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(ggplot2)
library(corrplot)
## corrplot 0.84 loaded
library(car)
##
## Attaching package: 'car'
## The following object is masked from 'package:dplyr':
##
## recode
library(MASS)
##
## Attaching package: 'MASS'
## The following object is masked from 'package:dplyr':
##
## select
library(perturb)
library(ROCR)
## Loading required package: gplots
##
## Attaching package: 'gplots'
## The following object is masked from 'package:stats':
##
## lowess
library(tidyr)
concrete <- read.csv('/Users/kevinpiger/Desktop/這個資料夾要燒到光碟裡/Concrete_Data.csv')
colnames(concrete) <- c('Cement','Blast', 'FlyAsh', 'Water', 'Superplasticizer', 'Coarse', 'Fine', 'Age', 'Concrete')
# 將ＰＡ改為每平方公尺承受力量 #
concrete <- concrete %>% mutate(kgC = Concrete * 10)
attach(concrete)
# kgC 超過400的為 1 ,其餘為 0 #
over400 = matrix(0,length(concrete[,1]),1)
over400 <- ifelse(kgC >= 400, 1, 0)
concrete <- cbind(concrete,over400)
str(concrete)
## 'data.frame': 1029 obs. of 11 variables:
## $ Cement : num 540 332 332 199 266 ...
## $ Blast : num 0 142 142 132 114 ...
## $ FlyAsh : num 0 0 0 0 0 0 0 0 0 0 ...
## $ Water : num 162 228 228 192 228 228 228 228 228 192 ...
## $ Superplasticizer: num 2.5 0 0 0 0 0 0 0 0 0 ...
## $ Coarse : num 1055 932 932 978 932 ...
## $ Fine : num 676 594 594 826 670 ...
## $ Age : int 28 270 365 360 90 365 28 28 28 90 ...
## $ Concrete : num 61.9 40.3 41 44.3 47 ...
## $ kgC : num 619 403 410 443 470 ...
## $ over400 : num 1 1 1 1 1 1 0 1 0 0 ...
#將一維數據標準化
std <- function(v){
v_bar <- mean(v)
s <- sd(v)
t_score <- (v - v_bar)/s
return(t_score)
}
temp <- concrete[,c(1:8,11)]
temp[,1:8] <- temp[,1:8] %>% apply(2,std) %>%as.data.frame()
# 看各變數對於應變數之boxplot #
df<-gather(temp,measure,num,Cement:Age)
df$over400<-df$over400 %>% as.factor()
ggplot(data=df)+geom_boxplot(aes(x=measure,y=num,fill=over400))
# 看各變數之間是否有相關 #
# 圖表呈現 #
round(cor(as.matrix(concrete[,1:8])),3)
## Cement Blast FlyAsh Water Superplasticizer Coarse
## Cement 1.000 -0.274 -0.397 -0.080 0.094 -0.112
## Blast -0.274 1.000 -0.325 0.107 0.043 -0.283
## FlyAsh -0.397 -0.325 1.000 -0.258 0.377 -0.009
## Water -0.080 0.107 -0.258 1.000 -0.658 -0.182
## Superplasticizer 0.094 0.043 0.377 -0.658 1.000 -0.266
## Coarse -0.112 -0.283 -0.009 -0.182 -0.266 1.000
## Fine -0.221 -0.283 0.078 -0.452 0.222 -0.178
## Age 0.083 -0.044 -0.155 0.277 -0.193 -0.003
## Fine Age
## Cement -0.221 0.083
## Blast -0.283 -0.044
## FlyAsh 0.078 -0.155
## Water -0.452 0.277
## Superplasticizer 0.222 -0.193
## Coarse -0.178 -0.003
## Fine 1.000 -0.157
## Age -0.157 1.000
corrplot(cor(as.matrix(concrete[,1:8])))
# 挑出70% 的資料進行建模 #
n <- nrow(concrete)
set.seed(106354003)
concrete_new <- concrete[sample(n),]
t_idx <- sample(seq_len(n), size = round(0.7 * n))
concrete_train <- concrete_new[t_idx,] %>% as.data.frame()
concrete_test <- concrete_new[ - t_idx,] %>% as.data.frame()
# 建立最初模型 #
# 羅吉斯回歸 #
modle1.0 <- glm(over400 ~ Cement + Blast + FlyAsh + Water + Superplasticizer +Superplasticizer*Water+ Coarse + Fine + Age + Water *Superplasticizer , data = concrete_train,family=binomial(link="logit"), na.action=na.exclude)
# 檢定個別變數係數是否顯著 #
anova(object=modle1.0, test="Chisq")
## Analysis of Deviance Table
##
## Model: binomial, link: logit
##
## Response: over400
##
## Terms added sequentially (first to last)
##
##
## Df Deviance Resid. Df Resid. Dev Pr(>Chi)
## NULL 719 942.97
## Cement 1 131.761 718 811.21 < 2.2e-16 ***
## Blast 1 21.565 717 789.65 3.420e-06 ***
## FlyAsh 1 42.210 716 747.44 8.199e-11 ***
## Water 1 15.566 715 731.87 7.969e-05 ***
## Superplasticizer 1 3.305 714 728.57 0.06905 .
## Coarse 1 1.904 713 726.66 0.16768
## Fine 1 0.306 712 726.36 0.58019
## Age 1 156.261 711 570.10 < 2.2e-16 ***
## Water:Superplasticizer 1 0.337 710 569.76 0.56141
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(modle1.0)
##
## Call:
## glm(formula = over400 ~ Cement + Blast + FlyAsh + Water + Superplasticizer +
## Superplasticizer * Water + Coarse + Fine + Age + Water *
## Superplasticizer, family = binomial(link = "logit"), data = concrete_train,
## na.action = na.exclude)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -3.4649 -0.5815 -0.3007 0.5425 2.5850
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -5.8563634 8.4376291 -0.694 0.487634
## Cement 0.0170178 0.0028196 6.035 1.58e-09 ***
## Blast 0.0112936 0.0032392 3.487 0.000489 ***
## FlyAsh 0.0128767 0.0042563 3.025 0.002484 **
## Water -0.0277790 0.0147047 -1.889 0.058876 .
## Superplasticizer -0.0528684 0.1914016 -0.276 0.782381
## Coarse 0.0020987 0.0029331 0.716 0.474296
## Fine 0.0002726 0.0033787 0.081 0.935684
## Age 0.0255224 0.0029644 8.610 < 2e-16 ***
## Water:Superplasticizer 0.0006541 0.0011137 0.587 0.556977
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 942.97 on 719 degrees of freedom
## Residual deviance: 569.76 on 710 degrees of freedom
## AIC: 589.76
##
## Number of Fisher Scoring iterations: 5
AIC(modle1.0)
## [1] 589.7588
summary(modle1.0)
##
## Call:
## glm(formula = over400 ~ Cement + Blast + FlyAsh + Water + Superplasticizer +
## Superplasticizer * Water + Coarse + Fine + Age + Water *
## Superplasticizer, family = binomial(link = "logit"), data = concrete_train,
## na.action = na.exclude)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -3.4649 -0.5815 -0.3007 0.5425 2.5850
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -5.8563634 8.4376291 -0.694 0.487634
## Cement 0.0170178 0.0028196 6.035 1.58e-09 ***
## Blast 0.0112936 0.0032392 3.487 0.000489 ***
## FlyAsh 0.0128767 0.0042563 3.025 0.002484 **
## Water -0.0277790 0.0147047 -1.889 0.058876 .
## Superplasticizer -0.0528684 0.1914016 -0.276 0.782381
## Coarse 0.0020987 0.0029331 0.716 0.474296
## Fine 0.0002726 0.0033787 0.081 0.935684
## Age 0.0255224 0.0029644 8.610 < 2e-16 ***
## Water:Superplasticizer 0.0006541 0.0011137 0.587 0.556977
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 942.97 on 719 degrees of freedom
## Residual deviance: 569.76 on 710 degrees of freedom
## AIC: 589.76
##
## Number of Fisher Scoring iterations: 5
# 有顯著的變數剩下 Cement,Blast,FlyAsh,Water, Age #
# 再進行一次羅基斯回歸 #
modle1.1 <- glm(over400 ~ Cement + Blast + FlyAsh + Water + Age -1, data = concrete_train, family=binomial(link="logit"), na.action=na.exclude)
anova(modle1.1,test = 'Chisq')
## Analysis of Deviance Table
##
## Model: binomial, link: logit
##
## Response: over400
##
## Terms added sequentially (first to last)
##
##
## Df Deviance Resid. Df Resid. Dev Pr(>Chi)
## NULL 720 998.13
## Cement 1 10.080 719 988.05 0.001499 **
## Blast 1 7.264 718 980.79 0.007037 **
## FlyAsh 1 27.306 717 953.48 1.737e-07 ***
## Water 1 216.354 716 737.13 < 2.2e-16 ***
## Age 1 160.902 715 576.23 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
AIC(modle1.1)
## [1] 586.2268
summary(modle1.1)
##
## Call:
## glm(formula = over400 ~ Cement + Blast + FlyAsh + Water + Age -
## 1, family = binomial(link = "logit"), data = concrete_train,
## na.action = na.exclude)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -3.4399 -0.5763 -0.3102 0.5326 2.6476
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## Cement 0.015691 0.001283 12.228 < 2e-16 ***
## Blast 0.010510 0.001414 7.435 1.04e-13 ***
## FlyAsh 0.012091 0.001891 6.395 1.60e-10 ***
## Water -0.042693 0.003156 -13.528 < 2e-16 ***
## Age 0.024672 0.002779 8.878 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 998.13 on 720 degrees of freedom
## Residual deviance: 576.23 on 715 degrees of freedom
## AIC: 586.23
##
## Number of Fisher Scoring iterations: 5
# 逐步回歸 #
step(modle1.0,direction = 'both')
## Start: AIC=589.76
## over400 ~ Cement + Blast + FlyAsh + Water + Superplasticizer +
## Superplasticizer * Water + Coarse + Fine + Age + Water *
## Superplasticizer
##
## Df Deviance AIC
## - Fine 1 569.77 587.77
## - Water:Superplasticizer 1 570.10 588.10
## - Coarse 1 570.27 588.27
## <none> 569.76 589.76
## - FlyAsh 1 579.36 597.36
## - Blast 1 582.27 600.27
## - Cement 1 610.72 628.72
## - Age 1 713.33 731.33
##
## Step: AIC=587.77
## over400 ~ Cement + Blast + FlyAsh + Water + Superplasticizer +
## Coarse + Age + Water:Superplasticizer
##
## Df Deviance AIC
## - Water:Superplasticizer 1 570.11 586.11
## - Coarse 1 570.98 586.98
## <none> 569.77 587.77
## + Fine 1 569.76 589.76
## - FlyAsh 1 590.61 606.61
## - Blast 1 610.78 626.78
## - Cement 1 707.57 723.57
## - Age 1 713.34 729.34
##
## Step: AIC=586.11
## over400 ~ Cement + Blast + FlyAsh + Water + Superplasticizer +
## Coarse + Age
##
## Df Deviance AIC
## - Coarse 1 571.22 585.22
## <none> 570.11 586.11
## - Superplasticizer 1 573.50 587.50
## + Water:Superplasticizer 1 569.77 587.77
## + Fine 1 570.10 588.10
## - Water 1 580.39 594.39
## - FlyAsh 1 593.80 607.80
## - Blast 1 612.35 626.35
## - Cement 1 707.75 721.75
## - Age 1 726.66 740.66
##
## Step: AIC=585.22
## over400 ~ Cement + Blast + FlyAsh + Water + Superplasticizer +
## Age
##
## Df Deviance AIC
## <none> 571.22 585.22
## - Superplasticizer 1 573.68 585.68
## + Coarse 1 570.11 586.11
## + Fine 1 570.60 586.60
## + Water:Superplasticizer 1 570.98 586.98
## - Water 1 590.11 602.11
## - FlyAsh 1 593.81 605.81
## - Blast 1 613.95 625.95
## - Cement 1 716.78 728.78
## - Age 1 728.57 740.57
##
## Call: glm(formula = over400 ~ Cement + Blast + FlyAsh + Water + Superplasticizer +
## Age, family = binomial(link = "logit"), data = concrete_train,
## na.action = na.exclude)
##
## Coefficients:
## (Intercept) Cement Blast FlyAsh
## -3.06354 0.01621 0.01049 0.01242
## Water Superplasticizer Age
## -0.02847 0.04599 0.02513
##
## Degrees of Freedom: 719 Total (i.e. Null); 713 Residual
## Null Deviance: 943
## Residual Deviance: 571.2 AIC: 585.2
model1.2 <- glm(formula = over400 ~ Cement+ Blast+ FlyAsh+ Water+ Superplasticizer
+Age, family=binomial(link="logit"), data = concrete_train)
summary(model1.2)
##
## Call:
## glm(formula = over400 ~ Cement + Blast + FlyAsh + Water + Superplasticizer +
## Age, family = binomial(link = "logit"), data = concrete_train)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -3.4635 -0.5833 -0.2988 0.5307 2.5170
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -3.063542 1.405969 -2.179 0.0293 *
## Cement 0.016212 0.001592 10.184 < 2e-16 ***
## Blast 0.010488 0.001639 6.398 1.57e-10 ***
## FlyAsh 0.012423 0.002706 4.592 4.40e-06 ***
## Water -0.028466 0.006881 -4.137 3.52e-05 ***
## Superplasticizer 0.045985 0.029515 1.558 0.1192
## Age 0.025126 0.002876 8.737 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 942.97 on 719 degrees of freedom
## Residual deviance: 571.22 on 713 degrees of freedom
## AIC: 585.22
##
## Number of Fisher Scoring iterations: 5
anova(model1.2, test = 'Chisq')
## Analysis of Deviance Table
##
## Model: binomial, link: logit
##
## Response: over400
##
## Terms added sequentially (first to last)
##
##
## Df Deviance Resid. Df Resid. Dev Pr(>Chi)
## NULL 719 942.97
## Cement 1 131.761 718 811.21 < 2.2e-16 ***
## Blast 1 21.565 717 789.65 3.420e-06 ***
## FlyAsh 1 42.210 716 747.44 8.199e-11 ***
## Water 1 15.566 715 731.87 7.969e-05 ***
## Superplasticizer 1 3.305 714 728.57 0.06905 .
## Age 1 157.342 713 571.22 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# 比較model1.1以及model1.2準確性, AIC #
# 原始模型刪減不顯著係數之變數 model1.1 #
modle_train <- glm(formula = over400 ~ Cement+ Blast+ FlyAsh+ Water
+Age - 1, family=binomial(link="logit"), data = concrete_train)
result <- predict(modle_train, newdata = concrete_test, type = "response")
result_Approved <- ifelse(result > 0.7, 1, 0)
cm <- table(concrete_test$over400, result_Approved, dnn = c("實際", "預測"))
cm
## 預測
## 實際 0 1
## 0 182 10
## 1 58 59
cm[4] / sum(cm[, 2])
## [1] 0.8550725
cm[1] / sum(cm[, 1])
## [1] 0.7583333
accuracy <- sum(diag(cm)) / sum(cm)
accuracy
## [1] 0.7799353
AIC(modle_train)
## [1] 586.2268
# 逐步回歸模型 model1.2 #
modle_train <- glm(formula = over400 ~ Cement+ Blast+ FlyAsh+ Water+ Superplasticizer
+Age, family=binomial(link="logit"), data = concrete_train)
result <- predict(modle_train, newdata = concrete_test, type = "response")
result_Approved <- ifelse(result > 0.7, 1, 0)
cm <- table(concrete_test$over400, result_Approved, dnn = c("實際", "預測"))
cm
## 預測
## 實際 0 1
## 0 179 13
## 1 60 57
cm[4] / sum(cm[, 2])
## [1] 0.8142857
cm[1] / sum(cm[, 1])
## [1] 0.748954
accuracy <- sum(diag(cm)) / sum(cm)
accuracy
## [1] 0.763754
AIC(modle_train)
## [1] 585.2244
# 最終模型確認 #
# 選用逐步迴歸之模型 ＃
model_final <- glm(formula = over400 ~ Cement+ Blast+ FlyAsh+ Water+ Superplasticizer
+ Age, family = binomial(link = "logit"), data =concrete_train, na.action = na.exclude)
summary(model_final)
##
## Call:
## glm(formula = over400 ~ Cement + Blast + FlyAsh + Water + Superplasticizer +
## Age, family = binomial(link = "logit"), data = concrete_train,
## na.action = na.exclude)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -3.4635 -0.5833 -0.2988 0.5307 2.5170
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -3.063542 1.405969 -2.179 0.0293 *
## Cement 0.016212 0.001592 10.184 < 2e-16 ***
## Blast 0.010488 0.001639 6.398 1.57e-10 ***
## FlyAsh 0.012423 0.002706 4.592 4.40e-06 ***
## Water -0.028466 0.006881 -4.137 3.52e-05 ***
## Superplasticizer 0.045985 0.029515 1.558 0.1192
## Age 0.025126 0.002876 8.737 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 942.97 on 719 degrees of freedom
## Residual deviance: 571.22 on 713 degrees of freedom
## AIC: 585.22
##
## Number of Fisher Scoring iterations: 5
anova(model_final,test = 'Chisq')
## Analysis of Deviance Table
##
## Model: binomial, link: logit
##
## Response: over400
##
## Terms added sequentially (first to last)
##
##
## Df Deviance Resid. Df Resid. Dev Pr(>Chi)
## NULL 719 942.97
## Cement 1 131.761 718 811.21 < 2.2e-16 ***
## Blast 1 21.565 717 789.65 3.420e-06 ***
## FlyAsh 1 42.210 716 747.44 8.199e-11 ***
## Water 1 15.566 715 731.87 7.969e-05 ***
## Superplasticizer 1 3.305 714 728.57 0.06905 .
## Age 1 157.342 713 571.22 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# 檢測共線性 #
vif(model_final)
## Cement Blast FlyAsh Water
## 2.161812 1.947822 2.848225 1.704262
## Superplasticizer Age
## 2.121355 1.192812
# 檢測是否有離群值 #
# 計算> 1 存在離群值 #
out <- cooks.distance(model_final)
out
## 380 18 774 140 970
## 3.547240e-04 4.196392e-03 1.492388e-04 3.384995e-04 7.471040e-04
## 562 762 287 1015 462
## 1.538546e-04 1.574881e-02 4.022226e-04 1.956532e-03 5.915088e-03
## 998 41 114 143 677
## 3.760821e-04 9.770760e-08 3.953719e-03 9.617852e-05 8.843760e-07
## 183 420 241 251 746
## 1.218328e-04 1.587436e-04 4.451319e-05 4.990092e-05 1.772489e-03
## 653 313 838 364 88
## 3.947945e-05 5.312155e-04 6.303636e-04 2.383976e-04 3.769154e-03
## 351 600 944 61 1005
## 2.940844e-03 3.462082e-05 1.399343e-04 2.343146e-04 1.627259e-04
## 267 352 541 199 906
## 2.866059e-03 1.687980e-03 2.511337e-05 4.314204e-05 4.320809e-04
## 78 341 989 712 255
## 3.056833e-03 1.507875e-03 2.713072e-05 1.611634e-04 8.524177e-05
## 873 347 471 845 582
## 3.344879e-05 1.933157e-03 1.264943e-04 1.819274e-03 1.782559e-05
## 29 681 896 750 175
## 5.145186e-04 6.638953e-06 1.754726e-03 3.037894e-03 3.745190e-05
## 278 375 650 438 413
## 1.929518e-03 5.131578e-05 6.354516e-05 4.514876e-03 1.856253e-04
## 208 367 660 580 1011
## 1.025748e-03 1.393901e-03 7.951873e-05 3.799832e-04 1.302648e-03
## 656 536 309 400 542
## 6.356163e-06 2.937745e-04 1.677868e-04 9.271661e-04 1.396936e-04
## 644 767 837 201 719
## 1.314802e-04 3.221897e-04 3.968950e-04 1.017796e-04 8.670852e-03
## 688 368 590 294 990
## 5.744896e-07 6.589726e-04 3.434902e-06 7.243223e-05 2.754373e-03
## 552 338 484 900 498
## 3.014786e-05 3.852543e-04 4.697680e-05 3.269939e-04 3.834478e-04
## 383 947 701 850 716
## 1.087921e-03 4.635764e-04 1.677575e-03 2.721778e-04 1.830369e-06
## 479 779 713 933 492
## 6.134084e-03 3.523377e-05 1.593385e-05 4.460470e-03 5.777672e-04
## 907 586 526 64 697
## 7.508706e-04 1.492988e-04 5.107309e-03 4.418050e-03 6.810503e-07
## 108 427 164 13 940
## 6.700332e-04 5.659049e-05 1.432417e-05 1.362828e-02 3.086843e-04
## 249 606 315 922 683
## 2.330735e-05 2.789418e-06 6.315487e-04 1.197402e-04 1.983613e-04
## 983 431 946 89 141
## 3.160276e-04 4.795368e-05 3.268102e-04 7.159582e-03 5.925942e-05
## 971 344 421 763 568
## 1.644719e-03 4.132215e-04 1.346441e-04 1.329401e-04 2.290010e-04
## 1020 628 403 861 572
## 2.801459e-03 4.340707e-06 8.236015e-04 1.140357e-03 2.328336e-05
## 523 941 592 638 988
## 3.180997e-04 1.454227e-05 3.070979e-04 2.489767e-04 7.654103e-05
## 1013 373 81 817 651
## 2.370291e-03 1.241440e-03 5.009563e-03 2.470275e-03 2.002250e-06
## 66 714 686 322 109
## 5.499378e-06 1.346430e-06 2.564769e-04 2.235343e-03 7.782677e-04
## 206 358 995 47 1024
## 4.738235e-05 5.626052e-04 6.233288e-04 3.693417e-04 5.471219e-04
## 57 676 967 691 742
## 6.072134e-06 1.811411e-05 3.998407e-05 5.670793e-06 4.454466e-04
## 675 177 361 463 731
## 8.993544e-05 3.745190e-05 2.387908e-03 1.842550e-03 3.860280e-05
## 528 374 165 415 561
## 5.338807e-03 3.370978e-05 1.262431e-05 1.987533e-05 4.464723e-04
## 736 23 252 524 583
## 3.368944e-06 4.747819e-03 1.346500e-04 3.180997e-04 1.627071e-03
## 1004 706 822 171 39
## 7.386259e-04 5.549886e-05 2.949141e-05 2.320159e-06 2.247442e-02
## 1012 243 876 603 539
## 1.081356e-03 3.455882e-03 2.203792e-05 1.544039e-02 4.454466e-04
## 891 836 615 45 318
## 3.346809e-04 2.405319e-04 1.006279e-02 2.695624e-04 6.669926e-04
## 973 220 560 986 570
## 8.130924e-05 3.357562e-05 5.139138e-05 4.358820e-04 3.452052e-05
## 930 987 60 770 454
## 1.334887e-03 4.113892e-03 1.543074e-04 3.860280e-05 1.231404e-04
## 620 966 766 371 626
## 1.083791e-01 2.030134e-05 2.037748e-04 2.835088e-04 2.198591e-06
## 91 333 489 855 456
## 3.769154e-03 4.383306e-04 3.595930e-03 1.081472e-03 4.409808e-03
## 924 84 781 529 513
## 8.680172e-05 4.969241e-03 1.100019e-05 1.101925e-04 4.856533e-04
## 867 519 728 335 636
## 5.847541e-04 2.752711e-03 5.928423e-05 4.402799e-04 4.229057e-05
## 381 811 870 915 984
## 2.307309e-03 3.504721e-05 5.327585e-05 5.539412e-04 2.030134e-05
## 869 1010 694 982 617
## 7.999214e-04 7.102765e-03 6.093453e-05 1.810835e-04 2.335072e-06
## 749 920 905 579 4
## 2.452240e-03 3.021585e-04 3.527328e-05 2.762211e-05 3.893472e-06
## 932 396 30 444 782
## 5.110350e-04 2.600111e-04 2.656441e-06 7.574841e-05 2.474131e-05
## 921 6 292 682 324
## 2.029668e-05 1.653566e-07 2.457652e-03 5.492833e-06 5.693905e-04
## 44 53 963 550 369
## 3.640328e-03 9.510675e-03 3.231908e-04 1.479791e-04 1.305011e-04
## 349 86 864 551 574
## 4.255491e-04 3.769154e-03 4.288271e-04 3.230364e-06 7.909510e-06
## 148 517 795 72 440
## 1.206348e-05 1.098454e-05 4.050768e-06 9.226105e-03 9.175031e-05
## 258 1000 470 87 607
## 2.264000e-03 4.083765e-03 2.330916e-03 3.729191e-03 5.004306e-06
## 664 516 36 703 190
## 2.851930e-05 9.396078e-06 9.377296e-05 1.675169e-05 1.478348e-05
## 521 259 624 117 738
## 3.798477e-04 7.020480e-05 3.096136e-05 8.743768e-04 1.517818e-05
## 755 494 610 196 449
## 1.197220e-06 9.218522e-05 1.085581e-01 5.877790e-05 1.320222e-03
## 1018 525 689 885 191
## 1.255177e-03 5.107309e-03 1.875523e-05 1.427763e-04 2.439882e-05
## 657 288 409 500 745
## 1.684610e-06 2.505741e-03 1.077262e-04 5.103407e-04 2.489858e-05
## 530 455 509 512 846
## 1.101925e-04 1.766141e-03 2.003823e-04 9.147394e-03 1.039252e-03
## 336 853 125 601 173
## 1.603295e-03 7.224785e-03 4.606287e-05 5.781795e-05 5.359154e-05
## 284 578 147 73 459
## 5.689864e-05 2.570808e-04 2.082377e-04 1.243038e-02 1.408832e-03
## 860 527 961 138 168
## 6.877821e-04 5.338807e-03 6.413309e-03 7.916627e-04 9.642105e-07
## 887 976 803 131 155
## 4.692353e-03 9.212678e-04 1.297805e-04 2.853392e-04 1.284944e-04
## 623 848 378 46 328
## 1.198744e-05 1.524751e-04 4.969118e-03 3.860280e-05 6.596009e-04
## 658 430 93 793 918
## 2.933507e-04 2.731231e-05 7.509049e-04 1.017500e-05 2.398428e-05
## 575 302 350 908 257
## 8.205912e-06 9.444602e-04 5.879476e-04 1.622436e-03 3.502399e-03
## 248 901 810 705 314
## 2.762872e-03 2.201904e-04 1.584747e-05 1.240527e-06 4.569383e-04
## 465 179 842 247 854
## 1.079414e-03 3.745190e-05 1.662847e-04 1.331171e-04 1.331018e-03
## 761 979 567 158 729
## 7.521059e-04 3.788302e-03 1.220349e-05 7.525044e-05 7.281273e-04
## 159 280 340 799 556
## 2.385823e-05 5.593818e-05 3.149424e-04 1.921181e-03 5.891009e-04
## 735 826 632 581 788
## 2.521253e-03 1.461438e-03 7.878098e-05 1.240217e-04 4.444618e-05
## 299 820 1028 223 122
## 1.854893e-04 9.019190e-08 1.420445e-04 1.286628e-03 1.935128e-05
## 163 760 802 200 1007
## 1.000263e-04 1.805788e-04 1.054932e-04 6.258529e-05 2.555555e-04
## 943 269 412 290 609
## 1.204389e-05 4.843549e-05 2.162170e-04 5.251890e-05 5.570251e-03
## 868 642 718 670 804
## 9.103047e-04 1.371273e-05 1.466827e-06 5.029648e-03 2.937745e-04
## 176 134 791 216 892
## 2.363075e-05 3.521696e-04 6.406692e-04 1.186471e-04 1.938807e-04
## 153 365 968 835 493
## 2.936423e-04 3.211655e-04 3.456098e-05 4.903950e-04 6.128967e-04
## 414 916 310 598 56
## 3.911650e-05 3.981008e-03 2.116008e-04 2.323331e-05 5.831801e-08
## 909 34 181 376 263
## 1.999738e-05 9.944153e-06 5.135944e-06 8.800839e-05 2.215618e-03
## 665 75 844 722 794
## 2.821283e-06 5.975886e-03 2.912046e-03 1.584747e-05 1.035987e-02
## 154 1027 360 880 188
## 9.313970e-05 5.343768e-05 1.167825e-03 1.254664e-05 3.540951e-03
## 996 227 24 236 92
## 5.060542e-05 1.187851e-02 1.143331e-06 6.368271e-03 1.544637e-03
## 654 229 508 936 679
## 3.584488e-06 2.108492e-05 7.867881e-03 3.362770e-05 1.483491e-05
## 167 540 645 732 222
## 1.621457e-05 1.461438e-03 1.838563e-04 4.444618e-05 1.821178e-04
## 461 9 778 616 776
## 1.411991e-03 1.105010e-03 1.565428e-05 1.069527e-01 4.962268e-05
## 1006 410 602 806 618
## 6.516696e-05 1.689836e-04 7.108623e-04 1.578956e-04 1.032382e-04
## 416 877 326 357 85
## 3.272481e-04 3.424225e-04 3.609469e-03 1.476253e-03 7.120082e-03
## 629 871 824 559 965
## 3.197245e-06 1.326567e-04 1.766053e-05 7.137826e-03 2.379298e-03
## 753 283 17 881 495
## 7.042736e-04 1.896898e-03 1.736486e-06 1.427763e-04 9.241016e-05
## 878 26 112 452 522
## 1.410968e-05 1.029721e-05 5.491133e-04 2.163754e-03 1.589133e-03
## 950 90 662 11 955
## 1.624677e-03 2.613292e-04 4.483539e-05 1.604236e-05 1.751137e-04
## 825 563 219 613 240
## 4.638091e-04 7.540846e-04 2.221260e-05 6.046233e-06 2.720524e-05
## 160 405 980 733 446
## 1.284944e-04 2.505079e-04 4.125095e-05 9.354898e-05 2.402881e-03
## 833 348 487 447 31
## 2.602184e-03 7.303389e-04 2.724152e-04 3.911608e-03 4.094046e-06
## 40 281 715 862 69
## 9.322414e-03 8.616696e-05 1.719591e-04 3.933893e-05 1.219147e-03
## 499 307 809 401 604
## 8.462187e-04 1.241725e-03 1.209752e-05 5.836609e-04 1.136439e-01
## 571 466 834 859 404
## 4.128946e-03 1.759041e-03 1.509052e-02 2.449903e-04 4.886670e-04
## 436 135 442 759 327
## 4.499324e-04 2.313665e-04 2.968133e-03 6.108686e-05 1.968203e-03
## 957 301 76 118 14
## 3.018496e-04 3.251468e-04 6.520765e-05 1.906176e-04 1.393007e-02
## 672 952 786 152 110
## 2.402822e-06 2.186191e-04 5.928423e-05 1.284944e-04 4.022327e-03
## 985 879 59 170 102
## 1.249528e-04 1.634630e-03 1.998102e-04 6.238495e-05 1.270150e-04
## 472 468 702 354 353
## 1.264943e-04 7.271554e-04 7.406006e-06 4.062169e-04 6.367949e-04
## 50 242 408 16 210
## 2.403633e-02 1.315999e-04 9.120171e-05 2.781762e-04 2.345618e-05
## 904 244 21 649 372
## 3.963531e-05 2.088363e-05 1.639276e-05 1.538410e-05 7.477388e-04
## 419 684 903 481 297
## 5.135852e-05 5.163546e-03 2.029668e-05 4.188128e-05 4.833436e-04
## 927 890 757 700 974
## 1.259465e-03 4.976906e-05 2.816042e-05 4.029541e-06 1.587072e-04
## 685 533 584 667 1029
## 4.753951e-06 7.859150e-06 2.111943e-03 3.745920e-04 2.501961e-04
## 942 954 821 723 402
## 1.649327e-03 3.124905e-04 1.722576e-05 3.504721e-05 1.806377e-03
## 356 520 246 997 215
## 2.666767e-03 3.391387e-04 4.726376e-05 1.653690e-03 7.316026e-05
## 10 981 588 1003 929
## 2.484697e-04 2.373999e-05 6.449482e-06 1.063173e-03 2.110675e-04
## 55 695 296 71 239
## 7.077857e-06 4.485703e-06 1.686326e-04 3.241693e-03 1.864185e-05
## 898 849 1001 612 394
## 6.478532e-03 6.855930e-05 2.957457e-03 1.624364e-05 4.840563e-03
## 126 98 751 150 772
## 1.906176e-04 4.460336e-04 1.644203e-03 1.979809e-04 1.492388e-04
## 648 162 577 203 841
## 9.917729e-06 3.770425e-05 1.918913e-05 2.596594e-03 3.976332e-04
## 432 884 764 754 475
## 9.340120e-05 4.741668e-04 1.420193e-04 5.230494e-05 5.966805e-03
## 450 506 474 991 95
## 3.875007e-03 1.509749e-04 1.417626e-04 1.527264e-02 4.669427e-04
## 384 544 548 390 518
## 2.621729e-04 9.169743e-06 2.079315e-05 1.796777e-03 8.303043e-05
## 895 634 934 910 856
## 9.118641e-04 2.411974e-05 3.127030e-04 7.920178e-05 2.320253e-03
## 977 717 237 63 797
## 1.649327e-03 3.484388e-06 4.651226e-03 5.585140e-04 1.470908e-05
## 883 789 978 80 115
## 3.440639e-04 9.354898e-05 5.712585e-04 9.226105e-03 1.656323e-03
## 558 585 631 142 773
## 1.835700e-04 7.527265e-04 3.634000e-05 5.507813e-05 2.981834e-04
## 696 655 156 282 913
## 2.348387e-06 4.339027e-05 4.599243e-04 2.351366e-04 9.477420e-04
## 230 38 1 743 185
## 3.107552e-05 3.243121e-03 3.313814e-04 4.393268e-04 1.507757e-05
## 295 709 969 557 441
## 1.043677e-04 1.092169e-04 4.799987e-04 9.016718e-05 4.430423e-05
## 422 678 346 418 407
## 1.524998e-04 4.807132e-04 3.328071e-03 3.378235e-05 1.119189e-04
## 99 359 832 483 370
## 5.364850e-05 8.693280e-04 2.851556e-05 4.188128e-05 1.826254e-04
## 741 666 204 888 182
## 2.916765e-03 1.372712e-04 2.119433e-05 3.273759e-05 3.745190e-05
## 337 316 478 482 238
## 8.892942e-04 9.506944e-04 3.065238e-04 4.188128e-05 3.641495e-03
## 1022 458 33 535 300
## 2.357164e-03 2.055834e-03 3.780360e-06 1.984070e-03 2.355993e-04
## 123 146 186 511 137
## 1.906176e-04 5.925942e-05 2.427818e-05 1.062703e-04 3.521696e-04
## 711 323 393 911 42
## 1.681442e-03 1.004634e-03 2.137946e-03 1.597328e-04 1.280426e-01
## 687 828 116 406 211
## 3.999700e-03 5.001030e-04 3.406850e-04 3.226254e-05 3.824351e-05
## 928 453 780 919 813
## 1.136867e-03 2.668814e-04 8.516878e-06 1.830272e-04 1.337069e-02
## 491 994 734 385 467
## 3.910676e-03 3.760948e-04 3.553598e-03 4.285931e-04 2.656211e-03
## 865 231 178 534 886
## 2.270576e-03 6.471860e-03 1.303018e-04 1.297805e-04 2.041541e-04
## 429 894 912 275 433
## 4.532836e-04 2.907649e-04 1.691885e-03 5.326417e-05 3.461945e-03
## 939 792 366 784 591
## 2.272451e-05 4.851191e-07 2.298038e-03 2.380783e-05 1.177112e-05
## 445 805 339 593 730
## 3.150305e-04 1.984070e-03 2.484415e-04 4.994094e-06 2.528030e-03
## 503 161 62 5 391
## 2.560124e-04 3.429885e-04 1.364422e-05 1.021707e-02 1.452862e-04
## 332 597 758 54 668
## 1.355511e-03 3.766896e-04 3.639409e-05 6.804307e-06 1.140878e-06
## 566 945 443 120 504
## 1.898494e-04 3.331268e-05 4.482252e-05 3.375693e-04 1.715295e-02
## 319 342 889 698 151
## 2.270488e-04 8.588084e-04 2.217589e-04 1.166708e-02 1.177553e-04
## 902 796 285 130 643
## 2.348327e-03 4.269918e-04 8.313413e-05 8.137812e-04 6.281043e-05
## 435 437 727 502 217
## 3.420419e-03 4.618246e-04 2.752272e-05 1.708013e-02 3.424462e-04
## 184 937 392 543 627
## 1.043473e-05 4.608912e-04 5.848143e-04 3.794419e-06 1.757340e-06
## 553 228 775 476 77
## 3.978037e-03 2.553943e-02 2.351438e-05 5.966805e-03 9.226105e-03
## 926 599 213 330 669
## 2.032264e-03 2.685634e-05 8.510190e-04 3.601309e-03 2.094680e-04
length(which(out>=1))
## [1] 0
# 不存在離群值 #
# 檢測影響點 #
eff <- cooks.distance(model_final)
eff
## 380 18 774 140 970
## 3.547240e-04 4.196392e-03 1.492388e-04 3.384995e-04 7.471040e-04
## 562 762 287 1015 462
## 1.538546e-04 1.574881e-02 4.022226e-04 1.956532e-03 5.915088e-03
## 998 41 114 143 677
## 3.760821e-04 9.770760e-08 3.953719e-03 9.617852e-05 8.843760e-07
## 183 420 241 251 746
## 1.218328e-04 1.587436e-04 4.451319e-05 4.990092e-05 1.772489e-03
## 653 313 838 364 88
## 3.947945e-05 5.312155e-04 6.303636e-04 2.383976e-04 3.769154e-03
## 351 600 944 61 1005
## 2.940844e-03 3.462082e-05 1.399343e-04 2.343146e-04 1.627259e-04
## 267 352 541 199 906
## 2.866059e-03 1.687980e-03 2.511337e-05 4.314204e-05 4.320809e-04
## 78 341 989 712 255
## 3.056833e-03 1.507875e-03 2.713072e-05 1.611634e-04 8.524177e-05
## 873 347 471 845 582
## 3.344879e-05 1.933157e-03 1.264943e-04 1.819274e-03 1.782559e-05
## 29 681 896 750 175
## 5.145186e-04 6.638953e-06 1.754726e-03 3.037894e-03 3.745190e-05
## 278 375 650 438 413
## 1.929518e-03 5.131578e-05 6.354516e-05 4.514876e-03 1.856253e-04
## 208 367 660 580 1011
## 1.025748e-03 1.393901e-03 7.951873e-05 3.799832e-04 1.302648e-03
## 656 536 309 400 542
## 6.356163e-06 2.937745e-04 1.677868e-04 9.271661e-04 1.396936e-04
## 644 767 837 201 719
## 1.314802e-04 3.221897e-04 3.968950e-04 1.017796e-04 8.670852e-03
## 688 368 590 294 990
## 5.744896e-07 6.589726e-04 3.434902e-06 7.243223e-05 2.754373e-03
## 552 338 484 900 498
## 3.014786e-05 3.852543e-04 4.697680e-05 3.269939e-04 3.834478e-04
## 383 947 701 850 716
## 1.087921e-03 4.635764e-04 1.677575e-03 2.721778e-04 1.830369e-06
## 479 779 713 933 492
## 6.134084e-03 3.523377e-05 1.593385e-05 4.460470e-03 5.777672e-04
## 907 586 526 64 697
## 7.508706e-04 1.492988e-04 5.107309e-03 4.418050e-03 6.810503e-07
## 108 427 164 13 940
## 6.700332e-04 5.659049e-05 1.432417e-05 1.362828e-02 3.086843e-04
## 249 606 315 922 683
## 2.330735e-05 2.789418e-06 6.315487e-04 1.197402e-04 1.983613e-04
## 983 431 946 89 141
## 3.160276e-04 4.795368e-05 3.268102e-04 7.159582e-03 5.925942e-05
## 971 344 421 763 568
## 1.644719e-03 4.132215e-04 1.346441e-04 1.329401e-04 2.290010e-04
## 1020 628 403 861 572
## 2.801459e-03 4.340707e-06 8.236015e-04 1.140357e-03 2.328336e-05
## 523 941 592 638 988
## 3.180997e-04 1.454227e-05 3.070979e-04 2.489767e-04 7.654103e-05
## 1013 373 81 817 651
## 2.370291e-03 1.241440e-03 5.009563e-03 2.470275e-03 2.002250e-06
## 66 714 686 322 109
## 5.499378e-06 1.346430e-06 2.564769e-04 2.235343e-03 7.782677e-04
## 206 358 995 47 1024
## 4.738235e-05 5.626052e-04 6.233288e-04 3.693417e-04 5.471219e-04
## 57 676 967 691 742
## 6.072134e-06 1.811411e-05 3.998407e-05 5.670793e-06 4.454466e-04
## 675 177 361 463 731
## 8.993544e-05 3.745190e-05 2.387908e-03 1.842550e-03 3.860280e-05
## 528 374 165 415 561
## 5.338807e-03 3.370978e-05 1.262431e-05 1.987533e-05 4.464723e-04
## 736 23 252 524 583
## 3.368944e-06 4.747819e-03 1.346500e-04 3.180997e-04 1.627071e-03
## 1004 706 822 171 39
## 7.386259e-04 5.549886e-05 2.949141e-05 2.320159e-06 2.247442e-02
## 1012 243 876 603 539
## 1.081356e-03 3.455882e-03 2.203792e-05 1.544039e-02 4.454466e-04
## 891 836 615 45 318
## 3.346809e-04 2.405319e-04 1.006279e-02 2.695624e-04 6.669926e-04
## 973 220 560 986 570
## 8.130924e-05 3.357562e-05 5.139138e-05 4.358820e-04 3.452052e-05
## 930 987 60 770 454
## 1.334887e-03 4.113892e-03 1.543074e-04 3.860280e-05 1.231404e-04
## 620 966 766 371 626
## 1.083791e-01 2.030134e-05 2.037748e-04 2.835088e-04 2.198591e-06
## 91 333 489 855 456
## 3.769154e-03 4.383306e-04 3.595930e-03 1.081472e-03 4.409808e-03
## 924 84 781 529 513
## 8.680172e-05 4.969241e-03 1.100019e-05 1.101925e-04 4.856533e-04
## 867 519 728 335 636
## 5.847541e-04 2.752711e-03 5.928423e-05 4.402799e-04 4.229057e-05
## 381 811 870 915 984
## 2.307309e-03 3.504721e-05 5.327585e-05 5.539412e-04 2.030134e-05
## 869 1010 694 982 617
## 7.999214e-04 7.102765e-03 6.093453e-05 1.810835e-04 2.335072e-06
## 749 920 905 579 4
## 2.452240e-03 3.021585e-04 3.527328e-05 2.762211e-05 3.893472e-06
## 932 396 30 444 782
## 5.110350e-04 2.600111e-04 2.656441e-06 7.574841e-05 2.474131e-05
## 921 6 292 682 324
## 2.029668e-05 1.653566e-07 2.457652e-03 5.492833e-06 5.693905e-04
## 44 53 963 550 369
## 3.640328e-03 9.510675e-03 3.231908e-04 1.479791e-04 1.305011e-04
## 349 86 864 551 574
## 4.255491e-04 3.769154e-03 4.288271e-04 3.230364e-06 7.909510e-06
## 148 517 795 72 440
## 1.206348e-05 1.098454e-05 4.050768e-06 9.226105e-03 9.175031e-05
## 258 1000 470 87 607
## 2.264000e-03 4.083765e-03 2.330916e-03 3.729191e-03 5.004306e-06
## 664 516 36 703 190
## 2.851930e-05 9.396078e-06 9.377296e-05 1.675169e-05 1.478348e-05
## 521 259 624 117 738
## 3.798477e-04 7.020480e-05 3.096136e-05 8.743768e-04 1.517818e-05
## 755 494 610 196 449
## 1.197220e-06 9.218522e-05 1.085581e-01 5.877790e-05 1.320222e-03
## 1018 525 689 885 191
## 1.255177e-03 5.107309e-03 1.875523e-05 1.427763e-04 2.439882e-05
## 657 288 409 500 745
## 1.684610e-06 2.505741e-03 1.077262e-04 5.103407e-04 2.489858e-05
## 530 455 509 512 846
## 1.101925e-04 1.766141e-03 2.003823e-04 9.147394e-03 1.039252e-03
## 336 853 125 601 173
## 1.603295e-03 7.224785e-03 4.606287e-05 5.781795e-05 5.359154e-05
## 284 578 147 73 459
## 5.689864e-05 2.570808e-04 2.082377e-04 1.243038e-02 1.408832e-03
## 860 527 961 138 168
## 6.877821e-04 5.338807e-03 6.413309e-03 7.916627e-04 9.642105e-07
## 887 976 803 131 155
## 4.692353e-03 9.212678e-04 1.297805e-04 2.853392e-04 1.284944e-04
## 623 848 378 46 328
## 1.198744e-05 1.524751e-04 4.969118e-03 3.860280e-05 6.596009e-04
## 658 430 93 793 918
## 2.933507e-04 2.731231e-05 7.509049e-04 1.017500e-05 2.398428e-05
## 575 302 350 908 257
## 8.205912e-06 9.444602e-04 5.879476e-04 1.622436e-03 3.502399e-03
## 248 901 810 705 314
## 2.762872e-03 2.201904e-04 1.584747e-05 1.240527e-06 4.569383e-04
## 465 179 842 247 854
## 1.079414e-03 3.745190e-05 1.662847e-04 1.331171e-04 1.331018e-03
## 761 979 567 158 729
## 7.521059e-04 3.788302e-03 1.220349e-05 7.525044e-05 7.281273e-04
## 159 280 340 799 556
## 2.385823e-05 5.593818e-05 3.149424e-04 1.921181e-03 5.891009e-04
## 735 826 632 581 788
## 2.521253e-03 1.461438e-03 7.878098e-05 1.240217e-04 4.444618e-05
## 299 820 1028 223 122
## 1.854893e-04 9.019190e-08 1.420445e-04 1.286628e-03 1.935128e-05
## 163 760 802 200 1007
## 1.000263e-04 1.805788e-04 1.054932e-04 6.258529e-05 2.555555e-04
## 943 269 412 290 609
## 1.204389e-05 4.843549e-05 2.162170e-04 5.251890e-05 5.570251e-03
## 868 642 718 670 804
## 9.103047e-04 1.371273e-05 1.466827e-06 5.029648e-03 2.937745e-04
## 176 134 791 216 892
## 2.363075e-05 3.521696e-04 6.406692e-04 1.186471e-04 1.938807e-04
## 153 365 968 835 493
## 2.936423e-04 3.211655e-04 3.456098e-05 4.903950e-04 6.128967e-04
## 414 916 310 598 56
## 3.911650e-05 3.981008e-03 2.116008e-04 2.323331e-05 5.831801e-08
## 909 34 181 376 263
## 1.999738e-05 9.944153e-06 5.135944e-06 8.800839e-05 2.215618e-03
## 665 75 844 722 794
## 2.821283e-06 5.975886e-03 2.912046e-03 1.584747e-05 1.035987e-02
## 154 1027 360 880 188
## 9.313970e-05 5.343768e-05 1.167825e-03 1.254664e-05 3.540951e-03
## 996 227 24 236 92
## 5.060542e-05 1.187851e-02 1.143331e-06 6.368271e-03 1.544637e-03
## 654 229 508 936 679
## 3.584488e-06 2.108492e-05 7.867881e-03 3.362770e-05 1.483491e-05
## 167 540 645 732 222
## 1.621457e-05 1.461438e-03 1.838563e-04 4.444618e-05 1.821178e-04
## 461 9 778 616 776
## 1.411991e-03 1.105010e-03 1.565428e-05 1.069527e-01 4.962268e-05
## 1006 410 602 806 618
## 6.516696e-05 1.689836e-04 7.108623e-04 1.578956e-04 1.032382e-04
## 416 877 326 357 85
## 3.272481e-04 3.424225e-04 3.609469e-03 1.476253e-03 7.120082e-03
## 629 871 824 559 965
## 3.197245e-06 1.326567e-04 1.766053e-05 7.137826e-03 2.379298e-03
## 753 283 17 881 495
## 7.042736e-04 1.896898e-03 1.736486e-06 1.427763e-04 9.241016e-05
## 878 26 112 452 522
## 1.410968e-05 1.029721e-05 5.491133e-04 2.163754e-03 1.589133e-03
## 950 90 662 11 955
## 1.624677e-03 2.613292e-04 4.483539e-05 1.604236e-05 1.751137e-04
## 825 563 219 613 240
## 4.638091e-04 7.540846e-04 2.221260e-05 6.046233e-06 2.720524e-05
## 160 405 980 733 446
## 1.284944e-04 2.505079e-04 4.125095e-05 9.354898e-05 2.402881e-03
## 833 348 487 447 31
## 2.602184e-03 7.303389e-04 2.724152e-04 3.911608e-03 4.094046e-06
## 40 281 715 862 69
## 9.322414e-03 8.616696e-05 1.719591e-04 3.933893e-05 1.219147e-03
## 499 307 809 401 604
## 8.462187e-04 1.241725e-03 1.209752e-05 5.836609e-04 1.136439e-01
## 571 466 834 859 404
## 4.128946e-03 1.759041e-03 1.509052e-02 2.449903e-04 4.886670e-04
## 436 135 442 759 327
## 4.499324e-04 2.313665e-04 2.968133e-03 6.108686e-05 1.968203e-03
## 957 301 76 118 14
## 3.018496e-04 3.251468e-04 6.520765e-05 1.906176e-04 1.393007e-02
## 672 952 786 152 110
## 2.402822e-06 2.186191e-04 5.928423e-05 1.284944e-04 4.022327e-03
## 985 879 59 170 102
## 1.249528e-04 1.634630e-03 1.998102e-04 6.238495e-05 1.270150e-04
## 472 468 702 354 353
## 1.264943e-04 7.271554e-04 7.406006e-06 4.062169e-04 6.367949e-04
## 50 242 408 16 210
## 2.403633e-02 1.315999e-04 9.120171e-05 2.781762e-04 2.345618e-05
## 904 244 21 649 372
## 3.963531e-05 2.088363e-05 1.639276e-05 1.538410e-05 7.477388e-04
## 419 684 903 481 297
## 5.135852e-05 5.163546e-03 2.029668e-05 4.188128e-05 4.833436e-04
## 927 890 757 700 974
## 1.259465e-03 4.976906e-05 2.816042e-05 4.029541e-06 1.587072e-04
## 685 533 584 667 1029
## 4.753951e-06 7.859150e-06 2.111943e-03 3.745920e-04 2.501961e-04
## 942 954 821 723 402
## 1.649327e-03 3.124905e-04 1.722576e-05 3.504721e-05 1.806377e-03
## 356 520 246 997 215
## 2.666767e-03 3.391387e-04 4.726376e-05 1.653690e-03 7.316026e-05
## 10 981 588 1003 929
## 2.484697e-04 2.373999e-05 6.449482e-06 1.063173e-03 2.110675e-04
## 55 695 296 71 239
## 7.077857e-06 4.485703e-06 1.686326e-04 3.241693e-03 1.864185e-05
## 898 849 1001 612 394
## 6.478532e-03 6.855930e-05 2.957457e-03 1.624364e-05 4.840563e-03
## 126 98 751 150 772
## 1.906176e-04 4.460336e-04 1.644203e-03 1.979809e-04 1.492388e-04
## 648 162 577 203 841
## 9.917729e-06 3.770425e-05 1.918913e-05 2.596594e-03 3.976332e-04
## 432 884 764 754 475
## 9.340120e-05 4.741668e-04 1.420193e-04 5.230494e-05 5.966805e-03
## 450 506 474 991 95
## 3.875007e-03 1.509749e-04 1.417626e-04 1.527264e-02 4.669427e-04
## 384 544 548 390 518
## 2.621729e-04 9.169743e-06 2.079315e-05 1.796777e-03 8.303043e-05
## 895 634 934 910 856
## 9.118641e-04 2.411974e-05 3.127030e-04 7.920178e-05 2.320253e-03
## 977 717 237 63 797
## 1.649327e-03 3.484388e-06 4.651226e-03 5.585140e-04 1.470908e-05
## 883 789 978 80 115
## 3.440639e-04 9.354898e-05 5.712585e-04 9.226105e-03 1.656323e-03
## 558 585 631 142 773
## 1.835700e-04 7.527265e-04 3.634000e-05 5.507813e-05 2.981834e-04
## 696 655 156 282 913
## 2.348387e-06 4.339027e-05 4.599243e-04 2.351366e-04 9.477420e-04
## 230 38 1 743 185
## 3.107552e-05 3.243121e-03 3.313814e-04 4.393268e-04 1.507757e-05
## 295 709 969 557 441
## 1.043677e-04 1.092169e-04 4.799987e-04 9.016718e-05 4.430423e-05
## 422 678 346 418 407
## 1.524998e-04 4.807132e-04 3.328071e-03 3.378235e-05 1.119189e-04
## 99 359 832 483 370
## 5.364850e-05 8.693280e-04 2.851556e-05 4.188128e-05 1.826254e-04
## 741 666 204 888 182
## 2.916765e-03 1.372712e-04 2.119433e-05 3.273759e-05 3.745190e-05
## 337 316 478 482 238
## 8.892942e-04 9.506944e-04 3.065238e-04 4.188128e-05 3.641495e-03
## 1022 458 33 535 300
## 2.357164e-03 2.055834e-03 3.780360e-06 1.984070e-03 2.355993e-04
## 123 146 186 511 137
## 1.906176e-04 5.925942e-05 2.427818e-05 1.062703e-04 3.521696e-04
## 711 323 393 911 42
## 1.681442e-03 1.004634e-03 2.137946e-03 1.597328e-04 1.280426e-01
## 687 828 116 406 211
## 3.999700e-03 5.001030e-04 3.406850e-04 3.226254e-05 3.824351e-05
## 928 453 780 919 813
## 1.136867e-03 2.668814e-04 8.516878e-06 1.830272e-04 1.337069e-02
## 491 994 734 385 467
## 3.910676e-03 3.760948e-04 3.553598e-03 4.285931e-04 2.656211e-03
## 865 231 178 534 886
## 2.270576e-03 6.471860e-03 1.303018e-04 1.297805e-04 2.041541e-04
## 429 894 912 275 433
## 4.532836e-04 2.907649e-04 1.691885e-03 5.326417e-05 3.461945e-03
## 939 792 366 784 591
## 2.272451e-05 4.851191e-07 2.298038e-03 2.380783e-05 1.177112e-05
## 445 805 339 593 730
## 3.150305e-04 1.984070e-03 2.484415e-04 4.994094e-06 2.528030e-03
## 503 161 62 5 391
## 2.560124e-04 3.429885e-04 1.364422e-05 1.021707e-02 1.452862e-04
## 332 597 758 54 668
## 1.355511e-03 3.766896e-04 3.639409e-05 6.804307e-06 1.140878e-06
## 566 945 443 120 504
## 1.898494e-04 3.331268e-05 4.482252e-05 3.375693e-04 1.715295e-02
## 319 342 889 698 151
## 2.270488e-04 8.588084e-04 2.217589e-04 1.166708e-02 1.177553e-04
## 902 796 285 130 643
## 2.348327e-03 4.269918e-04 8.313413e-05 8.137812e-04 6.281043e-05
## 435 437 727 502 217
## 3.420419e-03 4.618246e-04 2.752272e-05 1.708013e-02 3.424462e-04
## 184 937 392 543 627
## 1.043473e-05 4.608912e-04 5.848143e-04 3.794419e-06 1.757340e-06
## 553 228 775 476 77
## 3.978037e-03 2.553943e-02 2.351438e-05 5.966805e-03 9.226105e-03
## 926 599 213 330 669
## 2.032264e-03 2.685634e-05 8.510190e-04 3.601309e-03 2.094680e-04
# 檢測標準 #
# 計算影響點個數 #
qf(0.5,7,720-7)
## [1] 0.9074005
length(which(as.vector(eff) > qf(0.5,7,720-7)))
## [1] 0
#畫ROC曲線
pred <- prediction(result, concrete_test$over400)
perf <- performance(pred, measure = "tpr", x.measure = "fpr")
#計算AUC
auc <- performance(pred, "auc")
#畫圖
plot(perf, col = rainbow(5), main = "ROC curve", xlab = "1 - Specificity(FPR)", ylab = "Sensitivity(TPR)")
abline(0, 1)
#實際AUC值
text(0.5, 0.5,paste0("AUC= ",as.character(auc@y.values[[1]])))
# 將全部資料投入最適模型找最適合係數 #
model_final <- glm(formula = over400 ~ Cement+ Blast+ FlyAsh+ Water+ Superplasticizer
+ Age, family = binomial(link = "logit"), data =concrete, na.action = na.exclude)
summary(model_final)
##
## Call:
## glm(formula = over400 ~ Cement + Blast + FlyAsh + Water + Superplasticizer +
## Age, family = binomial(link = "logit"), data = concrete,
## na.action = na.exclude)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -3.3739 -0.6005 -0.3207 0.5575 2.7022
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -2.349277 1.139323 -2.062 0.0392 *
## Cement 0.015100 0.001259 11.992 < 2e-16 ***
## Blast 0.010384 0.001374 7.556 4.17e-14 ***
## FlyAsh 0.009697 0.002197 4.414 1.01e-05 ***
## Water -0.029783 0.005688 -5.236 1.64e-07 ***
## Superplasticizer 0.061294 0.024703 2.481 0.0131 *
## Age 0.024043 0.002278 10.552 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1353.2 on 1028 degrees of freedom
## Residual deviance: 836.6 on 1022 degrees of freedom
## AIC: 850.6
##
## Number of Fisher Scoring iterations: 5