even higher.
Negative Predicted Value is 93%
- This means, out of all the non-manipulator cases, the model predicted 93% of them correctly.
Prevalence is still only 17% which means that the data is still imbalanced.

UNDER SAMPLING

Data of Non-manipulators and Manipulators before and after under sampling.

table(trainData$MANIPULATOR)

## 
##   0   1 
## 109  24

underSampledData <- ovun.sample(MANIPULATOR~., data = trainData, method = "under", N = 48, seed = 1234)$data

table(underSampledData$MANIPULATOR)

## 
##  0  1 
## 24 24

Construct the basic model, run step wise regression and then build the confusion matrix with under sampled data

# Construct basic model
set.seed(1234)
reg_under <- glm (MANIPULATOR~., family = binomial, data = underSampledData)

## Warning: glm.fit: algorithm did not converge

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

summary(reg_under)

## 
## Call:
## glm(formula = MANIPULATOR ~ ., family = binomial, data = underSampledData)
## 
## Deviance Residuals: 
##        Min          1Q      Median          3Q         Max  
## -5.768e-04  -2.000e-08   0.000e+00   2.000e-08   1.908e-03  
## 
## Coefficients:
##              Estimate Std. Error z value Pr(>|z|)
## (Intercept)  -3374.93  199871.17  -0.017    0.987
## DSRI           755.22   45549.31   0.017    0.987
## GMI            110.95    7609.16   0.015    0.988
## AQI             92.52    8598.42   0.011    0.991
## SGI           1128.88   65560.51   0.017    0.986
## DEPI          1351.16  102150.76   0.013    0.989
## SGAI          -133.59    9191.40  -0.015    0.988
## ACCR          3204.63  202770.32   0.016    0.987
## LEVI          -253.68   16793.68  -0.015    0.988
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 6.6542e+01  on 47  degrees of freedom
## Residual deviance: 4.5701e-06  on 39  degrees of freedom
## AIC: 18
## 
## Number of Fisher Scoring iterations: 25

# Run the step wise regression and see the results
step_under <- step(reg_under, trace = 0)

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: algorithm did not converge

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: algorithm did not converge

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

summary (step_under)

## 
## Call:
## glm(formula = MANIPULATOR ~ DSRI + GMI + AQI + SGI + DEPI + ACCR + 
##     LEVI, family = binomial, data = underSampledData)
## 
## Deviance Residuals: 
##       Min         1Q     Median         3Q        Max  
## -0.003238   0.000000   0.000000   0.000000   0.003152  
## 
## Coefficients:
##             Estimate Std. Error z value Pr(>|z|)
## (Intercept) -16611.7   206933.6  -0.080    0.936
## DSRI          4918.4    60951.8   0.081    0.936
## GMI            604.8    10360.6   0.058    0.953
## AQI            601.6     8594.1   0.070    0.944
## SGI           5140.3    64937.1   0.079    0.937
## DEPI          4684.6    63999.0   0.073    0.942
## ACCR         20422.2   271322.9   0.075    0.940
## LEVI         -1186.4    19303.6  -0.061    0.951
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 6.6542e+01  on 47  degrees of freedom
## Residual deviance: 3.2090e-05  on 40  degrees of freedom
## AIC: 16
## 
## Number of Fisher Scoring iterations: 25

# Predict test data
testData <- testData [c(-10,-11)] # Remove the last two columns prob and predicted
testData$prob <- predict(step_under, newdata = testData, type = "response")
testData$predicted <- ifelse (testData$prob >0.50, 1,0)
testData$predicted <- as.factor (testData$predicted)
confusionMatrix(testData$predicted, testData$MANIPULATOR, positive = '1')

## Confusion Matrix and Statistics
## 
##           Reference
## Prediction  0  1
##          0 52  2
##          1 20 13
##                                           
##                Accuracy : 0.7471          
##                  95% CI : (0.6425, 0.8342)
##     No Information Rate : 0.8276          
##     P-Value [Acc > NIR] : 0.9794032       
##                                           
##                   Kappa : 0.3992          
##                                           
##  Mcnemar's Test P-Value : 0.0002896       
##                                           
##             Sensitivity : 0.8667          
##             Specificity : 0.7222          
##          Pos Pred Value : 0.3939          
##          Neg Pred Value : 0.9630          
##              Prevalence : 0.1724          
##          Detection Rate : 0.1494          
##    Detection Prevalence : 0.3793          
##       Balanced Accuracy : 0.7944          
##                                           
##        'Positive' Class : 1               
##

Findings

Basic model: DSRI, GMI, AQI, SGI, DEPI, SGAI, ACCR, LEVI
Stepwise model: DSRI, GMI, AQI, SGI, DEPI, ACCR, LEVI
Overall Classification Accuracy is 75% which is worse than the initial model without data balancing or the model with over sampling
In Non-Manipulator
- 52 predicted correctly
- 20 predicted incorrectly
In Manipulator
- 13 predicted correctly
- 2 predicted incorrectly
With 95% CI, this accuracy value is likely to be between 64% to 83%
No Information Rate is 83% which is higher than Accuracy. This indicates that the model which we developed is not better than that of the random precition.
P-Value is > 0.05 which means we accept H0 (Acc <= NIR) which means, the test is insignificant.
Sensitivity (Recall) is 87%
- This means, out of all the actual manipulator cases, the model predicted 87% of them correctly, whis is far better than the model with imbalanced data or with the over sampled data
- We need this to be as high as possible
Specificity is 72%
- This means, out of all the actual non-manipulator cases, the model predicted 72% of them correctly.
- This is lesser than Sensitivity and for a good model, we need Sensitivity > Specificity
Positive Predicted Value (Precision) is 39%
- This is out of all the predicted manipulator cases, the model predicted only 39% of them correctly.
- This needs to be even higher.
Negative Predicted Value is 96%
- This means, out of all the non-manipulator cases, the model predicted 96% of them correctly.
Prevalence is still only 17% which means that the data is still imbalanced.

APPLY BOTH OVER AND UNDER SAMPLING

Data of Non-manipulators and Manipulators before and after resampling.

table(trainData$MANIPULATOR)

## 
##   0   1 
## 109  24

bothSampledData <- ovun.sample(MANIPULATOR~., data = trainData, method = "both", N = nrow(trainData), p = .50, seed = 1234)$data

table(bothSampledData$MANIPULATOR)

## 
##  0  1 
## 75 58

prop.table (table(bothSampledData$MANIPULATOR))

## 
##         0         1 
## 0.5639098 0.4360902

Construct the basic model, run step wise regression and then build the confusion matrix with resampled data

# Construct the basic model
set.seed(1234)
reg_both <- glm (MANIPULATOR~., family = binomial, data = bothSampledData)

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

summary(reg_both)

## 
## Call:
## glm(formula = MANIPULATOR ~ ., family = binomial, data = bothSampledData)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.2401  -0.5406  -0.2362   0.3547   1.8885  
## 
## Coefficients:
##             Estimate Std. Error z value Pr(>|z|)    
## (Intercept)  -8.9566     2.1497  -4.166 3.09e-05 ***
## DSRI          2.2303     0.7110   3.137 0.001707 ** 
## GMI           2.8622     0.8470   3.379 0.000727 ***
## AQI           0.7870     0.2726   2.886 0.003896 ** 
## SGI           2.9411     0.7844   3.750 0.000177 ***
## DEPI         -1.0804     0.7620  -1.418 0.156231    
## SGAI         -0.2811     0.2491  -1.128 0.259132    
## ACCR         12.2746     3.3847   3.626 0.000287 ***
## LEVI         -0.6656     0.4218  -1.578 0.114599    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 182.198  on 132  degrees of freedom
## Residual deviance:  83.603  on 124  degrees of freedom
## AIC: 101.6
## 
## Number of Fisher Scoring iterations: 9

# Run the step wise regression and see the results

step_both <- step(reg_both, trace = 0)

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: algorithm did not converge

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

summary (step_both)

## 
## Call:
## glm(formula = MANIPULATOR ~ DSRI + GMI + AQI + SGI + ACCR, family = binomial, 
##     data = bothSampledData)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.0434  -0.5516  -0.2298   0.4377   2.1238  
## 
## Coefficients:
##             Estimate Std. Error z value Pr(>|z|)    
## (Intercept) -10.4568     1.9286  -5.422 5.89e-08 ***
## DSRI          1.4549     0.5292   2.749 0.005972 ** 
## GMI           3.4224     0.7900   4.332 1.48e-05 ***
## AQI           0.5806     0.2201   2.638 0.008329 ** 
## SGI           2.9255     0.6961   4.203 2.64e-05 ***
## ACCR         12.0150     3.1257   3.844 0.000121 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 182.198  on 132  degrees of freedom
## Residual deviance:  87.515  on 127  degrees of freedom
## AIC: 99.515
## 
## Number of Fisher Scoring iterations: 8

# Predict test data
testData <- testData [c(-10,-11)] # Remove the last two columns prob and predicted

testData$prob <- predict(step_both, newdata = testData, type = "response")
testData$predicted <- ifelse (testData$prob >0.50, 1,0)
testData$predicted <- as.factor (testData$predicted)
confusionMatrix(testData$predicted, testData$MANIPULATOR, positive = '1')

## Confusion Matrix and Statistics
## 
##           Reference
## Prediction  0  1
##          0 62  5
##          1 10 10
##                                           
##                Accuracy : 0.8276          
##                  95% CI : (0.7316, 0.9002)
##     No Information Rate : 0.8276          
##     P-Value [Acc > NIR] : 0.5684          
##                                           
##                   Kappa : 0.4663          
##                                           
##  Mcnemar's Test P-Value : 0.3017          
##                                           
##             Sensitivity : 0.6667          
##             Specificity : 0.8611          
##          Pos Pred Value : 0.5000          
##          Neg Pred Value : 0.9254          
##              Prevalence : 0.1724          
##          Detection Rate : 0.1149          
##    Detection Prevalence : 0.2299          
##       Balanced Accuracy : 0.7639          
##                                           
##        'Positive' Class : 1               
##

Findings from all 4 models

Overall Classification Accuracy - Percentage at which the model is accurate
Confusion Matrix

Predicted / Actual	0 = Non-Manipulator	1 = Manipulator
0 = Non-manipulator	True Negative (TN)	False Negative (FN - Type II Error)
1 = Manipulator	False Positive (FP - Type I Error)	True Positive (TP)

TP - Predicted as Manipulator and it is true
TN - Predicted as Non-Manipulator and it is true
FP - Predicted as Manipulator and it is false
FN - Predicted as Non-Manipulator and it is false
95% CI - Confidence interval at which the accuracy value is likely to fall
No Information Rate - Largest proportion of the observed class. If we do not develop any model, and simply classify the same into the largest category, then what will be the prediction accuracy
P-value
- Ha: Accuracy > No Information Rate (Overall model accuracy is greater than that of No Information Rate)
- H0: Accuracy <= No Information Rate
- If P-value < 0.05, we reject H0. Else accept Ha
Sensitivity (Recall) - Out of all the actual manipulator cases, percentage of correctly predicted manipulators by the model (TP / (TP + FN))
Specificity - Out of all the actual non-manipulator cases, percentage of correctly predicted non-manipulators by the model. Need Sensitivity > Specificity (TN / (TP + TN))
Positive Predicted Value (Precision) - Out of all the predicted manipulator cases, percentage of correctly predicted manipulators by the model (TP / (TP + FP))
Negative Predicted Value - Out of all the predicted non-manipulator cases, percentage of correctly predicted non-manipulators by the model (TN / (TN + FN))
Prevalence - If it is less, data is imbalanced. If it is closer to 0.5, data is balanced ((TP + FN) / (TP + FN + TN + FP))

Model	Overall Classification Accuracy	95% CI	No Information Rate	Sensitivity (Recall)	Specificity	Positive Predicted Value	Negative Predicted Value	Prevalence
Original Data	83%	73% to 90%	83%	40%	92%	50%	88%	17%
Over Sampling	84%	74% to 91%	83%	67%	87%	53%	93%	17%
Under Sampling	75%	64% to 83%	83%	87%	72%	39%	96%	17%
Both	83%	73% to 90%	83%	67%	86%	50%	93%	17%

Conclusions

For our model, Precision (Positive Predicted Value) is important as we want to be more confident of the true positives. So, we will choose that model where this is high.
Sensitivity / Recall isn’t recommended as false negatives is unacceptable.
So, we will go with Over Sampled model where we have the highest Precision.

Calculate the M-Score and Probability of Manipulator with the initial original data

# Get the coefficients from Over Sampling modle and display them
modelCoefs <- coef(step_over)
modelCoefs

## (Intercept)        DSRI         GMI         AQI         SGI        ACCR 
## -10.7305184   1.6321930   3.3377596   0.3525421   3.5155115  12.0506800 
##        LEVI 
##  -0.3835953

# Calculate the m-score which is the odds ratio and probability
earningsData_Copy <- earningsData

earningsData_Copy$mScore <- modelCoefs[1] + modelCoefs[2] * earningsData_Copy$DSRI + modelCoefs[3] * earningsData_Copy$GMI + modelCoefs[4] * earningsData_Copy$AQI + modelCoefs[5] * earningsData_Copy$SGI + modelCoefs[6] * earningsData_Copy$ACCR + modelCoefs[7] * earningsData_Copy$LEVI

earningsData_Copy$Probability <- exp(earningsData_Copy$mScore) / (1 + exp(earningsData_Copy$mScore))
earningsData_Copy$Prediction <- ifelse(earningsData_Copy$Probability > 0.5, "Manipulator", "Non-Manipulator")

kable(earningsData_Copy, format = "html", align = "c")

DSRI	GMI	AQI	SGI	DEPI	SGAI	ACCR	LEVI	MANIPULATOR	mScore	Probability	Prediction
1.6247416	1.1289269	7.1850534	0.3662115	1.3815191	1.6241449	-0.1668087	1.1610817	1	-2.9456290	0.0499435	Non-Manipulator
1.0000000	1.6064918	1.0049879	13.0814332	0.4000000	5.1982072	0.0604752	0.9867325	1	42.9562485	1.0000000	Manipulator
1.0000000	1.0156066	1.2413895	1.4750183	1.1693525	0.6476709	0.0367316	1.2643050	1	-0.1277291	0.4681111	Non-Manipulator
1.4862385	1.0000000	0.4655348	0.6728395	2.0000000	0.0928899	0.2734341	0.6809750	1	0.5964133	0.6448353	Manipulator
1.0000000	1.3690378	0.6371120	0.8613464	1.4546757	1.7414596	0.1230477	0.9390472	1	-0.1535300	0.4616927	Non-Manipulator
0.9055320	1.3609149	0.7839949	1.7933237	1.2782441	0.5052600	0.0546424	1.5431371	1	1.9372703	0.8740520	Manipulator
1.4474836	0.9984074	0.9665526	0.9118089	1.0588610	0.8984209	-0.0365516	0.4890732	1	-2.1173549	0.1074214	Non-Manipulator
7.6599762	0.5801841	1.0357910	1.4854401	0.6788332	0.6536511	0.0036520	1.1015913	1	8.9172410	0.9998660	Manipulator
1.3462790	2.4735627	0.7025301	0.9656245	0.9852729	0.5945107	-0.0134849	1.0284588	1	2.8083470	0.9431252	Manipulator
1.0000000	1.0000000	1.1666382	2.5925926	0.8503401	0.5571429	0.0010285	0.1630256	1	3.7148700	0.9762206	Manipulator
1.0000000	0.8631555	1.0097669	1.3950139	1.0018719	0.9878823	-0.0045735	1.0063938	1	-1.3983091	0.1980846	Non-Manipulator
1.4483886	0.7956711	4.0016884	1.0673772	1.0855468	3.7344914	0.0904579	0.2220901	1	0.4573174	0.6123776	Manipulator
1.2740483	1.0000000	1.0771002	0.9078743	1.2404358	3.7363726	0.3584569	0.3793479	1	2.4322333	0.9192525	Manipulator
1.0000000	1.4005828	4.5756922	1.1958993	1.1432738	0.8868691	0.0112590	0.3339770	1	1.4013711	0.8024014	Manipulator
1.2522421	1.0064799	1.1749240	1.2503040	0.9534113	1.1114944	-0.0134539	1.1180808	1	-1.1085808	0.2481356	Non-Manipulator
8.3476148	0.4952399	0.5730163	0.6721113	0.9418605	1.4878488	0.0608108	13.0585586	1	2.8358288	0.9445815	Manipulator
1.5259695	0.9614497	-0.4312655	1.3316461	1.0936753	0.8569668	0.0877686	1.1076812	1	0.1313936	0.5328012	Manipulator
1.7782406	0.7422458	-2.1300996	1.9373082	1.0000000	1.8066305	0.1463845	1.0795396	1	2.0589569	0.8868495	Manipulator
0.6153282	0.8593235	0.8993778	1.7160665	0.9426060	1.5660815	0.1328321	0.1385888	1	1.0395061	0.7387547	Manipulator
1.0000000	-1.4166667	16.4266502	0.4166667	0.0688227	2.4000000	-0.0040710	1.0000000	1	-7.0035885	0.0009078	Non-Manipulator
1.0000000	1.0000000	-1.5405442	2.6666667	0.1657609	1.0000000	0.0352440	0.0105802	1	3.4916808	0.9704501	Manipulator
1.0000000	0.8720097	0.6525097	13.0646531	1.1037165	0.0969564	0.0410279	1.1766547	1	40.0142643	1.0000000	Manipulator
15.3435121	0.0785096	0.9441843	0.0645376	0.2292935	49.3017807	-0.5605362	1.1667852	1	7.9324325	0.9996412	Manipulator
14.0000000	1.0000000	1.0000000	0.0769231	1.0000000	1.0000000	-0.0047170	1.0833333	1	15.6085048	0.9999998	Manipulator
2.0400000	1.0000000	0.2915308	0.2192982	1.0000000	1.0000000	0.7178423	1.0000000	1	5.0775301	0.9938033	Manipulator
0.1463415	46.4666667	1.0000000	2.2777778	1.0000000	0.2195122	0.0139373	0.0000000	1	153.1309504	1.0000000	Manipulator
2.2354861	1.0000000	0.4727173	1.1690208	1.0363636	0.9042977	0.5103363	0.5360653	1	6.4766125	0.9984633	Manipulator
2.1657121	0.9863940	0.9067293	1.1976092	1.0468190	1.3636940	0.0172505	1.2031727	1	0.3729058	0.5921609	Manipulator
1.0000000	1.5018098	1.5211900	1.2630261	0.9947910	0.7456599	0.0812586	1.3769396	1	1.3418546	0.7927948	Manipulator
36.2911848	-0.5153277	1.0144075	0.0276855	1.1428571	11.7942857	-0.0200106	1.0275929	1	46.6032880	1.0000000	Manipulator
1.0000000	1.0585964	1.1811049	1.5643863	0.8036669	1.1575109	0.0534229	0.8381874	1	0.6732796	0.6622371	Manipulator
1.3226623	1.0000000	0.9393216	1.2151822	1.0477818	1.2060636	0.0418681	0.8483335	1	-0.4516593	0.3889663	Non-Manipulator
1.0099338	1.0955838	5.7029044	0.9027431	1.2371744	0.6245879	0.0079198	2.5562362	1	-1.1263196	0.2448409	Non-Manipulator
1.0000000	1.0000000	0.4083859	1.0000000	1.0000000	1.0000000	0.3871333	0.3582690	1	2.4267079	0.9188414	Manipulator
1.0000000	1.0000000	1.0862810	4.5270204	0.5315411	2.2400979	0.0878416	8.5638663	1	8.3106787	0.9997542	Manipulator
0.6644488	1.4620870	52.8867336	0.8052778	0.6502497	1.3600675	-0.2629533	3.5541471	1	12.1777300	0.9999949	Manipulator
1.4274512	1.0051473	0.4657116	1.5698877	0.9063740	0.8494879	0.1975966	0.8420037	1	2.6956234	0.9367679	Manipulator
3.7535965	3.1014341	1.1635660	0.8479576	1.0028851	0.2760074	-0.5922579	1.0705850	1	1.5913456	0.8308053	Manipulator
1.0000000	0.9101333	0.9772508	1.5786850	1.0628225	0.9798503	0.1568508	0.7448946	1	1.4383091	0.8081927	Manipulator
1.6516739	0.9854594	1.1052543	1.1178741	0.9709790	0.8470720	0.0466283	0.9406575	0	-0.2248222	0.4440300	Non-Manipulator
1.1010141	0.9855653	9.8524158	1.0132778	1.0589476	0.8719003	-0.0440728	0.9849068	0	0.4827973	0.6184082	Manipulator
0.7748410	1.0000000	0.6410844	1.4337085	1.2634924	0.9838868	-0.0074432	1.0486633	0	-1.3537984	0.2052501	Non-Manipulator
1.0725736	1.0464275	1.0611331	1.0649329	0.9593362	0.7113004	-0.0081743	1.0217711	0	-1.8597223	0.1347354	Non-Manipulator
1.0371676	0.9718522	-2.3893492	1.4079025	0.8807285	1.2753938	0.0271793	1.1092761	0	-1.7846842	0.1437257	Non-Manipulator
1.1300943	0.8287790	1.2446719	0.6861500	1.0891178	4.2963713	-0.0123057	0.8857436	0	-3.7568130	0.0228249	Non-Manipulator
1.2412648	0.9017853	-0.3701159	0.9891429	1.0229240	1.1373483	0.0216760	0.8414007	0	-2.4092773	0.0824680	Non-Manipulator
0.5477482	0.7473015	5.1696908	0.3184357	0.5872580	1.6010646	-0.3276284	0.8175582	0	-8.6619328	0.0001730	Non-Manipulator
0.9978624	0.9500674	1.1601359	1.0063247	1.0311864	0.5996556	0.0437330	1.5705837	0	-2.0594309	0.1131029	Non-Manipulator
1.0751495	1.0371458	0.8288933	1.0730709	0.9656937	0.8392946	0.0224198	0.7426985	0	-1.4640324	0.1878513	Non-Manipulator
0.9113795	1.1777769	0.9643049	1.2091158	0.9181662	0.9508865	-0.0095843	0.9725859	0	-1.2097932	0.2297377	Non-Manipulator
1.3127912	0.9734548	0.5167552	1.0513250	1.0613639	1.0366944	-0.0844826	1.1063777	0	-2.9029823	0.0520063	Non-Manipulator
0.6903906	0.9546157	-2.1134576	1.0719694	1.1001557	1.2668272	-0.1319301	1.1376051	0	-5.4201800	0.0044068	Non-Manipulator
0.5314745	1.0029740	-3.7524022	0.9654501	0.8689867	1.0000000	0.0089344	2.5429515	0	-5.3119912	0.0049079	Non-Manipulator
1.0401485	1.1103103	0.8750159	1.2512940	1.1053244	1.1036195	-0.1137717	1.0202137	0	-2.3818041	0.0845708	Non-Manipulator
1.1288690	1.0665687	1.2559032	0.8632072	1.0846285	1.2339731	-0.0210441	1.4577449	0	-2.6634427	0.0651653	Non-Manipulator
0.8496254	0.9579597	1.7380963	1.0861562	1.1197299	0.7282437	-0.0987215	0.9800356	0	-3.2807780	0.0362365	Non-Manipulator
1.0370761	0.9865518	1.0558481	1.2456002	0.8577057	1.0160374	-0.0013879	0.9713494	0	-1.3831148	0.2005092	Non-Manipulator
0.6527760	-20.8118488	0.9471319	1.7001540	0.4368438	0.9183638	-0.0559675	1.3379305	0	-74.0068651	0.0000000	Non-Manipulator
1.5102337	1.4675184	1.1039441	0.7146063	0.8972958	0.3646016	-0.0895473	1.1068824	0	-1.9696092	0.1224309	Non-Manipulator
1.2700933	1.3182602	0.9704125	0.9321626	1.0623680	1.0896272	-0.1723549	1.1994447	0	-3.1754009	0.0401020	Non-Manipulator
0.7291950	1.2700159	1.1486073	1.1254780	1.0876156	0.9294409	-0.0568427	0.9330934	0	-1.9826835	0.1210331	Non-Manipulator
0.5923249	0.9053565	0.8437998	1.1452027	1.1037618	1.1408039	-0.0720304	0.6631052	0	-3.5407988	0.0281734	Non-Manipulator
1.5090183	1.0798830	0.6639746	0.9950054	1.0029660	1.0101299	-0.1397020	1.1556237	0	-3.0578829	0.0448784	Non-Manipulator
3.0186277	0.7891090	0.8169115	0.2563864	1.3698471	2.0275572	0.1107653	1.0585381	0	-1.0516070	0.2589166	Non-Manipulator
1.5149646	0.9973004	-0.3075410	1.0210164	1.0169746	1.1404782	-0.0356344	1.2767605	0	-2.3672587	0.0857037	Non-Manipulator
1.0204553	0.9017272	1.0282856	0.9418080	0.9763008	1.1883190	-0.0335377	0.9639401	0	-3.1556541	0.0408691	Non-Manipulator
1.0376152	1.1624107	0.9793732	1.0751856	1.0174047	1.0469745	-0.0595236	0.9203226	0	-2.1023157	0.1088720	Non-Manipulator
0.8861110	1.1457050	0.7956749	1.1061156	0.9486870	0.8655582	0.0152264	1.0922946	0	-1.5265662	0.1784966	Non-Manipulator
1.5499068	0.9967103	1.3436544	1.1271568	0.9206667	0.9654693	-0.1243589	0.9031088	0	-2.2828027	0.0925573	Non-Manipulator
0.8877977	0.9907124	1.1184070	1.0377644	0.7415737	1.0367870	-0.0537843	1.0573494	0	-2.9858747	0.0480681	Non-Manipulator
1.1518045	1.4148333	1.0173832	1.2852695	0.7002609	0.4929706	0.0104974	0.5635183	0	0.6592104	0.6590830	Manipulator
0.5831449	0.8700076	1.0849017	1.1565197	1.1192830	0.9291902	-0.0422535	0.7132848	0	-3.2094017	0.0388134	Non-Manipulator
0.9309178	0.9806198	1.2629806	1.1933054	0.9328976	0.9736808	-0.0860352	0.9629809	0	-2.7038525	0.0627464	Non-Manipulator
0.8394512	1.1028497	1.4357021	1.2548377	0.9307731	1.0436269	-0.0706993	0.8637014	0	-1.9450701	0.1250919	Non-Manipulator
1.1899892	1.0947896	0.8471105	1.0465264	1.0336437	0.9364947	0.0182734	0.9971003	0	-1.3186399	0.2110447	Non-Manipulator
4.9526418	1.4696724	-0.2362262	0.2219895	0.9383921	2.5426389	0.0368599	0.9114161	0	3.0502604	0.9547938	Manipulator
3.8322491	-0.9606797	1.4007040	1.1575358	1.4388129	1.4603791	0.1834194	1.1207373	0	-1.3385090	0.2077554	Non-Manipulator
1.1543346	1.0111097	1.1701206	0.9867752	1.0564131	1.0206563	-0.1108730	1.0385677	0	-3.3245289	0.0347392	Non-Manipulator
1.1410920	0.9709974	2.6381123	0.9119142	1.0373476	0.9961804	-0.0597125	0.9527077	0	-2.5762206	0.0706846	Non-Manipulator
0.9276849	0.9879195	0.5706057	1.1756584	1.0037132	0.9195829	0.0264766	1.0036190	0	-1.6506394	0.1610226	Non-Manipulator
0.5511651	0.9879326	0.9491908	0.8750000	1.2914811	0.9504223	-0.3713468	1.0460874	0	-7.9989829	0.0003357	Non-Manipulator
1.5872571	1.0058708	1.1046786	0.7310523	0.9572372	1.3902131	0.0197896	0.6771878	0	-1.8442733	0.1365467	Non-Manipulator
0.9421817	1.0667896	0.8403151	1.3612762	0.9293326	1.0292195	-0.0253234	0.9092936	0	-1.2041456	0.2307386	Non-Manipulator
0.9860572	0.9151485	0.9619823	1.0825965	1.1051685	0.9775689	-0.0220342	0.9606791	0	-2.5555567	0.0720541	Non-Manipulator
1.4602406	2.2858626	2.0080862	0.8360847	0.7720620	1.0651115	0.0459493	1.0550042	0	3.0787623	0.9560082	Manipulator
1.0395383	0.9148146	6.3433753	1.1426809	0.9749625	0.9061747	-0.0416521	0.8822615	0	-0.5673131	0.3618570	Non-Manipulator
1.6529963	1.0649121	1.1890434	0.8944448	1.1111807	0.9687030	0.0054268	1.0859614	0	-1.2656429	0.2200040	Non-Manipulator
0.9195551	1.0131695	0.9922188	1.1078265	1.0163848	0.9090445	0.0112301	0.6740946	0	-1.7267842	0.1509994	Non-Manipulator
0.7534068	1.5691869	0.6081088	1.1645313	1.6824375	0.8717324	-0.0136740	0.7639127	0	-0.4127518	0.3982525	Non-Manipulator
1.0744122	0.8297051	0.2315287	1.0043812	0.9778002	1.1013130	-0.0259537	0.8519979	0	-3.2345594	0.0378857	Non-Manipulator
1.2960387	1.4213376	0.8226402	0.9639683	1.2703637	0.9661859	0.0185830	1.0717903	0	-0.3793891	0.4062742	Non-Manipulator
1.6899290	1.1585990	1.2926860	0.6229868	1.9424859	0.9908009	-0.1204254	1.1780924	0	-3.3623781	0.0334922	Non-Manipulator
1.1162360	0.9975212	-0.8724745	1.0857073	1.0821643	0.9768803	-0.0098758	1.1540887	0	-2.6316009	0.0671321	Non-Manipulator
1.1452359	0.9590605	1.0516176	1.0417626	0.8820121	1.0188386	-0.0711494	1.0450827	0	-2.8853782	0.0528811	Non-Manipulator
1.2838470	1.2293211	-0.7635950	1.4509272	0.7581653	0.8386986	0.2006408	0.8718586	0	2.3831146	0.9155306	Manipulator
0.6447596	1.1280487	0.6848734	1.2402154	0.8570222	0.8295543	-0.0762830	0.9338472	0	-2.5890346	0.0698475	Non-Manipulator
0.6348343	0.9435196	0.5053562	1.1245209	1.0709104	0.9726914	-0.1276365	0.7589628	0	-4.2429205	0.0141621	Non-Manipulator
1.2430133	0.9547926	1.5842742	0.8903097	0.9756770	1.0057186	-0.1340371	0.9749900	0	-3.8156350	0.0215491	Non-Manipulator
0.8872778	1.0301136	1.0548932	1.0639372	1.2112824	1.0583183	-0.0258306	0.9962276	0	-2.4252848	0.0812648	Non-Manipulator
0.9437845	0.6357944	1.1592586	1.3320953	0.9646783	1.6298028	-0.2018943	0.9232485	0	-4.7633846	0.0084644	Non-Manipulator
0.9099212	0.8420439	1.4141344	0.8026157	0.9244660	1.4839044	-0.0215196	0.8599734	0	-3.7038720	0.0240360	Non-Manipulator
1.1211037	1.0056862	1.3722891	1.1200231	0.9915256	1.0297295	-0.0107467	0.8387814	0	-1.5739359	0.1716560	Non-Manipulator
1.0805245	1.0013786	1.0037187	1.1915115	0.9502420	0.9059557	-0.0530910	1.1419559	0	-2.1597387	0.1034247	Non-Manipulator
1.1926166	0.8780663	3.2528845	1.0193372	0.9865301	1.3852182	-0.0440167	0.9436854	0	-2.0153176	0.1176040	Non-Manipulator
1.3963879	0.8692832	0.8480910	0.8747522	1.0934972	2.7130971	-0.0426874	1.3256475	0	-3.1986204	0.0392177	Non-Manipulator
1.0441750	0.9662983	1.0228752	1.1323936	0.8970903	1.1751619	-0.0230377	0.9363260	0	-2.0961928	0.1094674	Non-Manipulator
1.0272556	0.8043276	0.6879182	1.3503507	0.4479683	0.8859843	0.1941147	1.0604750	0	0.5529279	0.6348146	Manipulator
0.5418763	0.9949464	1.2042960	1.2390473	1.0788443	0.8535113	-0.0746088	1.0042519	0	-3.0290434	0.0461309	Non-Manipulator
0.6005730	0.2815815	1.0877606	0.9170526	0.8658730	0.9987556	-0.1039577	1.0907668	0	-6.8741999	0.0010331	Non-Manipulator
3.2034890	1.0624192	1.0031954	0.3708950	4.2291191	1.0220460	0.0412626	0.8536828	0	-0.1283783	0.4679494	Non-Manipulator
0.0150960	1.0436989	0.8210165	0.9162210	1.1459470	1.0480712	-0.0669763	0.7853168	0	-4.8201878	0.0080007	Non-Manipulator
1.1910593	1.0145685	2.3157255	1.2308985	0.8038250	1.5219564	0.1046987	1.0143156	0	0.6161380	0.6493397	Manipulator
1.1382683	1.0797110	0.8006484	1.0668082	1.0558132	1.0787399	0.0600122	1.0029496	0	-0.8977300	0.2895172	Non-Manipulator
1.1343925	1.2090659	1.6609972	1.2359561	1.0843405	1.0741284	-0.0326578	1.2070593	0	-0.7693806	0.3166131	Non-Manipulator
1.1766962	1.0008968	1.1039884	1.0941853	1.1485009	0.9591159	-0.0134682	1.1564473	0	-1.8392558	0.1371393	Non-Manipulator
1.1998527	1.7832897	0.9249061	1.2266628	1.2128273	0.8750526	0.1323879	1.0158049	0	3.0241868	0.9536549	Manipulator
1.2801605	0.9617017	1.1060191	1.0220193	1.2519706	1.2522059	-0.1141188	0.8341306	0	-3.1434590	0.0413498	Non-Manipulator
1.1109954	1.4857032	0.7504062	1.3673245	1.0757982	1.0313985	0.1061437	1.1187564	0	1.9631096	0.8768691	Manipulator
1.1319732	1.0253946	1.1886804	1.0374195	1.0589649	1.1265581	-0.0230799	1.2387123	0	-2.1475714	0.1045584	Non-Manipulator
1.0490645	1.0717915	0.9924033	1.3284350	1.1165445	0.8492011	-0.0528306	1.0849423	0	-1.4736915	0.1863822	Non-Manipulator
0.7833799	1.1083493	0.9280609	1.7022967	0.8716810	1.6870861	-0.0538134	1.0087339	0	-0.4762973	0.3831269	Non-Manipulator
1.1864107	-0.4224211	0.7326836	3.1672668	2.1861047	1.5675167	-0.0226769	1.0989625	0	0.4940288	0.6210551	Manipulator
1.1357888	1.0164602	2.2345448	0.9708796	1.0988671	0.9947469	0.0239694	0.6373072	0	-1.2387031	0.2246618	Non-Manipulator
0.8419859	1.3494415	0.8822560	1.3786971	0.9894869	0.9420856	0.0701810	1.1218879	0	0.7211119	0.6728518	Manipulator
2.6560739	0.9865298	0.9928237	0.5714868	0.9190550	1.2088638	0.0503894	0.8817004	0	-0.4744035	0.3835745	Non-Manipulator
1.1771814	1.0155478	0.8722046	1.4151208	0.7881163	0.7801966	0.0476529	1.3032433	0	-0.0627827	0.4843095	Non-Manipulator
0.8557678	1.0000000	-0.6754860	1.2000477	0.6956110	0.8653502	0.0100873	1.0515386	0	-2.2971428	0.0913599	Non-Manipulator
1.1386982	1.0236517	1.0401495	1.2716235	0.9229462	1.1418444	0.0144210	0.9899184	0	-0.8240819	0.3048979	Non-Manipulator
0.9642787	0.9131243	1.1512540	1.0224500	1.0089838	0.8809974	-0.1025242	0.9467688	0	-3.7072029	0.0239580	Non-Manipulator
0.8063219	1.0353366	1.2853989	1.1337822	1.0431375	0.7483943	-0.0485056	1.1557825	0	-2.5476374	0.0725854	Non-Manipulator
1.3418228	0.7616328	1.3082302	1.0444722	0.9958875	1.1506102	-0.0278556	1.1157082	0	-2.6288558	0.0673042	Non-Manipulator
0.7792560	1.1545033	-1.6142427	1.1219667	1.0665942	0.7088228	0.0255589	1.0314131	0	-2.3176130	0.0896747	Non-Manipulator
0.9830257	0.6153528	0.8429987	1.1019305	1.0340944	1.0434993	-0.1967489	1.2502199	0	-5.7516259	0.0031675	Non-Manipulator
0.6336870	1.0147155	0.9416773	1.2858697	0.8086312	1.6290050	-0.0829508	0.9592357	0	-2.8244435	0.0560175	Non-Manipulator
1.0128621	1.0855065	0.5606472	1.0656779	1.0197382	0.9407293	-0.0761348	1.1293544	0	-2.8608084	0.0541253	Non-Manipulator
1.4596333	0.6902044	1.1729498	0.6013727	1.1662629	1.0000000	-0.2157305	1.2550625	0	-6.5978678	0.0013614	Non-Manipulator
1.3585661	0.9642246	0.8750061	1.1121789	0.9338891	1.0932588	0.0014884	1.2312139	0	-1.5307241	0.1778878	Non-Manipulator
0.7137346	-2.4711725	0.8342107	1.3412185	1.0914575	1.7586090	-0.0021355	0.9618076	0	-13.1992607	0.0000019	Non-Manipulator
0.7655702	1.0967262	1.2416358	0.9079199	0.9948926	1.2617192	-0.1164623	0.9849394	0	-3.9720882	0.0184859	Non-Manipulator
0.6667837	1.4772038	0.1239857	1.6313193	0.9994427	0.6507894	-0.0062024	0.9449469	0	0.6297638	0.6524359	Manipulator
0.9422462	0.9926843	0.7860243	1.1545350	1.3168555	1.0511449	-0.0160622	2.1134232	0	-2.5476215	0.0725864	Non-Manipulator
1.0842691	0.5172172	2.6605469	0.8683458	0.9544248	0.8881737	-0.0496457	1.1578990	0	-4.2862296	0.0135700	Non-Manipulator
1.3675977	1.1395882	1.1436588	0.9474353	0.9950454	1.2426023	-0.0821045	1.0829983	0	-2.3656041	0.0858334	Non-Manipulator
1.0928060	1.0000000	1.0949835	1.1168084	0.9442538	1.1486700	-0.0540295	0.9395380	0	-2.3084030	0.0904294	Non-Manipulator
1.3294023	1.5382413	0.9062507	1.1529335	0.9892475	1.2614440	0.1863118	1.2298431	0	2.7196667	0.9381772	Manipulator
1.1798710	1.0313630	1.0531171	0.9831866	1.0718222	0.9564953	0.0030705	1.1702730	0	-1.9465368	0.1249315	Non-Manipulator
1.0949420	0.9560342	1.0897934	1.4233519	0.8524574	1.3194937	0.0238774	1.0623391	0	-0.4841108	0.3812819	Non-Manipulator
1.2615174	2.1374267	0.8433746	0.9586800	1.0601798	1.1312214	-0.0037352	1.0311830	0	1.6897447	0.8441906	Manipulator
0.8315740	0.9743480	0.8376203	1.0047435	0.9566446	1.0686428	-0.1212348	0.6541849	0	-4.0055100	0.0178891	Non-Manipulator
0.5423777	0.8771986	1.0649364	1.6538921	0.8144178	1.1279738	0.0026549	0.9934032	0	-1.0767355	0.2541243	Non-Manipulator
1.1886187	0.7599242	1.2265152	1.0984233	0.9616837	0.8998098	0.0599161	1.0698283	0	-1.6484525	0.1613182	Non-Manipulator
1.2321914	1.0633013	0.0213493	0.9649564	0.8368853	1.1039609	0.0332890	0.9985262	0	-1.7523328	0.1477532	Non-Manipulator
1.0694060	1.1018645	-0.3569689	1.3092921	1.1030710	0.9063922	-0.0211553	1.1168899	0	-1.5136671	0.1803960	Non-Manipulator
4.7066719	-0.6833701	-2.1314849	0.2641226	1.2529079	1.4688292	-0.3765647	2.0439130	0	-10.4740553	0.0000283	Non-Manipulator
0.3682054	0.7382383	1.0918809	0.8280733	1.1140019	1.7474355	-0.0139884	0.7637745	0	-4.8309889	0.0079155	Non-Manipulator
1.0860630	1.0151545	0.5208938	1.0583864	1.0665062	1.0213458	0.0601894	1.0178127	0	-1.3302109	0.2091245	Non-Manipulator
1.0209539	5.2874560	-1.1071588	1.1415321	0.6646191	1.4430525	-0.1280382	0.9854290	0	10.2859278	0.9999659	Manipulator
1.0526508	1.0898599	1.4273454	0.9666720	1.0295544	1.0990488	-0.0566235	1.0040257	0	-2.5406447	0.0730575	Non-Manipulator
1.6294394	0.5552941	0.9170261	1.1066426	1.3250746	1.2206187	0.1204077	0.8915319	0	-0.8948086	0.2901185	Non-Manipulator
1.0891674	1.3671188	0.6746083	1.4930975	0.9578313	0.8644139	0.3270684	1.0372640	0	4.6406627	0.9904410	Manipulator
1.1483969	1.0967344	1.1888462	1.0805565	0.9620432	0.9609929	-0.1270164	0.5335012	0	-2.7129322	0.0622146	Non-Manipulator
1.3819983	0.6130169	0.8757479	0.9965197	1.0756134	1.4270198	-0.0444588	1.0229489	0	-3.5448704	0.0280621	Non-Manipulator
1.2534156	0.9699694	0.9793591	1.0264313	1.0708414	1.2330523	0.0406033	1.0627387	0	-1.4118452	0.1959432	Non-Manipulator
0.8034488	1.1739596	1.1826077	1.2199992	1.0685156	0.9532818	-0.0271015	1.0424360	0	-1.5213656	0.1792605	Non-Manipulator
0.6168898	0.4160078	0.5313485	1.8908678	3.1392551	0.3927856	-0.0156388	1.7214166	0	-2.3491966	0.0871296	Non-Manipulator
1.6933519	0.9265053	1.0283565	0.4165426	0.5051901	1.5494722	0.0005826	1.3268119	0	-3.5492284	0.0279435	Non-Manipulator
1.4047459	0.9345900	3.9875900	0.9267828	1.1038453	0.6964464	-0.1127035	1.0726615	0	-2.4239778	0.0813625	Non-Manipulator
0.9682326	0.9998751	1.0940056	1.2060656	1.0083162	0.7868206	0.0196576	1.1083091	0	-1.3754676	0.2017379	Non-Manipulator
2.0220315	-1.1356028	0.6214242	0.2768949	1.5091655	5.1043292	-0.0033884	1.2358707	0	-10.5429430	0.0000264	Non-Manipulator
1.1241582	0.9527442	1.2500471	1.0193130	1.0820128	1.0089863	-0.0360834	1.0479233	0	-2.5283513	0.0738944	Non-Manipulator
0.7457967	1.1133677	3.5222649	1.4431075	0.6779415	0.9997378	0.0438662	1.1402501	0	0.6091499	0.6477469	Manipulator
1.3815642	0.6174634	-0.6688350	0.6829797	1.3709670	0.7886075	-0.0458877	1.3599640	0	-5.3240178	0.0048495	Non-Manipulator
1.1718737	0.9964985	1.0247071	0.8983447	1.0322786	1.0581014	-0.0440325	1.1894730	0	-2.9592259	0.0493023	Non-Manipulator
0.8133732	1.3601952	1.0335734	1.2154681	1.0473230	0.9945431	-0.1260111	0.9518359	0	-2.1092009	0.1082058	Non-Manipulator
1.1026373	0.9878621	2.0371706	1.2166394	0.9885536	0.9254550	0.0355880	1.1289629	0	-0.6424627	0.3446901	Non-Manipulator
1.5604597	0.9058811	1.3092878	1.2054044	0.9436596	0.9887294	-0.0888569	1.0240086	0	-1.9243326	0.1273792	Non-Manipulator
0.8665799	1.0112353	-4.7123967	1.0249077	1.0681376	1.0574703	-0.0198142	1.0435592	0	-4.6381553	0.0095828	Non-Manipulator
1.0447626	1.1540945	2.1891075	1.4701580	0.9399885	1.2565508	0.0329088	0.9141502	0	0.8128456	0.6927156	Manipulator
0.9737888	1.0000000	1.7687200	1.2456023	0.9023129	0.7798302	-0.0279999	0.7495266	0	-1.4258035	0.1937534	Non-Manipulator
0.9785219	0.9976769	2.6282051	1.1067871	0.8523771	1.0130210	0.0076389	1.0026222	0	-1.2784478	0.2178146	Non-Manipulator
1.3184612	1.3497682	1.0724109	0.9780214	1.2317710	0.5925158	-0.0319183	1.0806035	0	-1.0561699	0.2580421	Non-Manipulator
0.9900830	1.0126704	1.0678418	0.9661278	0.9074346	1.1303931	0.0507843	0.9409530	0	-1.7105294	0.1530951	Non-Manipulator
1.0009418	1.0000000	0.5982301	1.9130918	0.8367368	0.8563726	-0.1194775	2.0689961	0	-1.0560729	0.2580606	Non-Manipulator
1.1989411	0.9492583	1.0861733	1.2600701	1.0032671	0.6095128	-0.1244758	1.0656580	0	-2.7013059	0.0628963	Non-Manipulator
1.6698616	1.0000000	1.0487378	0.6681663	1.0540065	0.5276267	-0.0159322	0.9371018	0	-2.5000135	0.0758572	Non-Manipulator
1.5962356	0.9841067	1.9945800	0.5372535	1.0017762	2.7822913	-0.0357053	0.9390134	0	-3.0390217	0.0456938	Non-Manipulator
0.9823994	0.4377219	1.2722035	1.0791647	1.0834219	1.0638796	-0.0067950	0.9092107	0	-3.8543741	0.0207473	Non-Manipulator
4.3666891	0.8573437	1.1789842	1.5311875	0.6888926	1.0485391	-0.0646816	1.0446488	0	3.8767372	0.9797022	Manipulator
0.4625391	1.0774403	1.0165885	1.2106643	0.8283455	0.4986629	-0.0695612	0.9567472	0	-2.9700973	0.0487952	Non-Manipulator
0.9053621	0.9971959	1.4205920	1.2434448	0.9391593	0.8747628	0.0027908	0.5305922	0	-1.2221308	0.2275617	Non-Manipulator
0.9818600	0.9430047	1.0401092	0.9979233	0.9675028	1.0907199	-0.1196128	0.9400609	0	-3.9075362	0.0196943	Non-Manipulator
0.6290123	1.0121636	1.5531649	1.3561618	0.8503641	1.1622904	0.0650645	0.8533763	0	-0.5536110	0.3650270	Non-Manipulator
1.3282258	1.0000000	1.0551367	0.9649782	1.0152688	0.9211492	-0.0843408	0.9257241	0	-2.8319330	0.0556228	Non-Manipulator
0.9413643	1.0000000	0.7815276	1.1530189	0.9561506	1.5801388	-0.1232787	0.8808851	0	-3.3507935	0.0338692	Non-Manipulator
0.6846472	1.3316146	0.9784974	0.6028925	0.9996751	1.3014184	-0.1069146	1.2708443	0	-4.4798791	0.0112077	Non-Manipulator
0.9064776	1.1173152	1.9521019	1.0035470	0.9016311	0.9844599	-0.0881360	0.7524820	0	-2.6562106	0.0656073	Non-Manipulator
0.9259960	0.9386059	-0.2877417	1.1654175	1.0019079	1.2040499	-0.0116029	1.0382802	0	-2.6287783	0.0673091	Non-Manipulator
1.0031572	1.0217826	0.4379811	1.3740001	1.1500033	1.0178002	0.1089464	0.9842432	0	0.2373399	0.5590580	Manipulator
1.0664227	0.8357531	1.4841648	1.1583797	0.8284590	1.2084517	-0.1016223	1.0758572	0	-3.2421512	0.0376099	Non-Manipulator
0.9434642	1.1830182	1.0038501	0.8909600	1.7511074	1.8001888	-0.0164841	0.9038513	0	-2.3012504	0.0910195	Non-Manipulator
1.0080286	0.8846495	1.2589248	1.0542344	1.0909714	0.9373962	-0.0444454	0.9889219	0	-2.8974201	0.0522812	Non-Manipulator
0.9203359	1.0518352	-0.6184836	0.9938461	1.1091014	1.0390778	-0.0578195	0.9899370	0	-3.5182435	0.0287976	Non-Manipulator
0.5806438	1.5652977	1.0187327	1.2833577	0.7903174	0.9623617	-0.0897653	1.0882889	0	-1.1865986	0.2338678	Non-Manipulator
0.6086299	1.3592607	0.6756935	0.9888852	1.1461599	0.2463934	-0.0772190	0.9578634	0	-2.7835567	0.0582192	Non-Manipulator
2.2987174	0.8282047	1.4176667	0.3566133	0.9928319	2.7971947	0.0270788	0.6934143	0	-2.4004271	0.0831401	Non-Manipulator
0.9395176	0.9684366	0.9459607	1.2430085	1.0213302	0.9191539	-0.0084002	0.9665350	0	-1.7333206	0.1501633	Non-Manipulator
0.6434779	1.4479366	4.5587072	1.0797592	0.5327476	0.9261324	0.0332375	0.8019311	0	0.6485859	0.6566917	Manipulator
2.1791502	1.1572175	1.0737340	0.9820204	0.7401288	0.8027234	0.0453680	1.0085356	0	0.6794756	0.6636216	Manipulator
0.9823922	0.8608333	1.1159177	1.1971008	0.9946824	1.0982299	-0.1637457	0.9687974	0	-3.9968532	0.0180419	Non-Manipulator
0.6814433	1.0210770	0.9395782	0.8409231	1.2935338	1.1089556	0.0268865	0.9132988	0	-2.9489829	0.0497846	Non-Manipulator
1.2530472	0.9945321	0.3010319	0.9693309	1.0700047	0.8639408	0.0531343	1.0173072	0	-1.6019035	0.1677157	Non-Manipulator
0.6942527	1.0148342	2.0073558	0.9559892	0.9533883	0.8582277	-0.2661440	1.6708469	0	-5.9897680	0.0024980	Non-Manipulator
1.8034831	0.8693593	-1.5565687	1.0721339	0.9962768	0.7333337	0.0807357	1.1367855	0	-1.1279756	0.2445349	Non-Manipulator
0.9780062	0.9502079	0.8971953	1.0633986	0.8737707	1.1258085	-0.0635964	0.5066311	0	-2.8686902	0.0537232	Non-Manipulator
0.7879538	1.0000000	0.8263780	1.1353082	0.9355863	1.7888016	-0.0871621	1.0120600	0	-3.2627277	0.0368722	Non-Manipulator
1.0020263	0.9981181	-0.9176047	1.0889615	1.0305268	1.0767704	-0.0010788	1.0800093	0	-2.6860647	0.0638007	Non-Manipulator
0.9093650	1.1702979	1.9718743	1.2790135	0.9716053	0.9859391	-0.0358540	1.0251020	0	-0.9738201	0.2741197	Non-Manipulator
0.9374027	0.9732923	1.1311307	1.0835771	1.0500106	0.9595124	-0.0952789	0.9763318	0	-3.2664738	0.0367394	Non-Manipulator
1.0449441	1.0214244	4.4378873	0.8707899	1.0264893	1.0604925	-0.1571463	0.9160698	0	-3.2350044	0.0378695	Non-Manipulator
0.9586639	0.9169850	0.9996518	1.1215239	1.0961739	0.9275385	-0.1452471	0.9353514	0	-3.9190918	0.0194724	Non-Manipulator