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
concrete <- read.csv('/Users/kevinpiger/Desktop/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)
# 看各變數之間是否有相關 #
# 圖表呈現 #
cor(as.matrix(concrete[,1:8]))
## Cement Blast FlyAsh Water
## Cement 1.00000000 -0.27406887 -0.396750794 -0.07964953
## Blast -0.27406887 1.00000000 -0.324514293 0.10657015
## FlyAsh -0.39675079 -0.32451429 1.000000000 -0.25793405
## Water -0.07964953 0.10657015 -0.257934049 1.00000000
## Superplasticizer 0.09417923 0.04277701 0.377194443 -0.65847778
## Coarse -0.11180196 -0.28348360 -0.009256799 -0.18166455
## Fine -0.22060328 -0.28292147 0.078189625 -0.45225658
## Age 0.08287040 -0.04449653 -0.154660632 0.27749289
## Superplasticizer Coarse Fine Age
## Cement 0.09417923 -0.111801961 -0.22060328 0.082870400
## Blast 0.04277701 -0.283483598 -0.28292147 -0.044496534
## FlyAsh 0.37719444 -0.009256799 0.07818963 -0.154660632
## Water -0.65847778 -0.181664549 -0.45225658 0.277492894
## Superplasticizer 1.00000000 -0.265624550 0.22215867 -0.192912119
## Coarse -0.26562455 1.000000000 -0.17765186 -0.002782346
## Fine 0.22215867 -0.177651858 1.00000000 -0.156544499
## Age -0.19291212 -0.002782346 -0.15654450 1.000000000
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()
head(concrete_train)
## Cement Blast FlyAsh Water Superplasticizer Coarse Fine Age Concrete
## 380 475.0 0.0 59.0 142.0 1.9 1098.0 641.0 28 57.23
## 18 380.0 95.0 0.0 228.0 0.0 932.0 594.0 90 40.56
## 774 382.0 0.0 0.0 186.0 0.0 1111.0 784.0 7 11.47
## 140 313.3 262.2 0.0 175.5 8.6 1046.9 611.8 56 64.90
## 970 314.0 145.3 113.2 178.9 8.0 869.1 690.2 28 46.23
## 562 382.5 0.0 0.0 185.7 0.0 1047.8 739.3 7 24.07
## kgC over400
## 380 572.3 1
## 18 405.6 1
## 774 114.7 0
## 140 649.0 1
## 970 462.3 1
## 562 240.7 0
# 建立最初模型 #
# 羅吉斯回歸 #
modle1.0 <- glm(over400 ~ Cement + Blast + FlyAsh + Water + Superplasticizer + 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
AIC(modle1.0)
## [1] 589.7588
summary(modle1.0)
##
## Call:
## glm(formula = over400 ~ Cement + Blast + FlyAsh + Water + Superplasticizer +
## 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 , 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 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 ***
## Age 1 158.188 714 573.68 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
AIC(modle1.1)
## [1] 585.6844
summary(modle1.1)
##
## Call:
## glm(formula = over400 ~ Cement + Blast + FlyAsh + Water + Age,
## family = binomial(link = "logit"), data = concrete_train,
## na.action = na.exclude)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -3.4643 -0.5775 -0.2954 0.5527 2.5602
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.980547 1.243772 -1.592 0.111
## Cement 0.016967 0.001547 10.971 < 2e-16 ***
## Blast 0.011386 0.001528 7.452 9.23e-14 ***
## FlyAsh 0.014389 0.002416 5.956 2.59e-09 ***
## Water -0.035007 0.005658 -6.187 6.12e-10 ***
## Age 0.024995 0.002845 8.786 < 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: 573.68 on 714 degrees of freedom
## AIC: 585.68
##
## Number of Fisher Scoring iterations: 5
# 檢測是否有離群值 #
# > 1 存在離群值 #
out <- cooks.distance(modle1.1)
out
## 380 18 774 140 970
## 7.185198e-05 5.150208e-03 1.917560e-04 3.789731e-04 6.444140e-04
## 562 762 287 1015 462
## 1.974346e-04 1.808328e-02 4.954777e-04 1.831638e-03 5.492571e-03
## 998 41 114 143 677
## 2.019569e-04 1.335852e-07 3.904121e-03 1.518696e-04 1.110544e-06
## 183 420 241 251 746
## 1.522640e-04 1.956484e-04 4.451270e-05 5.589898e-05 2.300718e-03
## 653 313 838 364 88
## 4.893172e-05 6.415617e-04 2.702383e-04 2.948498e-04 3.718393e-03
## 351 600 944 61 1005
## 3.331349e-03 4.292651e-05 1.662274e-04 3.436463e-04 1.157055e-04
## 267 352 541 199 906
## 2.968464e-03 1.902841e-03 3.223880e-05 5.396380e-05 4.091397e-04
## 78 341 989 712 255
## 2.684107e-03 1.779255e-03 1.431459e-05 2.199750e-04 9.872104e-05
## 873 347 471 845 582
## 1.313461e-05 1.897007e-03 1.475547e-04 2.078355e-03 2.421878e-05
## 29 681 896 750 175
## 5.602958e-04 8.477336e-06 1.623626e-03 2.774408e-03 4.824477e-05
## 278 375 650 438 413
## 2.262774e-03 5.562240e-05 7.408297e-05 3.781083e-03 2.275658e-04
## 208 367 660 580 1011
## 1.220810e-03 1.459393e-03 1.022206e-04 3.824184e-04 1.546565e-03
## 656 536 309 400 542
## 8.411397e-06 3.670029e-04 1.800716e-04 7.574795e-04 1.642123e-04
## 644 767 837 201 719
## 1.668121e-04 3.920933e-04 2.467008e-04 1.263043e-04 9.188111e-03
## 688 368 590 294 990
## 6.436413e-07 6.861298e-04 4.301725e-06 7.832775e-05 1.281989e-03
## 552 338 484 900 498
## 4.257244e-05 4.338202e-04 4.903211e-05 1.710622e-04 4.133042e-04
## 383 947 701 850 716
## 1.245367e-03 2.287444e-04 1.117334e-03 1.485097e-04 2.395916e-06
## 479 779 713 933 492
## 7.159151e-03 4.577298e-05 2.226930e-05 5.525190e-03 6.943164e-04
## 907 586 526 64 697
## 6.502930e-04 1.917726e-04 5.803358e-03 5.743124e-03 7.626695e-07
## 108 427 164 13 940
## 7.474722e-04 5.570479e-05 2.070667e-05 1.573826e-02 1.005033e-04
## 249 606 315 922 683
## 2.610149e-05 3.162560e-06 6.570085e-04 1.409728e-04 2.615108e-04
## 983 431 946 89 141
## 3.538339e-04 5.387260e-05 1.458375e-04 6.590086e-03 7.575136e-05
## 971 344 421 763 568
## 1.115337e-03 5.227766e-04 1.430528e-04 1.729046e-04 2.898238e-04
## 1020 628 403 861 572
## 3.108463e-03 5.529957e-06 9.362913e-04 1.003689e-03 3.079286e-05
## 523 941 592 638 988
## 2.701651e-04 1.528329e-05 3.743069e-04 3.071557e-04 3.145912e-05
## 1013 373 81 817 651
## 2.957574e-03 1.519689e-03 4.246689e-03 1.680078e-03 2.325119e-06
## 66 714 686 322 109
## 5.434705e-06 1.661612e-06 3.230784e-04 2.230489e-03 9.140934e-04
## 206 358 995 47 1024
## 5.768665e-05 6.981245e-04 2.659061e-04 4.728074e-04 2.220763e-04
## 57 676 967 691 742
## 8.030113e-06 2.414049e-05 1.762114e-05 6.988706e-06 3.404347e-04
## 675 177 361 463 731
## 1.029437e-04 4.824477e-05 2.551376e-03 1.294071e-03 4.993586e-05
## 528 374 165 415 561
## 6.038305e-03 3.656264e-05 1.875687e-05 2.140024e-05 5.325721e-04
## 736 23 252 524 583
## 4.205314e-06 4.736946e-03 1.504717e-04 2.701651e-04 1.932891e-03
## 1004 706 822 171 39
## 8.000828e-04 6.764469e-05 3.376494e-05 4.882266e-06 2.530711e-02
## 1012 243 876 603 539
## 1.214235e-03 4.070191e-03 2.261957e-05 1.791278e-02 3.404347e-04
## 891 836 615 45 318
## 1.643454e-04 1.341456e-04 1.174514e-02 2.961017e-04 8.363805e-04
## 973 220 560 986 570
## 9.661196e-05 4.348217e-05 6.498453e-05 2.404238e-04 4.467813e-05
## 930 987 60 770 454
## 1.680698e-03 1.687410e-03 2.290162e-04 4.993586e-05 1.316083e-04
## 620 966 766 371 626
## 1.237144e-01 1.328431e-05 2.566252e-04 2.849028e-04 2.526496e-06
## 91 333 489 855 456
## 3.718393e-03 4.998428e-04 3.612332e-03 1.209045e-03 5.173450e-03
## 924 84 781 529 513
## 9.644218e-05 4.970561e-03 1.370968e-05 9.424355e-05 3.842896e-04
## 867 519 728 335 636
## 2.264024e-04 2.180928e-03 7.492060e-05 5.275838e-04 5.522161e-05
## 381 811 870 915 984
## 1.607271e-03 4.386052e-05 6.158914e-05 6.049965e-04 1.328431e-05
## 869 1010 694 982 617
## 5.513626e-04 8.654955e-03 7.544213e-05 1.105327e-04 2.585744e-06
## 749 920 905 579 4
## 3.097030e-03 3.478708e-04 2.985659e-05 3.648923e-05 4.045541e-06
## 932 396 30 444 782
## 5.010604e-04 2.856480e-04 4.107086e-06 8.519303e-05 3.065360e-05
## 921 6 292 682 324
## 1.361857e-05 2.228969e-07 2.887160e-03 6.361666e-06 4.636952e-04
## 44 53 963 550 369
## 4.543429e-03 1.098307e-02 1.727640e-04 1.912543e-04 1.316835e-04
## 349 86 864 551 574
## 5.199707e-04 3.718393e-03 1.510432e-04 3.852600e-06 1.124431e-05
## 148 517 795 72 440
## 2.177314e-05 1.461089e-05 2.872242e-06 6.132318e-03 8.986135e-05
## 258 1000 470 87 607
## 2.678160e-03 4.812145e-03 2.783713e-03 4.352607e-03 5.662369e-06
## 664 516 36 703 190
## 3.655573e-05 1.252727e-05 1.055924e-04 2.182669e-05 1.509592e-05
## 521 259 624 117 738
## 4.431603e-04 6.794455e-05 3.838276e-05 9.730320e-04 1.984333e-05
## 755 494 610 196 449
## 6.301793e-07 1.160265e-04 1.242242e-01 6.811370e-05 1.216035e-03
## 1018 525 689 885 191
## 1.001278e-03 5.803358e-03 2.609802e-05 1.702337e-04 2.481514e-05
## 657 288 409 500 745
## 1.881627e-06 2.591018e-03 1.340682e-04 3.746800e-04 3.223016e-05
## 530 455 509 512 846
## 9.424355e-05 2.069125e-03 1.575281e-04 1.027503e-02 1.225860e-03
## 336 853 125 601 173
## 1.815574e-03 8.758443e-03 7.529716e-05 7.135865e-05 7.417773e-05
## 284 578 147 73 459
## 7.292260e-05 3.433011e-04 2.521308e-04 6.707939e-03 1.495145e-03
## 860 527 961 138 168
## 7.635597e-04 6.038305e-03 7.387629e-03 9.090088e-04 2.161607e-06
## 887 976 803 131 155
## 5.107010e-03 6.673673e-04 1.688133e-04 3.301233e-04 1.584072e-04
## 623 848 378 46 328
## 1.497702e-05 1.161802e-04 5.956902e-03 4.993586e-05 8.510213e-04
## 658 430 93 793 918
## 3.655877e-04 2.977442e-05 8.735749e-04 1.133017e-05 1.977726e-05
## 575 302 350 908 257
## 1.023718e-05 1.098763e-03 7.159672e-04 1.092238e-03 4.129061e-03
## 248 901 810 705 314
## 3.134544e-03 2.480331e-04 1.998960e-05 1.469210e-06 4.744665e-04
## 465 179 842 247 854
## 1.198232e-03 4.824477e-05 1.595533e-04 1.167657e-04 1.588727e-03
## 761 979 567 158 729
## 8.823868e-04 4.023390e-03 1.655074e-05 1.006361e-04 8.941013e-04
## 159 280 340 799 556
## 3.494463e-05 6.288157e-05 3.393807e-04 8.443351e-04 7.384088e-04
## 735 826 632 581 788
## 2.606594e-03 1.817063e-03 1.019360e-04 1.692352e-04 5.730802e-05
## 299 820 1028 223 122
## 1.969480e-04 6.717553e-08 6.770255e-05 1.554551e-03 3.192207e-05
## 163 760 802 200 1007
## 1.132528e-04 2.137730e-04 1.350116e-04 7.799815e-05 1.457775e-04
## 943 269 412 290 609
## 9.373306e-06 5.964569e-05 2.680648e-04 6.218343e-05 6.247174e-03
## 868 642 718 670 804
## 1.073494e-03 1.788378e-05 1.736413e-06 4.309591e-03 3.670029e-04
## 176 134 791 216 892
## 3.345951e-05 4.200543e-04 6.509779e-04 1.266877e-04 6.003199e-05
## 153 365 968 835 493
## 3.750334e-04 3.932787e-04 2.906097e-05 1.921621e-04 6.943164e-04
## 414 916 310 598 56
## 3.866187e-05 4.030752e-03 2.266737e-04 2.891428e-05 8.088256e-08
## 909 34 181 376 263
## 2.419149e-05 1.491655e-05 8.621338e-06 9.532991e-05 2.675688e-03
## 665 75 844 722 794
## 3.618528e-06 6.614375e-03 3.266342e-03 1.998960e-05 1.152100e-02
## 154 1027 360 880 188
## 1.172531e-04 6.141561e-05 1.444579e-03 9.708394e-06 4.142415e-03
## 996 227 24 236 92
## 3.650381e-05 1.028809e-02 1.805657e-06 6.883764e-03 1.516923e-03
## 654 229 508 936 679
## 4.232587e-06 1.787549e-05 9.399492e-03 1.325675e-05 1.818387e-05
## 167 540 645 732 222
## 2.040541e-05 1.817063e-03 2.537192e-04 5.730802e-05 2.207223e-04
## 461 9 778 616 776
## 1.476298e-03 1.210010e-03 2.059704e-05 1.226360e-01 6.541757e-05
## 1006 410 602 806 618
## 3.715509e-05 1.943723e-04 8.591409e-04 2.022842e-04 1.126561e-04
## 416 877 326 357 85
## 3.862031e-04 1.027630e-04 3.940245e-03 1.571186e-03 4.962436e-03
## 629 871 824 559 965
## 4.148435e-06 6.601547e-05 1.962535e-05 7.544065e-03 2.331361e-03
## 753 283 17 881 495
## 2.922345e-04 2.262774e-03 2.713124e-06 1.702337e-04 1.160265e-04
## 878 26 112 452 522
## 1.490525e-05 1.354922e-05 6.907186e-04 2.430953e-03 1.235378e-03
## 950 90 662 11 955
## 1.198891e-03 3.257893e-04 6.102292e-05 2.090358e-05 5.930257e-05
## 825 563 219 613 240
## 5.498560e-04 9.706583e-04 2.946756e-05 7.474370e-06 2.732902e-05
## 160 405 980 733 446
## 1.584072e-04 2.596814e-04 5.722436e-05 1.185507e-04 2.574928e-03
## 833 348 487 447 31
## 1.263372e-03 7.077685e-04 3.096808e-04 2.415430e-03 6.264984e-06
## 40 281 715 862 69
## 1.084425e-02 9.698863e-05 2.117130e-04 2.620765e-05 3.123289e-04
## 499 307 809 401 604
## 7.365914e-04 1.335272e-03 1.538723e-05 7.061867e-04 1.302212e-01
## 571 466 834 859 404
## 4.590833e-03 1.766336e-03 5.506566e-03 1.759536e-04 3.967888e-04
## 436 135 442 759 327
## 4.498389e-04 2.975715e-04 3.472443e-03 7.264292e-05 2.247795e-03
## 957 301 76 118 14
## 3.448103e-04 3.432704e-04 9.980120e-05 2.236707e-04 1.593775e-02
## 672 952 786 152 110
## 3.084592e-06 2.667909e-04 7.492060e-05 1.584072e-04 4.690685e-03
## 985 879 59 170 102
## 1.421104e-04 1.765439e-03 2.226235e-04 8.157878e-05 1.966163e-04
## 472 468 702 354 353
## 1.475547e-04 8.508808e-04 9.776016e-06 3.209163e-04 7.110637e-04
## 50 242 408 16 210
## 2.719971e-02 1.304488e-04 1.030053e-04 3.673380e-04 2.731114e-05
## 904 244 21 649 372
## 1.789290e-05 1.924851e-05 2.226710e-05 2.055167e-05 7.553574e-04
## 419 684 903 481 297
## 5.703673e-05 3.907338e-03 1.361857e-05 4.903211e-05 5.241785e-04
## 927 890 757 700 974
## 1.397536e-03 2.213612e-05 3.358893e-05 5.497093e-06 6.244620e-05
## 685 533 584 667 1029
## 6.473811e-06 9.739582e-06 2.585111e-03 4.873449e-04 1.566665e-04
## 942 954 821 723 402
## 1.770766e-03 1.676714e-04 1.975666e-05 4.386052e-05 1.927731e-03
## 356 520 246 997 215
## 2.730939e-03 4.015394e-04 4.246159e-05 1.761576e-03 7.815060e-05
## 10 981 588 1003 929
## 3.160110e-04 2.021707e-05 8.785347e-06 1.246318e-03 2.778754e-04
## 55 695 296 71 239
## 9.337630e-06 5.848383e-06 1.826179e-04 3.683052e-03 1.878624e-05
## 898 849 1001 612 394
## 7.431488e-03 3.635586e-05 3.329720e-03 1.996926e-05 3.150624e-03
## 126 98 751 150 772
## 2.236707e-04 5.424195e-04 7.127644e-04 2.546530e-04 1.917560e-04
## 648 162 577 203 841
## 1.242738e-05 4.628006e-05 2.684535e-05 2.881021e-03 2.054861e-04
## 432 884 764 754 475
## 9.470917e-05 2.285355e-04 1.838172e-04 2.329224e-05 6.964139e-03
## 450 506 474 991 95
## 2.656907e-03 1.100451e-04 1.475547e-04 5.527998e-03 5.284379e-04
## 384 544 548 390 518
## 2.856480e-04 1.135201e-05 2.560905e-05 2.164848e-03 1.074710e-04
## 895 634 934 910 856
## 1.003947e-03 3.158486e-05 3.706896e-04 9.647425e-05 2.901975e-03
## 977 717 237 63 797
## 1.770766e-03 4.389810e-06 4.966614e-03 8.001660e-04 1.298975e-05
## 883 789 978 80 115
## 1.421191e-04 1.185507e-04 6.152142e-04 6.132318e-03 1.625559e-03
## 558 585 631 142 773
## 1.993793e-04 6.680012e-04 4.822008e-05 6.992262e-05 3.644047e-04
## 696 655 156 282 913
## 2.725883e-06 5.710542e-05 5.214301e-04 2.640481e-04 6.422915e-04
## 230 38 1 743 185
## 2.600977e-05 4.117595e-03 1.615417e-04 5.254017e-04 1.730653e-05
## 295 709 969 557 441
## 1.129272e-04 1.375343e-04 4.222931e-04 1.060373e-04 4.758836e-05
## 422 678 346 418 407
## 1.879051e-04 4.873993e-04 3.323723e-03 3.791309e-05 1.390805e-04
## 99 359 832 483 370
## 8.290172e-05 1.084160e-03 1.444291e-05 4.903211e-05 1.838640e-04
## 741 666 204 888 182
## 2.328366e-03 1.891514e-04 2.598737e-05 2.243589e-05 4.824477e-05
## 337 316 478 482 238
## 1.007246e-03 9.929421e-04 3.560014e-04 4.903211e-05 4.112233e-03
## 1022 458 33 535 300
## 2.801515e-03 1.895377e-03 5.126136e-06 1.873398e-03 2.495258e-04
## 123 146 186 511 137
## 2.236707e-04 7.575136e-05 2.785380e-05 9.702368e-05 4.200543e-04
## 711 323 393 911 42
## 1.381962e-03 1.195689e-03 2.423498e-03 6.336842e-05 1.458661e-01
## 687 828 116 406 211
## 3.639585e-03 1.178641e-04 4.000345e-04 3.871000e-05 4.453712e-05
## 928 453 780 919 813
## 1.456093e-03 2.602925e-04 1.069983e-05 1.120756e-04 1.562342e-02
## 491 994 734 385 467
## 3.761997e-03 2.462608e-04 3.708437e-03 3.855439e-04 3.140176e-03
## 865 231 178 534 886
## 2.701242e-03 6.893292e-03 1.486196e-04 1.688133e-04 8.713539e-05
## 429 894 912 275 433
## 5.347727e-04 3.408389e-04 2.003331e-03 6.288157e-05 3.738998e-03
## 939 792 366 784 591
## 2.218172e-05 5.097641e-07 2.419257e-03 3.052726e-05 1.488131e-05
## 445 805 339 593 730
## 2.849974e-04 1.873398e-03 2.676763e-04 6.344868e-06 3.053428e-03
## 503 161 62 5 391
## 2.201347e-04 4.070085e-04 1.723693e-05 1.176608e-02 2.064026e-04
## 332 597 758 54 668
## 1.551116e-03 3.636871e-04 4.336485e-05 9.352940e-06 1.408614e-06
## 566 945 443 120 504
## 2.026515e-04 2.707292e-05 4.883172e-05 4.853041e-04 2.019840e-02
## 319 342 889 698 151
## 1.668301e-04 1.021919e-03 2.705196e-04 1.095857e-02 1.390913e-04
## 902 796 285 130 643
## 2.329952e-03 3.709585e-04 1.054947e-04 1.009158e-03 8.233072e-05
## 435 437 727 502 217
## 3.632833e-03 5.091075e-04 3.520880e-05 2.107693e-02 3.657092e-04
## 184 937 392 543 627
## 1.198392e-05 5.509620e-04 6.997071e-04 4.522341e-06 2.246271e-06
## 553 228 775 476 77
## 4.653296e-03 2.079385e-02 3.022476e-05 6.964139e-03 6.132318e-03
## 926 599 213 330 669
## 2.151033e-03 3.337791e-05 9.725473e-04 4.117986e-03 2.391684e-04
length(which(out>=1))
## [1] 0
# 不存在離群值 #
# 檢測共線性 #
vif(modle1.1)
## Cement Blast FlyAsh Water Age
## 2.028632 1.720565 2.291008 1.141951 1.189933
# 檢測影響點 #
eff <- cooks.distance(modle1.1)
eff
## 380 18 774 140 970
## 7.185198e-05 5.150208e-03 1.917560e-04 3.789731e-04 6.444140e-04
## 562 762 287 1015 462
## 1.974346e-04 1.808328e-02 4.954777e-04 1.831638e-03 5.492571e-03
## 998 41 114 143 677
## 2.019569e-04 1.335852e-07 3.904121e-03 1.518696e-04 1.110544e-06
## 183 420 241 251 746
## 1.522640e-04 1.956484e-04 4.451270e-05 5.589898e-05 2.300718e-03
## 653 313 838 364 88
## 4.893172e-05 6.415617e-04 2.702383e-04 2.948498e-04 3.718393e-03
## 351 600 944 61 1005
## 3.331349e-03 4.292651e-05 1.662274e-04 3.436463e-04 1.157055e-04
## 267 352 541 199 906
## 2.968464e-03 1.902841e-03 3.223880e-05 5.396380e-05 4.091397e-04
## 78 341 989 712 255
## 2.684107e-03 1.779255e-03 1.431459e-05 2.199750e-04 9.872104e-05
## 873 347 471 845 582
## 1.313461e-05 1.897007e-03 1.475547e-04 2.078355e-03 2.421878e-05
## 29 681 896 750 175
## 5.602958e-04 8.477336e-06 1.623626e-03 2.774408e-03 4.824477e-05
## 278 375 650 438 413
## 2.262774e-03 5.562240e-05 7.408297e-05 3.781083e-03 2.275658e-04
## 208 367 660 580 1011
## 1.220810e-03 1.459393e-03 1.022206e-04 3.824184e-04 1.546565e-03
## 656 536 309 400 542
## 8.411397e-06 3.670029e-04 1.800716e-04 7.574795e-04 1.642123e-04
## 644 767 837 201 719
## 1.668121e-04 3.920933e-04 2.467008e-04 1.263043e-04 9.188111e-03
## 688 368 590 294 990
## 6.436413e-07 6.861298e-04 4.301725e-06 7.832775e-05 1.281989e-03
## 552 338 484 900 498
## 4.257244e-05 4.338202e-04 4.903211e-05 1.710622e-04 4.133042e-04
## 383 947 701 850 716
## 1.245367e-03 2.287444e-04 1.117334e-03 1.485097e-04 2.395916e-06
## 479 779 713 933 492
## 7.159151e-03 4.577298e-05 2.226930e-05 5.525190e-03 6.943164e-04
## 907 586 526 64 697
## 6.502930e-04 1.917726e-04 5.803358e-03 5.743124e-03 7.626695e-07
## 108 427 164 13 940
## 7.474722e-04 5.570479e-05 2.070667e-05 1.573826e-02 1.005033e-04
## 249 606 315 922 683
## 2.610149e-05 3.162560e-06 6.570085e-04 1.409728e-04 2.615108e-04
## 983 431 946 89 141
## 3.538339e-04 5.387260e-05 1.458375e-04 6.590086e-03 7.575136e-05
## 971 344 421 763 568
## 1.115337e-03 5.227766e-04 1.430528e-04 1.729046e-04 2.898238e-04
## 1020 628 403 861 572
## 3.108463e-03 5.529957e-06 9.362913e-04 1.003689e-03 3.079286e-05
## 523 941 592 638 988
## 2.701651e-04 1.528329e-05 3.743069e-04 3.071557e-04 3.145912e-05
## 1013 373 81 817 651
## 2.957574e-03 1.519689e-03 4.246689e-03 1.680078e-03 2.325119e-06
## 66 714 686 322 109
## 5.434705e-06 1.661612e-06 3.230784e-04 2.230489e-03 9.140934e-04
## 206 358 995 47 1024
## 5.768665e-05 6.981245e-04 2.659061e-04 4.728074e-04 2.220763e-04
## 57 676 967 691 742
## 8.030113e-06 2.414049e-05 1.762114e-05 6.988706e-06 3.404347e-04
## 675 177 361 463 731
## 1.029437e-04 4.824477e-05 2.551376e-03 1.294071e-03 4.993586e-05
## 528 374 165 415 561
## 6.038305e-03 3.656264e-05 1.875687e-05 2.140024e-05 5.325721e-04
## 736 23 252 524 583
## 4.205314e-06 4.736946e-03 1.504717e-04 2.701651e-04 1.932891e-03
## 1004 706 822 171 39
## 8.000828e-04 6.764469e-05 3.376494e-05 4.882266e-06 2.530711e-02
## 1012 243 876 603 539
## 1.214235e-03 4.070191e-03 2.261957e-05 1.791278e-02 3.404347e-04
## 891 836 615 45 318
## 1.643454e-04 1.341456e-04 1.174514e-02 2.961017e-04 8.363805e-04
## 973 220 560 986 570
## 9.661196e-05 4.348217e-05 6.498453e-05 2.404238e-04 4.467813e-05
## 930 987 60 770 454
## 1.680698e-03 1.687410e-03 2.290162e-04 4.993586e-05 1.316083e-04
## 620 966 766 371 626
## 1.237144e-01 1.328431e-05 2.566252e-04 2.849028e-04 2.526496e-06
## 91 333 489 855 456
## 3.718393e-03 4.998428e-04 3.612332e-03 1.209045e-03 5.173450e-03
## 924 84 781 529 513
## 9.644218e-05 4.970561e-03 1.370968e-05 9.424355e-05 3.842896e-04
## 867 519 728 335 636
## 2.264024e-04 2.180928e-03 7.492060e-05 5.275838e-04 5.522161e-05
## 381 811 870 915 984
## 1.607271e-03 4.386052e-05 6.158914e-05 6.049965e-04 1.328431e-05
## 869 1010 694 982 617
## 5.513626e-04 8.654955e-03 7.544213e-05 1.105327e-04 2.585744e-06
## 749 920 905 579 4
## 3.097030e-03 3.478708e-04 2.985659e-05 3.648923e-05 4.045541e-06
## 932 396 30 444 782
## 5.010604e-04 2.856480e-04 4.107086e-06 8.519303e-05 3.065360e-05
## 921 6 292 682 324
## 1.361857e-05 2.228969e-07 2.887160e-03 6.361666e-06 4.636952e-04
## 44 53 963 550 369
## 4.543429e-03 1.098307e-02 1.727640e-04 1.912543e-04 1.316835e-04
## 349 86 864 551 574
## 5.199707e-04 3.718393e-03 1.510432e-04 3.852600e-06 1.124431e-05
## 148 517 795 72 440
## 2.177314e-05 1.461089e-05 2.872242e-06 6.132318e-03 8.986135e-05
## 258 1000 470 87 607
## 2.678160e-03 4.812145e-03 2.783713e-03 4.352607e-03 5.662369e-06
## 664 516 36 703 190
## 3.655573e-05 1.252727e-05 1.055924e-04 2.182669e-05 1.509592e-05
## 521 259 624 117 738
## 4.431603e-04 6.794455e-05 3.838276e-05 9.730320e-04 1.984333e-05
## 755 494 610 196 449
## 6.301793e-07 1.160265e-04 1.242242e-01 6.811370e-05 1.216035e-03
## 1018 525 689 885 191
## 1.001278e-03 5.803358e-03 2.609802e-05 1.702337e-04 2.481514e-05
## 657 288 409 500 745
## 1.881627e-06 2.591018e-03 1.340682e-04 3.746800e-04 3.223016e-05
## 530 455 509 512 846
## 9.424355e-05 2.069125e-03 1.575281e-04 1.027503e-02 1.225860e-03
## 336 853 125 601 173
## 1.815574e-03 8.758443e-03 7.529716e-05 7.135865e-05 7.417773e-05
## 284 578 147 73 459
## 7.292260e-05 3.433011e-04 2.521308e-04 6.707939e-03 1.495145e-03
## 860 527 961 138 168
## 7.635597e-04 6.038305e-03 7.387629e-03 9.090088e-04 2.161607e-06
## 887 976 803 131 155
## 5.107010e-03 6.673673e-04 1.688133e-04 3.301233e-04 1.584072e-04
## 623 848 378 46 328
## 1.497702e-05 1.161802e-04 5.956902e-03 4.993586e-05 8.510213e-04
## 658 430 93 793 918
## 3.655877e-04 2.977442e-05 8.735749e-04 1.133017e-05 1.977726e-05
## 575 302 350 908 257
## 1.023718e-05 1.098763e-03 7.159672e-04 1.092238e-03 4.129061e-03
## 248 901 810 705 314
## 3.134544e-03 2.480331e-04 1.998960e-05 1.469210e-06 4.744665e-04
## 465 179 842 247 854
## 1.198232e-03 4.824477e-05 1.595533e-04 1.167657e-04 1.588727e-03
## 761 979 567 158 729
## 8.823868e-04 4.023390e-03 1.655074e-05 1.006361e-04 8.941013e-04
## 159 280 340 799 556
## 3.494463e-05 6.288157e-05 3.393807e-04 8.443351e-04 7.384088e-04
## 735 826 632 581 788
## 2.606594e-03 1.817063e-03 1.019360e-04 1.692352e-04 5.730802e-05
## 299 820 1028 223 122
## 1.969480e-04 6.717553e-08 6.770255e-05 1.554551e-03 3.192207e-05
## 163 760 802 200 1007
## 1.132528e-04 2.137730e-04 1.350116e-04 7.799815e-05 1.457775e-04
## 943 269 412 290 609
## 9.373306e-06 5.964569e-05 2.680648e-04 6.218343e-05 6.247174e-03
## 868 642 718 670 804
## 1.073494e-03 1.788378e-05 1.736413e-06 4.309591e-03 3.670029e-04
## 176 134 791 216 892
## 3.345951e-05 4.200543e-04 6.509779e-04 1.266877e-04 6.003199e-05
## 153 365 968 835 493
## 3.750334e-04 3.932787e-04 2.906097e-05 1.921621e-04 6.943164e-04
## 414 916 310 598 56
## 3.866187e-05 4.030752e-03 2.266737e-04 2.891428e-05 8.088256e-08
## 909 34 181 376 263
## 2.419149e-05 1.491655e-05 8.621338e-06 9.532991e-05 2.675688e-03
## 665 75 844 722 794
## 3.618528e-06 6.614375e-03 3.266342e-03 1.998960e-05 1.152100e-02
## 154 1027 360 880 188
## 1.172531e-04 6.141561e-05 1.444579e-03 9.708394e-06 4.142415e-03
## 996 227 24 236 92
## 3.650381e-05 1.028809e-02 1.805657e-06 6.883764e-03 1.516923e-03
## 654 229 508 936 679
## 4.232587e-06 1.787549e-05 9.399492e-03 1.325675e-05 1.818387e-05
## 167 540 645 732 222
## 2.040541e-05 1.817063e-03 2.537192e-04 5.730802e-05 2.207223e-04
## 461 9 778 616 776
## 1.476298e-03 1.210010e-03 2.059704e-05 1.226360e-01 6.541757e-05
## 1006 410 602 806 618
## 3.715509e-05 1.943723e-04 8.591409e-04 2.022842e-04 1.126561e-04
## 416 877 326 357 85
## 3.862031e-04 1.027630e-04 3.940245e-03 1.571186e-03 4.962436e-03
## 629 871 824 559 965
## 4.148435e-06 6.601547e-05 1.962535e-05 7.544065e-03 2.331361e-03
## 753 283 17 881 495
## 2.922345e-04 2.262774e-03 2.713124e-06 1.702337e-04 1.160265e-04
## 878 26 112 452 522
## 1.490525e-05 1.354922e-05 6.907186e-04 2.430953e-03 1.235378e-03
## 950 90 662 11 955
## 1.198891e-03 3.257893e-04 6.102292e-05 2.090358e-05 5.930257e-05
## 825 563 219 613 240
## 5.498560e-04 9.706583e-04 2.946756e-05 7.474370e-06 2.732902e-05
## 160 405 980 733 446
## 1.584072e-04 2.596814e-04 5.722436e-05 1.185507e-04 2.574928e-03
## 833 348 487 447 31
## 1.263372e-03 7.077685e-04 3.096808e-04 2.415430e-03 6.264984e-06
## 40 281 715 862 69
## 1.084425e-02 9.698863e-05 2.117130e-04 2.620765e-05 3.123289e-04
## 499 307 809 401 604
## 7.365914e-04 1.335272e-03 1.538723e-05 7.061867e-04 1.302212e-01
## 571 466 834 859 404
## 4.590833e-03 1.766336e-03 5.506566e-03 1.759536e-04 3.967888e-04
## 436 135 442 759 327
## 4.498389e-04 2.975715e-04 3.472443e-03 7.264292e-05 2.247795e-03
## 957 301 76 118 14
## 3.448103e-04 3.432704e-04 9.980120e-05 2.236707e-04 1.593775e-02
## 672 952 786 152 110
## 3.084592e-06 2.667909e-04 7.492060e-05 1.584072e-04 4.690685e-03
## 985 879 59 170 102
## 1.421104e-04 1.765439e-03 2.226235e-04 8.157878e-05 1.966163e-04
## 472 468 702 354 353
## 1.475547e-04 8.508808e-04 9.776016e-06 3.209163e-04 7.110637e-04
## 50 242 408 16 210
## 2.719971e-02 1.304488e-04 1.030053e-04 3.673380e-04 2.731114e-05
## 904 244 21 649 372
## 1.789290e-05 1.924851e-05 2.226710e-05 2.055167e-05 7.553574e-04
## 419 684 903 481 297
## 5.703673e-05 3.907338e-03 1.361857e-05 4.903211e-05 5.241785e-04
## 927 890 757 700 974
## 1.397536e-03 2.213612e-05 3.358893e-05 5.497093e-06 6.244620e-05
## 685 533 584 667 1029
## 6.473811e-06 9.739582e-06 2.585111e-03 4.873449e-04 1.566665e-04
## 942 954 821 723 402
## 1.770766e-03 1.676714e-04 1.975666e-05 4.386052e-05 1.927731e-03
## 356 520 246 997 215
## 2.730939e-03 4.015394e-04 4.246159e-05 1.761576e-03 7.815060e-05
## 10 981 588 1003 929
## 3.160110e-04 2.021707e-05 8.785347e-06 1.246318e-03 2.778754e-04
## 55 695 296 71 239
## 9.337630e-06 5.848383e-06 1.826179e-04 3.683052e-03 1.878624e-05
## 898 849 1001 612 394
## 7.431488e-03 3.635586e-05 3.329720e-03 1.996926e-05 3.150624e-03
## 126 98 751 150 772
## 2.236707e-04 5.424195e-04 7.127644e-04 2.546530e-04 1.917560e-04
## 648 162 577 203 841
## 1.242738e-05 4.628006e-05 2.684535e-05 2.881021e-03 2.054861e-04
## 432 884 764 754 475
## 9.470917e-05 2.285355e-04 1.838172e-04 2.329224e-05 6.964139e-03
## 450 506 474 991 95
## 2.656907e-03 1.100451e-04 1.475547e-04 5.527998e-03 5.284379e-04
## 384 544 548 390 518
## 2.856480e-04 1.135201e-05 2.560905e-05 2.164848e-03 1.074710e-04
## 895 634 934 910 856
## 1.003947e-03 3.158486e-05 3.706896e-04 9.647425e-05 2.901975e-03
## 977 717 237 63 797
## 1.770766e-03 4.389810e-06 4.966614e-03 8.001660e-04 1.298975e-05
## 883 789 978 80 115
## 1.421191e-04 1.185507e-04 6.152142e-04 6.132318e-03 1.625559e-03
## 558 585 631 142 773
## 1.993793e-04 6.680012e-04 4.822008e-05 6.992262e-05 3.644047e-04
## 696 655 156 282 913
## 2.725883e-06 5.710542e-05 5.214301e-04 2.640481e-04 6.422915e-04
## 230 38 1 743 185
## 2.600977e-05 4.117595e-03 1.615417e-04 5.254017e-04 1.730653e-05
## 295 709 969 557 441
## 1.129272e-04 1.375343e-04 4.222931e-04 1.060373e-04 4.758836e-05
## 422 678 346 418 407
## 1.879051e-04 4.873993e-04 3.323723e-03 3.791309e-05 1.390805e-04
## 99 359 832 483 370
## 8.290172e-05 1.084160e-03 1.444291e-05 4.903211e-05 1.838640e-04
## 741 666 204 888 182
## 2.328366e-03 1.891514e-04 2.598737e-05 2.243589e-05 4.824477e-05
## 337 316 478 482 238
## 1.007246e-03 9.929421e-04 3.560014e-04 4.903211e-05 4.112233e-03
## 1022 458 33 535 300
## 2.801515e-03 1.895377e-03 5.126136e-06 1.873398e-03 2.495258e-04
## 123 146 186 511 137
## 2.236707e-04 7.575136e-05 2.785380e-05 9.702368e-05 4.200543e-04
## 711 323 393 911 42
## 1.381962e-03 1.195689e-03 2.423498e-03 6.336842e-05 1.458661e-01
## 687 828 116 406 211
## 3.639585e-03 1.178641e-04 4.000345e-04 3.871000e-05 4.453712e-05
## 928 453 780 919 813
## 1.456093e-03 2.602925e-04 1.069983e-05 1.120756e-04 1.562342e-02
## 491 994 734 385 467
## 3.761997e-03 2.462608e-04 3.708437e-03 3.855439e-04 3.140176e-03
## 865 231 178 534 886
## 2.701242e-03 6.893292e-03 1.486196e-04 1.688133e-04 8.713539e-05
## 429 894 912 275 433
## 5.347727e-04 3.408389e-04 2.003331e-03 6.288157e-05 3.738998e-03
## 939 792 366 784 591
## 2.218172e-05 5.097641e-07 2.419257e-03 3.052726e-05 1.488131e-05
## 445 805 339 593 730
## 2.849974e-04 1.873398e-03 2.676763e-04 6.344868e-06 3.053428e-03
## 503 161 62 5 391
## 2.201347e-04 4.070085e-04 1.723693e-05 1.176608e-02 2.064026e-04
## 332 597 758 54 668
## 1.551116e-03 3.636871e-04 4.336485e-05 9.352940e-06 1.408614e-06
## 566 945 443 120 504
## 2.026515e-04 2.707292e-05 4.883172e-05 4.853041e-04 2.019840e-02
## 319 342 889 698 151
## 1.668301e-04 1.021919e-03 2.705196e-04 1.095857e-02 1.390913e-04
## 902 796 285 130 643
## 2.329952e-03 3.709585e-04 1.054947e-04 1.009158e-03 8.233072e-05
## 435 437 727 502 217
## 3.632833e-03 5.091075e-04 3.520880e-05 2.107693e-02 3.657092e-04
## 184 937 392 543 627
## 1.198392e-05 5.509620e-04 6.997071e-04 4.522341e-06 2.246271e-06
## 553 228 775 476 77
## 4.653296e-03 2.079385e-02 3.022476e-05 6.964139e-03 6.132318e-03
## 926 599 213 330 669
## 2.151033e-03 3.337791e-05 9.725473e-04 4.117986e-03 2.391684e-04
# 檢測標準 #
qf(0.5,6,720-6)
## [1] 0.8921954
length(which(as.vector(eff) > qf(0.5,6,720)))
## [1] 0
# 逐步回歸 #
step(modle1.0,direction = 'both')
## Start: AIC=589.76
## over400 ~ Cement + Blast + FlyAsh + Water + Superplasticizer +
## 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
# 機器學習 #
# 逐步回歸模型 #
modle_train <- glm(formula = over400 ~ Cement+ Blast+ FlyAsh+ Water+ Superplasticizer
+Age, family=binomial(link="logit"), data = concrete_train)
AIC(modle_train)
## [1] 585.2244
result <- predict(modle_train, newdata = concrete_test, type = "response")
result_Approved <- ifelse(result > 0.7, 1, 0)
cm <- table(concrete_test$over400, result_Approved, dnn = c("實際", "預測"))
cm
## 預測
## 實際 0 1
## 0 179 13
## 1 60 57
cm[4] / sum(cm[, 2])
## [1] 0.8142857
cm[1] / sum(cm[, 1])
## [1] 0.748954
accuracy <- sum(diag(cm)) / sum(cm)
accuracy
## [1] 0.763754
# 機器學習 #
# 原始模型刪減不顯著係數之變數 #
modle_train <- glm(formula = over400 ~ Cement+ Blast+ FlyAsh+ Water
+Age, family=binomial(link="logit"), data = concrete_train)
AIC(modle_train)
## [1] 585.6844
result <- predict(modle_train, newdata = concrete_test, type = "response")
result_Approved <- ifelse(result > 0.7, 1, 0)
cm <- table(concrete_test$over400, result_Approved, dnn = c("實際", "預測"))
cm
## 預測
## 實際 0 1
## 0 180 12
## 1 60 57
cm[4] / sum(cm[, 2])
## [1] 0.826087
cm[1] / sum(cm[, 1])
## [1] 0.75
accuracy <- sum(diag(cm)) / sum(cm)
accuracy
## [1] 0.7669903
#
# 最終模型確認 #
modle_final <- glm(formula = over400 ~ Cement+ Blast+ FlyAsh+ Water+ Superplasticizer
+ Age, family = binomial(link = "logit"), data =concrete_train, na.action = na.exclude)
summary(modle_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
#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]])))
