HW_4
Kei Cheng
6/8/2020
Question 9.1 Using the same crime data set uscrime.txt as in Question 8.2, apply Principal Component Analysis and then create a regression model using the first few principal components. Specify your new model in terms of the original variables (not the principal components), and compare its quality to that of your solution to Question 8.2. You can use the R function prcomp for PCA. (Note that to first scale the data, you can include scale. = TRUE to scale as part of the PCA function. Don’t forget that, to make a prediction for the new city, you’ll need to unscale the coefficients (i.e., do the scaling calculation in reverse)!)
PC1 explains 40% of the total variance, so it means 40% of the information in the dataset can be encapsulated by PC1. PC2 explains 18 %
#clear environment
rm(list = ls())
# Import data
uscrime <- read.table('uscrime.txt', stringsAsFactors = FALSE, header = TRUE)
head(uscrime)## M So Ed Po1 Po2 LF M.F Pop NW U1 U2 Wealth Ineq Prob
## 1 15.1 1 9.1 5.8 5.6 0.510 95.0 33 30.1 0.108 4.1 3940 26.1 0.084602
## 2 14.3 0 11.3 10.3 9.5 0.583 101.2 13 10.2 0.096 3.6 5570 19.4 0.029599
## 3 14.2 1 8.9 4.5 4.4 0.533 96.9 18 21.9 0.094 3.3 3180 25.0 0.083401
## 4 13.6 0 12.1 14.9 14.1 0.577 99.4 157 8.0 0.102 3.9 6730 16.7 0.015801
## 5 14.1 0 12.1 10.9 10.1 0.591 98.5 18 3.0 0.091 2.0 5780 17.4 0.041399
## 6 12.1 0 11.0 11.8 11.5 0.547 96.4 25 4.4 0.084 2.9 6890 12.6 0.034201
## Time Crime
## 1 26.2011 791
## 2 25.2999 1635
## 3 24.3006 578
## 4 29.9012 1969
## 5 21.2998 1234
## 6 20.9995 682summary(uscrime)## M So Ed Po1
## Min. :11.90 Min. :0.0000 Min. : 8.70 Min. : 4.50
## 1st Qu.:13.00 1st Qu.:0.0000 1st Qu.: 9.75 1st Qu.: 6.25
## Median :13.60 Median :0.0000 Median :10.80 Median : 7.80
## Mean :13.86 Mean :0.3404 Mean :10.56 Mean : 8.50
## 3rd Qu.:14.60 3rd Qu.:1.0000 3rd Qu.:11.45 3rd Qu.:10.45
## Max. :17.70 Max. :1.0000 Max. :12.20 Max. :16.60
## Po2 LF M.F Pop
## Min. : 4.100 Min. :0.4800 Min. : 93.40 Min. : 3.00
## 1st Qu.: 5.850 1st Qu.:0.5305 1st Qu.: 96.45 1st Qu.: 10.00
## Median : 7.300 Median :0.5600 Median : 97.70 Median : 25.00
## Mean : 8.023 Mean :0.5612 Mean : 98.30 Mean : 36.62
## 3rd Qu.: 9.700 3rd Qu.:0.5930 3rd Qu.: 99.20 3rd Qu.: 41.50
## Max. :15.700 Max. :0.6410 Max. :107.10 Max. :168.00
## NW U1 U2 Wealth
## Min. : 0.20 Min. :0.07000 Min. :2.000 Min. :2880
## 1st Qu.: 2.40 1st Qu.:0.08050 1st Qu.:2.750 1st Qu.:4595
## Median : 7.60 Median :0.09200 Median :3.400 Median :5370
## Mean :10.11 Mean :0.09547 Mean :3.398 Mean :5254
## 3rd Qu.:13.25 3rd Qu.:0.10400 3rd Qu.:3.850 3rd Qu.:5915
## Max. :42.30 Max. :0.14200 Max. :5.800 Max. :6890
## Ineq Prob Time Crime
## Min. :12.60 Min. :0.00690 Min. :12.20 Min. : 342.0
## 1st Qu.:16.55 1st Qu.:0.03270 1st Qu.:21.60 1st Qu.: 658.5
## Median :17.60 Median :0.04210 Median :25.80 Median : 831.0
## Mean :19.40 Mean :0.04709 Mean :26.60 Mean : 905.1
## 3rd Qu.:22.75 3rd Qu.:0.05445 3rd Qu.:30.45 3rd Qu.:1057.5
## Max. :27.60 Max. :0.11980 Max. :44.00 Max. :1993.0uscrime_pca <- prcomp(uscrime[,1:15], scale. = T)
summary(uscrime_pca)## Importance of components:
## PC1 PC2 PC3 PC4 PC5 PC6 PC7
## Standard deviation 2.4534 1.6739 1.4160 1.07806 0.97893 0.74377 0.56729
## Proportion of Variance 0.4013 0.1868 0.1337 0.07748 0.06389 0.03688 0.02145
## Cumulative Proportion 0.4013 0.5880 0.7217 0.79920 0.86308 0.89996 0.92142
## PC8 PC9 PC10 PC11 PC12 PC13 PC14
## Standard deviation 0.55444 0.48493 0.44708 0.41915 0.35804 0.26333 0.2418
## Proportion of Variance 0.02049 0.01568 0.01333 0.01171 0.00855 0.00462 0.0039
## Cumulative Proportion 0.94191 0.95759 0.97091 0.98263 0.99117 0.99579 0.9997
## PC15
## Standard deviation 0.06793
## Proportion of Variance 0.00031
## Cumulative Proportion 1.00000From the scree plot below, I set a cut-off of an eigenvalue > 1, and it suggested to use four variances. Since the first four factors together explain most of the variability in the dataset, it makes sense to only use these data. I used the code from https://rpubs.com/JanpuHou/278584 to build a pcaChart function to calculate the variances and proportion of variances. 
## [1] "proportions of variance:"
## [1] 0.401263510 0.186789802 0.133662956 0.077480520 0.063886598 0.036879593
## [7] 0.021454579 0.020493418 0.015677019 0.013325395 0.011712360 0.008546007
## [13] 0.004622779 0.003897851 0.000307611
Now I will use the first four PCs to create a model. After creating a model, I will get coefficients in terms of the original data and unscale them. The R-squared and R-squared adjusted values are the same as in the PCA model, but much lower compared to my last week’s model. Last week, my R-square and R-square adjusted values are 0.7659 and 0.7307, respectively.
## PC1 PC2 PC3 PC4
## [1,] -4.1992835 -1.09383120 -1.11907395 0.67178115 791
## [2,] 1.1726630 0.67701360 -0.05244634 -0.08350709 1635
## [3,] -4.1737248 0.27677501 -0.37107658 0.37793995 578
## [4,] 3.8349617 -2.57690596 0.22793998 0.38262331 1969
## [5,] 1.8392999 1.33098564 1.27882805 0.71814305 1234
## [6,] 2.9072336 -0.33054213 0.53288181 1.22140635 682
## [7,] 0.2457752 -0.07362562 -0.90742064 1.13685873 963
## [8,] -0.1301330 -1.35985577 0.59753132 1.44045387 1555
## [9,] -3.6103169 -0.68621008 1.28372246 0.55171150 856
## [10,] 1.1672376 3.03207033 0.37984502 -0.28887026 705
## [11,] 2.5384879 -2.66771358 1.54424656 -0.87671210 1674
## [12,] 1.0065920 -0.06044849 1.18861346 -1.31261964 849
## [13,] 0.5161143 0.97485189 1.83351610 -1.59117618 511
## [14,] 0.4265556 1.85044812 1.02893477 -0.07789173 664
## [15,] -3.3435299 0.05182823 -1.01358113 0.08840211 798
## [16,] -3.0310689 -2.10295524 -1.82993161 0.52347187 946
## [17,] -0.2262961 1.44939774 -1.37565975 0.28960865 539
## [18,] -0.1127499 -0.39407030 -0.38836278 3.97985093 929
## [19,] 2.9195668 -1.58646124 0.97612613 0.78629766 750
## [20,] 2.2998485 -1.73396487 -2.82423222 -0.23281758 1225
## [21,] 1.1501667 0.13531015 0.28506743 -2.19770548 742
## [22,] -5.6594827 -1.09730404 0.10043541 -0.05245484 439
## [23,] -0.1011749 -0.57911362 0.71128354 -0.44394773 1216
## [24,] 1.3836281 1.95052341 -2.98485490 -0.35942784 968
## [25,] 0.2727756 2.63013778 1.83189535 0.05207518 523
## [26,] 4.0565577 1.17534729 -0.81690756 1.66990720 1993
## [27,] 0.8929694 0.79236692 1.26822542 -0.57575615 342
## [28,] 0.1514495 1.44873320 0.10857670 -0.51040146 1216
## [29,] 3.5592481 -4.76202163 0.75080576 0.64692974 1043
## [30,] -4.1184576 -0.38073981 1.43463965 0.63330834 696
## [31,] -0.6811731 1.66926027 -2.88645794 -1.30977099 373
## [32,] 1.7157269 -1.30836339 -0.55971313 -0.70557980 754
## [33,] -1.8860627 0.59058174 1.43570145 0.18239089 1072
## [34,] 1.9526349 0.52395429 -0.75642216 0.44289927 923
## [35,] 1.5888864 -3.12998571 -1.73107199 -1.68604766 653
## [36,] 1.0709414 -1.65628271 0.79436888 -1.85172698 1272
## [37,] -4.1101715 0.15766712 2.36296974 -0.56868399 831
## [38,] -0.7254706 2.89263339 -0.36348376 -0.50612576 566
## [39,] -3.3451254 -0.95045293 0.19551398 -0.27716645 826
## [40,] -1.0644466 -1.05265304 0.82886286 -0.12042931 1151
## [41,] 1.4933989 1.86712106 1.81853582 -1.06112429 880
## [42,] -0.6789284 1.83156328 -1.65435992 0.95121379 542
## [43,] -2.4164258 -0.46701087 1.42808323 0.41149015 823
## [44,] 2.2978729 0.41865689 -0.64422929 -0.63462770 1030
## [45,] -2.9245282 -1.19488555 -3.35139309 -1.48966984 455
## [46,] 1.7654525 0.95655926 0.98576138 1.05683769 508
## [47,] 2.3125056 2.56161119 -1.58223354 0.59863946 849##
## Call:
## lm(formula = V5 ~ ., data = as.data.frame(uscrime_pc))
##
## Residuals:
## Min 1Q Median 3Q Max
## -557.76 -210.91 -29.08 197.26 810.35
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 905.09 49.07 18.443 < 2e-16 ***
## PC1 65.22 20.22 3.225 0.00244 **
## PC2 -70.08 29.63 -2.365 0.02273 *
## PC3 25.19 35.03 0.719 0.47602
## PC4 69.45 46.01 1.509 0.13872
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 336.4 on 42 degrees of freedom
## Multiple R-squared: 0.3091, Adjusted R-squared: 0.2433
## F-statistic: 4.698 on 4 and 42 DF, p-value: 0.003178## [1] 0.3091121## [1] 0.2433132After comparing the R-squared values, I will use the PCA model to predict the crime rate in the new city. The predict crime rate for the new city is 1112, which make sense comparing to other crime rates. However, my model from last week predicted that the crime rate to be 1304.
#Ues the new city data given from last week.
test_df <- data.frame(M = 14.0,
So = 0,
Ed = 10.0,
Po1 = 12.0,
Po2 = 15.5,
LF = 0.640,
M.F = 94.0,
Pop = 150,
NW = 1.1,
U1 = 0.120,
U2 = 3.6,
Wealth = 3200,
Ineq = 20.1,
Prob = 0.04,
Time = 39.0)
#Apply the PCA data to the test data
predict1 <- data.frame(predict(uscrime_pca, test_df))
#Then use the model to predict the new crime rate
predict2 <- predict(model_1, predict1)
predict2## 1
## 1112.678Question 10.1 Using the same crime data set uscrime.txt as in Questions 8.2 and 9.1, find the best model you can using (a) a regression tree model, and (b) a random forest model. In R, you can use the tree package or the rpart package, and the randomForest package. For each model, describe one or two qualitative takeaways you get from analyzing the results (i.e., don’t just stop when you have a good model, but interpret it too).
The tree model has an R-squared value of 72%, which is pretty. Then I tried the prune.tree function to see if it will improve the model’s performance. But it turns out that pruning the tree gives me a lower R-squared value, which is 67%.
## randomForest 4.6-14## Type rfNews() to see new features/changes/bug fixes.##
## Regression tree:
## tree(formula = Crime ~ ., data = uscrime)
## Variables actually used in tree construction:
## [1] "Po1" "Pop" "LF" "NW"
## Number of terminal nodes: 7
## Residual mean deviance: 47390 = 1896000 / 40
## Distribution of residuals:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -573.900 -98.300 -1.545 0.000 110.600 490.100
## [1] 0.7244962
## [1] 0.6691333The forest model give a R-squared value of 40%. The random forest methond is good at avoiding overfitting.
##
## Call:
## randomForest(formula = Crime ~ ., data = uscrime)
## Type of random forest: regression
## Number of trees: 500
## No. of variables tried at each split: 5
##
## Mean of squared residuals: 87461.6
## % Var explained: 40.26
## [1] 0.4025958Question 10.2 Describe a situation or problem from your job, everyday life, current events, etc., for which a logistic regression model would be appropriate. List some (up to 5) predictors that you might use.
A Logistic regression that can be used when the response is a probability or a binary. I can use it to estimate the probability that a person is getting infected by COVID-19. Some predictors are the amount of time a person spends in the public and the number of close family members who have coronavirus.
Question 10.3
My 5th iteration is odd.
set.seed(1)
g_credit <- read.table('germancredit.txt', stringsAsFactors = FALSE, header = F)
head(g_credit)## V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12 V13 V14 V15 V16 V17 V18
## 1 A11 6 A34 A43 1169 A65 A75 4 A93 A101 4 A121 67 A143 A152 2 A173 1
## 2 A12 48 A32 A43 5951 A61 A73 2 A92 A101 2 A121 22 A143 A152 1 A173 1
## 3 A14 12 A34 A46 2096 A61 A74 2 A93 A101 3 A121 49 A143 A152 1 A172 2
## 4 A11 42 A32 A42 7882 A61 A74 2 A93 A103 4 A122 45 A143 A153 1 A173 2
## 5 A11 24 A33 A40 4870 A61 A73 3 A93 A101 4 A124 53 A143 A153 2 A173 2
## 6 A14 36 A32 A46 9055 A65 A73 2 A93 A101 4 A124 35 A143 A153 1 A172 2
## V19 V20 V21
## 1 A192 A201 1
## 2 A191 A201 2
## 3 A191 A201 1
## 4 A191 A201 1
## 5 A191 A201 2
## 6 A192 A201 1#Convert1 and 2 to 0 and 1
g_credit$V21[g_credit$V21==1]<-0
g_credit$V21[g_credit$V21==2]<-1
#Split the data: 70% train data & 30% test data
data_train <-g_credit[sample(1:nrow(g_credit), size = round(nrow(g_credit)*0.7), replace = F),]
data_test <-g_credit[-sample(1:nrow(g_credit), size = round(nrow(g_credit)*0.7), replace = F),]
log_model <- glm(V21~., family = binomial(link = "logit"), data = data_train)
summary(log_model)##
## Call:
## glm(formula = V21 ~ ., family = binomial(link = "logit"), data = data_train)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.4438 -0.6861 -0.3608 0.6750 2.4540
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 3.823e-01 1.332e+00 0.287 0.774162
## V1A12 -5.201e-01 2.681e-01 -1.940 0.052408 .
## V1A13 -1.150e+00 4.473e-01 -2.570 0.010173 *
## V1A14 -1.675e+00 2.750e-01 -6.091 1.12e-09 ***
## V2 2.570e-02 1.159e-02 2.217 0.026647 *
## V3A31 8.440e-02 6.580e-01 0.128 0.897943
## V3A32 -8.078e-01 4.996e-01 -1.617 0.105907
## V3A33 -7.683e-01 5.372e-01 -1.430 0.152634
## V3A34 -1.446e+00 5.127e-01 -2.821 0.004784 **
## V4A41 -1.513e+00 4.479e-01 -3.379 0.000728 ***
## V4A410 -2.412e+00 1.160e+00 -2.080 0.037543 *
## V4A42 -5.496e-01 3.195e-01 -1.720 0.085354 .
## V4A43 -9.142e-01 3.024e-01 -3.023 0.002503 **
## V4A44 -4.163e-01 9.455e-01 -0.440 0.659751
## V4A45 -1.562e-01 6.742e-01 -0.232 0.816732
## V4A46 -2.569e-01 5.085e-01 -0.505 0.613382
## V4A48 -1.531e+01 4.556e+02 -0.034 0.973202
## V4A49 -5.397e-01 4.017e-01 -1.344 0.179086
## V5 1.076e-04 5.600e-05 1.922 0.054633 .
## V6A62 -3.474e-01 3.579e-01 -0.971 0.331777
## V6A63 -2.440e-01 4.761e-01 -0.513 0.608232
## V6A64 -1.379e+00 6.535e-01 -2.110 0.034823 *
## V6A65 -8.106e-01 3.223e-01 -2.515 0.011910 *
## V7A72 -1.814e-01 5.243e-01 -0.346 0.729300
## V7A73 -5.253e-01 5.001e-01 -1.050 0.293529
## V7A74 -1.129e+00 5.455e-01 -2.070 0.038431 *
## V7A75 -5.927e-01 5.052e-01 -1.173 0.240705
## V8 3.523e-01 1.094e-01 3.219 0.001284 **
## V9A92 4.849e-02 4.760e-01 0.102 0.918863
## V9A93 -4.446e-01 4.691e-01 -0.948 0.343279
## V9A94 -4.288e-01 5.837e-01 -0.735 0.462524
## V10A102 3.052e-01 5.338e-01 0.572 0.567472
## V10A103 -3.086e-01 5.237e-01 -0.589 0.555669
## V11 -1.080e-01 1.073e-01 -1.007 0.314147
## V12A122 2.219e-01 3.161e-01 0.702 0.482767
## V12A123 3.274e-01 2.922e-01 1.120 0.262504
## V12A124 1.156e+00 5.656e-01 2.044 0.040944 *
## V13 -2.257e-02 1.140e-02 -1.980 0.047667 *
## V14A142 -5.214e-01 4.925e-01 -1.059 0.289757
## V14A143 -7.780e-01 2.848e-01 -2.732 0.006299 **
## V15A152 -6.323e-01 2.870e-01 -2.203 0.027579 *
## V15A153 -6.674e-01 6.202e-01 -1.076 0.281931
## V16 2.866e-01 2.236e-01 1.282 0.199939
## V17A172 1.565e+00 8.891e-01 1.760 0.078442 .
## V17A173 1.564e+00 8.582e-01 1.823 0.068370 .
## V17A174 1.400e+00 8.772e-01 1.596 0.110563
## V18 1.645e-01 3.004e-01 0.548 0.583871
## V19A192 -3.319e-01 2.413e-01 -1.376 0.168942
## V20A202 -2.137e+00 8.573e-01 -2.493 0.012665 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 851.79 on 699 degrees of freedom
## Residual deviance: 613.21 on 651 degrees of freedom
## AIC: 711.21
##
## Number of Fisher Scoring iterations: 14#1st iteration
log_model <- glm(V21~V1+V2+V3+V4+V6+V7+V8+V12+V13+V14+V15+V20, family = binomial(link = "logit"), data = data_train)
summary(log_model)##
## Call:
## glm(formula = V21 ~ V1 + V2 + V3 + V4 + V6 + V7 + V8 + V12 +
## V13 + V14 + V15 + V20, family = binomial(link = "logit"),
## data = data_train)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.1343 -0.7151 -0.3829 0.6860 2.4613
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.954704 0.891687 2.192 0.028369 *
## V1A12 -0.576472 0.261484 -2.205 0.027481 *
## V1A13 -1.246843 0.431631 -2.889 0.003869 **
## V1A14 -1.633312 0.268529 -6.082 1.18e-09 ***
## V2 0.036245 0.009018 4.019 5.83e-05 ***
## V3A31 -0.077212 0.626544 -0.123 0.901921
## V3A32 -0.971152 0.467517 -2.077 0.037778 *
## V3A33 -0.743337 0.523613 -1.420 0.155715
## V3A34 -1.447406 0.498458 -2.904 0.003687 **
## V4A41 -1.375418 0.415248 -3.312 0.000925 ***
## V4A410 -2.141135 1.005226 -2.130 0.033171 *
## V4A42 -0.448810 0.306760 -1.463 0.143450
## V4A43 -0.939346 0.291483 -3.223 0.001270 **
## V4A44 -0.492708 0.950608 -0.518 0.604243
## V4A45 -0.238889 0.676434 -0.353 0.723969
## V4A46 -0.268251 0.499637 -0.537 0.591342
## V4A48 -15.257528 451.906122 -0.034 0.973066
## V4A49 -0.570040 0.388370 -1.468 0.142165
## V6A62 -0.307611 0.343036 -0.897 0.369862
## V6A63 -0.484692 0.466898 -1.038 0.299218
## V6A64 -1.212443 0.622420 -1.948 0.051421 .
## V6A65 -0.810257 0.313011 -2.589 0.009637 **
## V7A72 0.199964 0.461824 0.433 0.665025
## V7A73 -0.179579 0.428502 -0.419 0.675153
## V7A74 -0.874730 0.481305 -1.817 0.069154 .
## V7A75 -0.318585 0.442407 -0.720 0.471453
## V8 0.235399 0.095022 2.477 0.013237 *
## V12A122 0.282784 0.305057 0.927 0.353932
## V12A123 0.433363 0.275990 1.570 0.116365
## V12A124 1.052152 0.533417 1.972 0.048555 *
## V13 -0.022929 0.010929 -2.098 0.035904 *
## V14A142 -0.485528 0.484466 -1.002 0.316251
## V14A143 -0.716748 0.278048 -2.578 0.009944 **
## V15A152 -0.592894 0.264661 -2.240 0.025078 *
## V15A153 -0.512743 0.587424 -0.873 0.382735
## V20A202 -2.057069 0.840733 -2.447 0.014415 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 851.79 on 699 degrees of freedom
## Residual deviance: 628.99 on 664 degrees of freedom
## AIC: 700.99
##
## Number of Fisher Scoring iterations: 14#2nd
log_model <- glm(V21~V1+V2+V3+V4+V5+V6+V7+V8+V9+V10+V12+V14+V16+V20, family = binomial(link = "logit"), data = data_train)
summary(log_model)##
## Call:
## glm(formula = V21 ~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V9 +
## V10 + V12 + V14 + V16 + V20, family = binomial(link = "logit"),
## data = data_train)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.2462 -0.6956 -0.3953 0.6760 2.4277
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.303e-01 9.669e-01 0.135 0.89278
## V1A12 -5.800e-01 2.627e-01 -2.208 0.02724 *
## V1A13 -1.332e+00 4.334e-01 -3.074 0.00211 **
## V1A14 -1.710e+00 2.692e-01 -6.353 2.12e-10 ***
## V2 2.722e-02 1.137e-02 2.394 0.01665 *
## V3A31 9.884e-02 6.436e-01 0.154 0.87794
## V3A32 -7.908e-01 4.866e-01 -1.625 0.10415
## V3A33 -7.357e-01 5.249e-01 -1.402 0.16105
## V3A34 -1.483e+00 5.000e-01 -2.966 0.00302 **
## V4A41 -1.427e+00 4.381e-01 -3.257 0.00112 **
## V4A410 -2.681e+00 1.112e+00 -2.411 0.01592 *
## V4A42 -4.295e-01 3.053e-01 -1.407 0.15938
## V4A43 -8.399e-01 2.944e-01 -2.853 0.00433 **
## V4A44 -3.986e-01 9.629e-01 -0.414 0.67893
## V4A45 -3.058e-01 6.584e-01 -0.465 0.64228
## V4A46 -1.262e-01 4.882e-01 -0.258 0.79606
## V4A48 -1.528e+01 4.594e+02 -0.033 0.97348
## V4A49 -5.376e-01 3.911e-01 -1.375 0.16928
## V5 8.507e-05 5.311e-05 1.602 0.10919
## V6A62 -1.985e-01 3.434e-01 -0.578 0.56309
## V6A63 -4.018e-01 4.662e-01 -0.862 0.38883
## V6A64 -1.325e+00 6.314e-01 -2.098 0.03589 *
## V6A65 -8.503e-01 3.144e-01 -2.705 0.00683 **
## V7A72 4.714e-01 4.537e-01 1.039 0.29882
## V7A73 9.016e-02 4.253e-01 0.212 0.83212
## V7A74 -5.633e-01 4.757e-01 -1.184 0.23640
## V7A75 -2.568e-01 4.444e-01 -0.578 0.56339
## V8 3.071e-01 1.056e-01 2.908 0.00364 **
## V9A92 9.178e-02 4.517e-01 0.203 0.83898
## V9A93 -4.491e-01 4.507e-01 -0.997 0.31897
## V9A94 -3.538e-01 5.594e-01 -0.632 0.52709
## V10A102 2.701e-01 5.233e-01 0.516 0.60577
## V10A103 -3.480e-01 5.203e-01 -0.669 0.50356
## V12A122 1.943e-01 3.063e-01 0.634 0.52597
## V12A123 3.065e-01 2.814e-01 1.089 0.27607
## V12A124 7.751e-01 3.716e-01 2.086 0.03699 *
## V14A142 -5.525e-01 4.866e-01 -1.135 0.25621
## V14A143 -7.336e-01 2.805e-01 -2.615 0.00892 **
## V16 2.078e-01 2.124e-01 0.979 0.32782
## V20A202 -1.753e+00 8.231e-01 -2.130 0.03320 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 851.79 on 699 degrees of freedom
## Residual deviance: 630.28 on 660 degrees of freedom
## AIC: 710.28
##
## Number of Fisher Scoring iterations: 14#3rd
log_model <- glm(V21~V1+V2+V3+V4+V5+V6+V7+V8+V9+V10+V12+V14+V20, family = binomial(link = "logit"), data = data_train)
summary(log_model)##
## Call:
## glm(formula = V21 ~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V9 +
## V10 + V12 + V14 + V20, family = binomial(link = "logit"),
## data = data_train)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.2538 -0.6875 -0.3929 0.6807 2.4314
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 5.263e-01 8.765e-01 0.600 0.54824
## V1A12 -5.966e-01 2.622e-01 -2.275 0.02289 *
## V1A13 -1.356e+00 4.325e-01 -3.135 0.00172 **
## V1A14 -1.718e+00 2.691e-01 -6.384 1.72e-10 ***
## V2 2.635e-02 1.130e-02 2.332 0.01972 *
## V3A31 -3.508e-02 6.271e-01 -0.056 0.95538
## V3A32 -9.209e-01 4.673e-01 -1.971 0.04873 *
## V3A33 -7.445e-01 5.238e-01 -1.421 0.15527
## V3A34 -1.459e+00 4.977e-01 -2.931 0.00338 **
## V4A41 -1.426e+00 4.360e-01 -3.271 0.00107 **
## V4A410 -2.723e+00 1.098e+00 -2.480 0.01314 *
## V4A42 -4.378e-01 3.044e-01 -1.438 0.15039
## V4A43 -8.542e-01 2.940e-01 -2.906 0.00366 **
## V4A44 -4.385e-01 9.574e-01 -0.458 0.64694
## V4A45 -2.727e-01 6.605e-01 -0.413 0.67974
## V4A46 -1.540e-01 4.876e-01 -0.316 0.75207
## V4A48 -1.532e+01 4.568e+02 -0.034 0.97324
## V4A49 -5.229e-01 3.907e-01 -1.338 0.18080
## V5 8.716e-05 5.297e-05 1.645 0.09987 .
## V6A62 -1.814e-01 3.413e-01 -0.532 0.59496
## V6A63 -4.269e-01 4.659e-01 -0.916 0.35948
## V6A64 -1.310e+00 6.297e-01 -2.080 0.03757 *
## V6A65 -8.523e-01 3.145e-01 -2.710 0.00673 **
## V7A72 4.529e-01 4.537e-01 0.998 0.31821
## V7A73 7.190e-02 4.250e-01 0.169 0.86566
## V7A74 -5.610e-01 4.757e-01 -1.179 0.23829
## V7A75 -2.426e-01 4.445e-01 -0.546 0.58516
## V8 3.048e-01 1.052e-01 2.897 0.00376 **
## V9A92 1.048e-01 4.508e-01 0.232 0.81616
## V9A93 -4.416e-01 4.501e-01 -0.981 0.32653
## V9A94 -3.395e-01 5.596e-01 -0.607 0.54403
## V10A102 2.699e-01 5.236e-01 0.515 0.60621
## V10A103 -3.433e-01 5.204e-01 -0.660 0.50943
## V12A122 1.797e-01 3.056e-01 0.588 0.55646
## V12A123 3.088e-01 2.809e-01 1.099 0.27171
## V12A124 7.765e-01 3.708e-01 2.094 0.03623 *
## V14A142 -5.193e-01 4.846e-01 -1.072 0.28381
## V14A143 -7.343e-01 2.807e-01 -2.616 0.00889 **
## V20A202 -1.784e+00 8.245e-01 -2.164 0.03046 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 851.79 on 699 degrees of freedom
## Residual deviance: 631.24 on 661 degrees of freedom
## AIC: 709.24
##
## Number of Fisher Scoring iterations: 14#4th
log_model <- glm(V21~V1+V2+V4+V6+V8+V12+V14+V20, family = binomial(link = "logit"), data = data_train)
summary (log_model)##
## Call:
## glm(formula = V21 ~ V1 + V2 + V4 + V6 + V8 + V12 + V14 + V20,
## family = binomial(link = "logit"), data = data_train)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.1199 -0.7472 -0.4480 0.8419 2.4787
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.379306 0.459861 -0.825 0.40947
## V1A12 -0.474383 0.243169 -1.951 0.05108 .
## V1A13 -1.288365 0.410994 -3.135 0.00172 **
## V1A14 -1.781931 0.255820 -6.966 3.27e-12 ***
## V2 0.036188 0.008534 4.240 2.23e-05 ***
## V4A41 -1.417220 0.412459 -3.436 0.00059 ***
## V4A410 -2.127508 0.944392 -2.253 0.02427 *
## V4A42 -0.267599 0.287295 -0.931 0.35162
## V4A43 -0.808736 0.273735 -2.954 0.00313 **
## V4A44 -0.230516 0.887256 -0.260 0.79501
## V4A45 -0.181337 0.651500 -0.278 0.78075
## V4A46 -0.061361 0.464150 -0.132 0.89483
## V4A48 -14.810511 477.911966 -0.031 0.97528
## V4A49 -0.375642 0.359514 -1.045 0.29609
## V6A62 -0.128174 0.322781 -0.397 0.69130
## V6A63 -0.446054 0.430723 -1.036 0.30039
## V6A64 -1.179433 0.586282 -2.012 0.04425 *
## V6A65 -0.840802 0.293142 -2.868 0.00413 **
## V8 0.149793 0.089951 1.665 0.09586 .
## V12A122 0.344182 0.286458 1.202 0.22955
## V12A123 0.481438 0.261817 1.839 0.06594 .
## V12A124 0.912335 0.340060 2.683 0.00730 **
## V14A142 -0.324016 0.460411 -0.704 0.48159
## V14A143 -0.713641 0.262421 -2.719 0.00654 **
## V20A202 -1.617442 0.797811 -2.027 0.04263 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 851.79 on 699 degrees of freedom
## Residual deviance: 673.80 on 675 degrees of freedom
## AIC: 723.8
##
## Number of Fisher Scoring iterations: 14#5th
log_model <- glm(V21~V1+V2+V4+V6+V12+V14+V20, family = binomial(link = "logit"), data = data_train)
summary (log_model)##
## Call:
## glm(formula = V21 ~ V1 + V2 + V4 + V6 + V12 + V14 + V20, family = binomial(link = "logit"),
## data = data_train)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.1905 -0.7603 -0.4411 0.8490 2.4410
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.032372 0.387388 0.084 0.933402
## V1A12 -0.505237 0.241951 -2.088 0.036782 *
## V1A13 -1.311344 0.409828 -3.200 0.001376 **
## V1A14 -1.782295 0.255256 -6.982 2.90e-12 ***
## V2 0.035996 0.008477 4.246 2.17e-05 ***
## V4A41 -1.450269 0.409841 -3.539 0.000402 ***
## V4A410 -2.178718 0.942274 -2.312 0.020767 *
## V4A42 -0.268855 0.286809 -0.937 0.348553
## V4A43 -0.753365 0.270826 -2.782 0.005407 **
## V4A44 -0.167882 0.885500 -0.190 0.849631
## V4A45 -0.113295 0.647735 -0.175 0.861151
## V4A46 -0.045035 0.463882 -0.097 0.922661
## V4A48 -14.699464 478.891973 -0.031 0.975513
## V4A49 -0.377384 0.359077 -1.051 0.293266
## V6A62 -0.123506 0.321369 -0.384 0.700748
## V6A63 -0.502831 0.430984 -1.167 0.243329
## V6A64 -1.119890 0.582743 -1.922 0.054637 .
## V6A65 -0.806688 0.290646 -2.775 0.005512 **
## V12A122 0.361450 0.285866 1.264 0.206086
## V12A123 0.499577 0.261619 1.910 0.056190 .
## V12A124 0.975833 0.338287 2.885 0.003919 **
## V14A142 -0.255563 0.456179 -0.560 0.575326
## V14A143 -0.696566 0.262338 -2.655 0.007925 **
## V20A202 -1.631364 0.789137 -2.067 0.038708 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 851.79 on 699 degrees of freedom
## Residual deviance: 676.60 on 676 degrees of freedom
## AIC: 724.6
##
## Number of Fisher Scoring iterations: 14#Create a binary variable for significant varible
data_train$V1A12[data_train$V1 == "A12"] <- 1
data_train$V1A12[data_train$V1 != "A12"] <- 0
data_train$V1A13[data_train$V1 == "A13"] <- 1
data_train$V1A13[data_train$V1 != "A13"] <- 0
data_train$V1A14[data_train$V1 == "A14"] <- 1
data_train$V1A14[data_train$V1 != "A14"] <- 0
data_train$V4A41[data_train$V1 == "A41"] <- 1
data_train$V4A41[data_train$V1 != "A41"] <- 0
data_train$V4A410[data_train$V1 == "A410"] <- 1
data_train$V4A410[data_train$V1 != "A410"] <- 0
data_train$V4A43[data_train$V1 == "A43"] <- 1
data_train$V4A43[data_train$V1 != "A43"] <- 0
data_train$V6A65[data_train$V1 == "A65"] <- 1
data_train$V6A65[data_train$V1 != "A65"] <- 0
data_train$V12A124[data_train$V1 == "A124"] <- 1
data_train$V12A124[data_train$V1 != "A124"] <- 0
data_train$V14A143[data_train$V1 == "A143"] <- 1
data_train$V14A143[data_train$V1 != "A143"] <- 0
data_train$V20A202[data_train$V1 == "A202"] <- 1
data_train$V20A202[data_train$V1 != "A202"] <- 0
#New model
log_model <- glm(V21~V1A12+V1A13+V1A14+V2+V4A41+V4A410+V4A43+V6A65+V12A124+V14A143+V20A202, family = binomial(link = "logit"), data = data_train)
summary (log_model)##
## Call:
## glm(formula = V21 ~ V1A12 + V1A13 + V1A14 + V2 + V4A41 + V4A410 +
## V4A43 + V6A65 + V12A124 + V14A143 + V20A202, family = binomial(link = "logit"),
## data = data_train)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.6202 -0.8274 -0.5204 0.9805 2.2733
##
## Coefficients: (7 not defined because of singularities)
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.839332 0.218057 -3.849 0.000119 ***
## V1A12 -0.516218 0.217998 -2.368 0.017885 *
## V1A13 -1.258624 0.388276 -3.242 0.001189 **
## V1A14 -1.895848 0.234655 -8.079 6.51e-16 ***
## V2 0.038297 0.007309 5.240 1.61e-07 ***
## V4A41 NA NA NA NA
## V4A410 NA NA NA NA
## V4A43 NA NA NA NA
## V6A65 NA NA NA NA
## V12A124 NA NA NA NA
## V14A143 NA NA NA NA
## V20A202 NA NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 851.79 on 699 degrees of freedom
## Residual deviance: 739.43 on 695 degrees of freedom
## AIC: 749.43
##
## Number of Fisher Scoring iterations: 4#Validation
data_test$V1A12[data_test$V1 == "A12"] <- 1
data_test$V1A12[data_test$V1 != "A12"] <- 0
data_test$V1A13[data_test$V1 == "A13"] <- 1
data_test$V1A13[data_test$V1 != "A13"] <- 0
data_test$V1A14[data_test$V1 == "A14"] <- 1
data_test$V1A14[data_test$V1 != "A14"] <- 0
#Predict model
predict_log <- predict(log_model,data_train, type = "response")## Warning in predict.lm(object, newdata, se.fit, scale = 1, type = if (type == :
## prediction from a rank-deficient fit may be misleadingpredict_log## 836 679 129 930 509 471 299
## 0.40618182 0.51993633 0.28987529 0.40618182 0.13990724 0.39259198 0.11447335
## 270 978 187 307 597 277 874
## 0.13990724 0.33934604 0.26680771 0.16990783 0.51993633 0.11447335 0.10333275
## 950 494 330 775 841 591 725
## 0.13990724 0.24494263 0.24494263 0.16268335 0.63166062 0.40618182 0.15431244
## 37 105 729 878 485 677 802
## 0.28967957 0.09316229 0.61838285 0.20480962 0.09316229 0.13990724 0.33934604
## 987 382 601 940 801 852 931
## 0.38001209 0.33934604 0.25209441 0.13990724 0.13990724 0.13990724 0.51993633
## 326 984 554 422 111 404 924
## 0.36982703 0.63166062 0.28987529 0.28987529 0.24494263 0.09983788 0.28987529
## 532 506 556 889 343 582 121
## 0.31408290 0.08688997 0.28987529 0.20480962 0.33934604 0.28987529 0.49122531
## 40 684 537 375 248 198 378
## 0.26680771 0.13990724 0.35216135 0.71955388 0.07548046 0.28987529 0.07819675
## 39 435 810 390 280 672 526
## 0.15251761 0.37879588 0.31408290 0.08389919 0.13990724 0.20480962 0.41099912
## 642 45 402 22 718 742 193
## 0.31408290 0.73084371 0.33934604 0.35216135 0.11447335 0.27436593 0.42030050
## 371 499 104 965 767 492 838
## 0.20480962 0.33934604 0.26680771 0.24494263 0.57677970 0.42030050 0.07030630
## 616 615 843 465 525 808 977
## 0.61838285 0.11447335 0.11447335 0.11447335 0.33934604 0.09316229 0.24494263
## 176 345 791 110 84 871 29
## 0.16990783 0.15251761 0.36555824 0.30589179 0.51993633 0.20480962 0.25209441
## 141 252 733 620 304 545 557
## 0.13375285 0.16268335 0.25938328 0.09316229 0.38784836 0.09316229 0.33934604
## 661 287 614 145 329 487 855
## 0.16268335 0.73084371 0.51993633 0.12664540 0.32755224 0.09316229 0.20480962
## 851 630 498 858 816 619 576
## 0.48165848 0.08389919 0.13990724 0.10333275 0.50578224 0.44852058 0.10333275
## 490 736 103 316 51 907 290
## 0.07548046 0.50578224 0.07548046 0.63166062 0.39259198 0.49122531 0.51993633
## 650 998 811 282 143 442 285
## 0.40618182 0.09316229 0.25938328 0.09316229 0.54851627 0.40618182 0.39259198
## 682 48 501 716 511 295 536
## 0.09316229 0.35216135 0.51993633 0.16990783 0.40618182 0.28967957 0.21522269
## 693 214 918 737 339 346 675
## 0.39259198 0.27907455 0.35216135 0.39259198 0.51993633 0.10333275 0.12664540
## 43 1 910 590 959 796 628
## 0.33934604 0.35216135 0.26680771 0.40618182 0.55798154 0.08389919 0.26680771
## 233 293 573 369 451 86 483
## 0.09316229 0.51993633 0.13990724 0.63166062 0.20480962 0.09316229 0.57677970
## 327 622 355 819 812 49 361
## 0.09316229 0.11447335 0.08688997 0.63166062 0.24494263 0.08997689 0.33934604
## 885 242 440 758 817 818 247
## 0.39259198 0.07548046 0.16268335 0.17894572 0.07548046 0.07548046 0.09316229
## 751 219 135 961 958 377 408
## 0.35216135 0.51993633 0.39236522 0.07548046 0.26680771 0.11447335 0.43416391
## 884 565 467 356 130 891 65
## 0.11447335 0.39259198 0.51993633 0.39259198 0.40618182 0.54851627 0.13990724
## 842 359 992 124 77 218 610
## 0.12664540 0.09316229 0.10333275 0.15251761 0.68333211 0.32755224 0.10333275
## 194 19 273 418 543 419 686
## 0.07548046 0.39259198 0.61838285 0.46257206 0.57677970 0.12664540 0.39236522
## 403 749 587 16 951 777 604
## 0.13990724 0.12664540 0.37879588 0.51993633 0.33934604 0.20480962 0.20480962
## 634 664 138 719 500 761 939
## 0.08389919 0.24494263 0.28987529 0.23526142 0.13375285 0.10333275 0.71955388
## 229 423 421 140 126 938 508
## 0.08389919 0.28987529 0.10333275 0.16268335 0.40618182 0.24494263 0.31408290
## 854 968 271 821 577 512 849
## 0.46257206 0.10333275 0.11447335 0.09316229 0.28987529 0.20480962 0.37879588
## 504 457 358 724 127 645 41
## 0.39259198 0.39697893 0.20480962 0.26680771 0.40618182 0.46257206 0.16990783
## 548 305 413 955 880 309 773
## 0.13990724 0.28967957 0.09316229 0.40618182 0.16990783 0.25938328 0.12664540
## 441 117 764 470 900 562 336
## 0.09316229 0.68333211 0.12664540 0.13990724 0.46257206 0.51993633 0.35216135
## 349 72 857 474 168 872 788
## 0.07548046 0.07819675 0.08688997 0.07548046 0.28205590 0.13375285 0.28967957
## 455 783 822 625 234 484 952
## 0.51993633 0.28987529 0.16268335 0.46257206 0.33934604 0.10333275 0.63166062
## 73 539 553 15 762 294 62
## 0.36982703 0.73084371 0.73084371 0.43416391 0.46257206 0.38001209 0.31408290
## 941 644 35 381 814 820 697
## 0.09316229 0.13990724 0.16268335 0.48165848 0.73084371 0.46257206 0.28987529
## 846 665 31 549 28 735 148
## 0.36555824 0.13375285 0.33934604 0.40618182 0.16268335 0.07030630 0.09316229
## 772 572 284 334 980 268 93
## 0.63166062 0.16990783 0.10333275 0.28967957 0.31408290 0.13990724 0.09316229
## 756 300 834 976 241 33 883
## 0.51993633 0.36555824 0.39259198 0.23526142 0.51993633 0.33934604 0.44852058
## 437 792 848 217 108 781 993
## 0.07548046 0.13990724 0.13990724 0.46257206 0.28987529 0.53445032 0.46257206
## 209 338 609 584 824 568 434
## 0.51993633 0.43416391 0.11447335 0.50578224 0.36982703 0.13990724 0.13990724
## 201 354 357 755 973 514 116
## 0.08389919 0.40618182 0.09316229 0.09316229 0.51993633 0.28987529 0.28967957
## 643 962 853 701 668 439 197
## 0.10333275 0.36555824 0.10333275 0.09316229 0.28967957 0.68333211 0.07548046
## 220 462 994 235 513 752 173
## 0.08688997 0.43416391 0.63166062 0.07030630 0.17894572 0.46257206 0.39259198
## 83 673 407 324 185 922 180
## 0.11447335 0.39236522 0.13990724 0.46257206 0.33934604 0.28967957 0.49122531
## 464 493 444 167 982 995 291
## 0.28987529 0.07548046 0.09316229 0.46257206 0.28967957 0.09316229 0.09316229
## 653 833 867 839 862 657 56
## 0.51993633 0.70765404 0.46257206 0.51993633 0.11447335 0.28987529 0.07548046
## 25 81 472 898 985 647 480
## 0.08688997 0.13990724 0.35216135 0.09316229 0.13990724 0.57677970 0.43416391
## 928 3 179 161 384 436 720
## 0.73084371 0.09316229 0.09316229 0.13990724 0.16268335 0.28987529 0.35672284
## 260 60 448 488 181 510 133
## 0.08997689 0.63166062 0.25209441 0.13990724 0.20480962 0.22415574 0.10333275
## 618 428 547 827 279 658 948
## 0.35216135 0.11447335 0.13990724 0.46257206 0.07548046 0.28967957 0.09316229
## 611 721 150 932 169 598 823
## 0.40618182 0.14763314 0.11447335 0.26680771 0.13990724 0.39259198 0.63166062
## 702 530 956 789 91 164 544
## 0.73084371 0.35216135 0.51993633 0.61838285 0.09316229 0.27436593 0.19645233
## 479 825 119 920 790 607 731
## 0.28987529 0.11447335 0.60454940 0.51993633 0.66653042 0.13990724 0.39259198
## 638 89 533 981 690 648 71
## 0.39236522 0.46257206 0.09316229 0.44852058 0.40618182 0.09316229 0.20480962
## 639 315 831 414 663 570 972
## 0.09316229 0.12512477 0.13990724 0.08688997 0.12664540 0.73084371 0.13990724
## 546 674 574 705 670 832 770
## 0.51993633 0.07548046 0.43416391 0.42030050 0.27907455 0.46257206 0.09316229
## 392 281 5 964 925 20 183
## 0.28987529 0.10333275 0.51993633 0.13990724 0.51993633 0.13990724 0.49122531
## 694 79 687 69 473 798 296
## 0.35216135 0.33913286 0.15251761 0.20480962 0.37879588 0.09316229 0.61838285
## 909 132 42 894 966 887 397
## 0.10333275 0.63166062 0.28987529 0.50578224 0.44852058 0.39259198 0.40618182
## 264 177 368 433 139 520 320
## 0.09316229 0.40618182 0.46257206 0.35216135 0.31408290 0.07548046 0.43416391
## 115 453 450 551 396 799 813
## 0.40618182 0.09316229 0.31408290 0.09316229 0.53445032 0.13990724 0.63166062
## 159 606 495 109 519 740 393
## 0.39259198 0.51993633 0.40618182 0.51993633 0.35216135 0.44852058 0.63166062
## 704 936 112 27 222 266 158
## 0.44852058 0.44852058 0.17894572 0.07548046 0.40618182 0.31408290 0.40618182
## 765 654 386 175 712 261 166
## 0.13990724 0.50578224 0.11447335 0.49122531 0.35216135 0.40618182 0.07548046
## 552 340 92 412 99 516 128
## 0.07548046 0.27436593 0.40618182 0.18673133 0.50578224 0.35216135 0.28987529
## 646 919 943 805 192 410 85
## 0.20480962 0.51993633 0.13990724 0.28987529 0.61838285 0.16268335 0.38784836
## 213 302 311 208 957 895 383
## 0.54851627 0.50578224 0.61838285 0.28987529 0.27907455 0.11447335 0.13094217
## 216 988 259 652 87 743 768
## 0.24494263 0.09644851 0.10333275 0.28987529 0.33934604 0.12664540 0.08688997
## 906 303 937 240 868 312 4
## 0.40618182 0.23526142 0.14763314 0.57677970 0.09316229 0.13990724 0.68333211
## 711 58 308 975 757 829 342
## 0.11447335 0.20480962 0.40618182 0.16990783 0.13375285 0.63166062 0.49122531
## 870 626 845 203 122 44 571
## 0.40618182 0.10333275 0.11447335 0.15431244 0.13990724 0.57677970 0.51993633
## 267 734 873 100 313 134 468
## 0.20480962 0.13990724 0.51993633 0.35672284 0.23526142 0.11447335 0.28967957
## 232 310 360 11 608 923 631
## 0.08389919 0.26680771 0.57677970 0.28987529 0.50578224 0.37879588 0.51993633
## 482 649 256 265 54 146 524
## 0.39259198 0.23526142 0.71955388 0.08688997 0.11447335 0.61838285 0.13990724
## 911 236 328 215 6 481 555
## 0.20480962 0.51993633 0.13990724 0.20480962 0.20480962 0.28987529 0.26680771
## 515 250 579 258 869 446 288
## 0.13990724 0.11447335 0.50578224 0.40618182 0.20480962 0.08389919 0.61838285
## 744 567 593 847 806 605 205
## 0.51993633 0.40618182 0.12664540 0.11447335 0.63166062 0.15251761 0.09316229
## 243 780 946 399 55 182 581
## 0.73084371 0.33934604 0.61838285 0.28987529 0.50578224 0.50578224 0.33934604
## 61 348 635 921 662 137 325
## 0.26680771 0.39259198 0.39259198 0.11447335 0.40618182 0.15431244 0.11447335
## 592 362 66 101 901 245 206
## 0.39259198 0.16268335 0.15431244 0.13990724 0.44359471 0.09316229 0.57677970
## 600 974 627 431 380 411 153
## 0.13990724 0.81129814 0.13375285 0.07285106 0.07548046 0.39259198 0.32755224
## 17 190 708 478 680 699 621
## 0.13990724 0.33934604 0.28987529 0.23526142 0.11447335 0.11447335 0.36555824
## 586 954 276 766 558 454 563
## 0.46257206 0.20480962 0.08389919 0.28987529 0.12664540 0.13990724 0.13375285
## 283 353 426 226 184 36 341
## 0.19645233 0.11447335 0.33934604 0.20480962 0.13990724 0.59092725 0.39259198
## 52 162 807 912 67 602 882
## 0.42030050 0.11447335 0.24494263 0.39259198 0.09316229 0.26680771 0.13990724
## 876 935 335 828 507 363 489
## 0.28205590 0.40618182 0.51993633 0.11447335 0.17894572 0.16268335 0.08688997
## 395 286 367 689 425 13 613
## 0.08389919 0.72324407 0.11447335 0.08389919 0.28987529 0.28987529 0.49122531
## 905 7 82 389 257 449 420
## 0.13990724 0.13990724 0.10333275 0.31408290 0.13990724 0.16268335 0.33934604
## 960 913 529 710 225 942 306
## 0.39259198 0.44852058 0.63166062 0.26680771 0.10333275 0.08688997 0.07548046
## 727 538 771 469 594 97 715
## 0.10333275 0.33934604 0.51993633 0.18673133 0.39259198 0.09316229 0.71955388
## 466 651 732 856 207 902 929
## 0.51993633 0.73084371 0.51993633 0.13990724 0.09316229 0.12246976 0.16990783
## 703 859 803 476 947 80 477
## 0.23526142 0.43416391 0.48165848 0.46257206 0.51993633 0.44852058 0.22415574
## 916 251 12 560 406 350 521
## 0.61838285 0.35216135 0.73084371 0.33934604 0.39259198 0.26680771 0.13990724
## 8 983 904 787 30 9 879
## 0.50578224 0.21522269 0.10333275 0.13094217 0.81129814 0.09316229 0.37879588
## 333 518 860 278 564 102 424
## 0.71955388 0.20480962 0.08389919 0.40618182 0.50578224 0.50578224 0.12664540
## 118 713 211 990 917 722 365
## 0.38784836 0.12664540 0.08389919 0.39259198 0.08688997 0.24494263 0.46257206