##
## 影响居民消费价格指数的主成分分析
## 使用主成分进行聚类分析
## 进行主成分回归分析
## 加载包
library(readxl)
## Warning: package 'readxl' was built under R version 3.3.2
library(psych)
library(VIM)
## Warning: package 'VIM' was built under R version 3.3.2
## Loading required package: colorspace
## Warning: package 'colorspace' was built under R version 3.3.2
## Loading required package: grid
## Loading required package: data.table
## Warning: package 'data.table' was built under R version 3.3.2
## VIM is ready to use.
## Since version 4.0.0 the GUI is in its own package VIMGUI.
##
## Please use the package to use the new (and old) GUI.
## Suggestions and bug-reports can be submitted at: https://github.com/alexkowa/VIM/issues
##
## Attaching package: 'VIM'
## The following object is masked from 'package:datasets':
##
## sleep
library(xlsx)
## Loading required package: rJava
## Warning: package 'rJava' was built under R version 3.3.2
## Loading required package: xlsxjars
par(family = "STKaiti")
## 读取数据
mydata <- read_excel("22232.xls")
mydata <- mydata[1:80,]
## 查看数据
head(mydata)
## # A tibble: 6 x 16
## 时间 居民消费价格指数 食品烟酒 粮食 肉禽及其制品 蛋类 水产品 鲜菜
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 2017年8月… 100. 101. 100. 101. 114. 98.9 108.
## 2 2017年7月… 100. 100. 100. 99.5 103. 99.8 107.
## 3 2017年6月… 99.8 99.3 100. 97.8 105. 99.5 98.9
## 4 2017年5月… 99.9 99.6 100. 98.2 96.6 101. 93.8
## 5 2017年4月… 100. 99.7 100. 98.8 99.4 102. 95.0
## 6 2017年3月… 99.7 98.7 100. 97.5 96.0 99.7 92.1
## # ... with 8 more variables: 鲜果 <dbl>, 衣着 <dbl>, 居住 <dbl>,
## # 生活用品及服务 <dbl>, 交通和通信 <dbl>, 教育文化和娱乐 <dbl>,
## # 医疗保健 <dbl>, 其他用品和服务 <dbl>
summary(mydata)
## 时间 居民消费价格指数 食品烟酒 粮食
## Length:80 Min. : 99.1 Min. : 97.10 Min. : 99.9
## Class :character 1st Qu.: 99.9 1st Qu.: 99.38 1st Qu.:100.1
## Mode :character Median :100.1 Median :100.00 Median :100.2
## Mean :100.2 Mean :100.31 Mean :100.3
## 3rd Qu.:100.5 3rd Qu.:101.20 3rd Qu.:100.3
## Max. :101.6 Max. :104.60 Max. :101.2
## 肉禽及其制品 蛋类 水产品 鲜菜
## Min. : 93.30 Min. : 91.90 Min. : 86.2 Min. : 78.50
## 1st Qu.: 98.88 1st Qu.: 98.22 1st Qu.: 99.0 1st Qu.: 94.58
## Median :100.00 Median : 99.45 Median : 99.7 Median :100.15
## Mean :100.34 Mean :100.21 Mean :100.4 Mean :101.16
## 3rd Qu.:101.42 3rd Qu.:102.53 3rd Qu.:101.2 3rd Qu.:105.65
## Max. :107.10 Max. :113.50 Max. :112.7 Max. :129.90
## 鲜果 衣着 居住 生活用品及服务
## Min. : 86.5 Min. : 99.6 Min. : 99.0 Min. : 99.7
## 1st Qu.: 97.8 1st Qu.: 99.9 1st Qu.: 99.8 1st Qu.:100.0
## Median : 99.5 Median :100.1 Median :100.2 Median :100.1
## Mean :100.1 Mean :100.1 Mean :100.2 Mean :100.1
## 3rd Qu.:102.8 3rd Qu.:100.2 3rd Qu.:100.6 3rd Qu.:100.2
## Max. :111.0 Max. :102.1 Max. :101.6 Max. :100.6
## 交通和通信 教育文化和娱乐 医疗保健 其他用品和服务
## Min. : 99.3 Min. : 99.1 Min. : 99.1 Min. : 97.1
## 1st Qu.:100.0 1st Qu.: 99.7 1st Qu.: 99.9 1st Qu.:100.0
## Median :100.1 Median :100.0 Median :100.2 Median :100.1
## Mean :100.1 Mean :100.0 Mean :100.2 Mean :100.2
## 3rd Qu.:100.2 3rd Qu.:100.3 3rd Qu.:100.5 3rd Qu.:100.3
## Max. :101.4 Max. :101.6 Max. :101.1 Max. :102.8
## 对数据是否有缺失值可视化
par(family = "STKaiti",cex = 0.8)
VIM::aggr(mydata)
## 没有缺失值
## 自动发现合适的主成分个数
pca1 <- fa.parallel(mydata[,3:16],fa = "pc",n.iter=40)
## The estimated weights for the factor scores are probably incorrect. Try a different factor extraction method.
## Parallel analysis suggests that the number of factors = NA and the number of components = 1
## 主成分分析特征值
pca1$pc.values
## [1] 4.30640334 1.45218100 1.25812465 1.18331734 1.11249117 0.97804237
## [7] 0.85463085 0.72018235 0.66539057 0.54171801 0.35848865 0.33292350
## [13] 0.16307527 0.07303092
## 从图上可以看出特征值突变的特征为1个特征，但是特征值大于1的特征有5个
## 下面先假设有5个特征，进行详细的主成分分析
## 主成分分析,不指定主成分 个数
pca_2 <- princomp( mydata[,3:16],cor = TRUE)
## 这里输出了所有的主成分
summary(pca_2,loadings = TRUE)
## Importance of components:
## Comp.1 Comp.2 Comp.3 Comp.4
## Standard deviation 2.0751875 1.2050647 1.12166156 1.08780391
## Proportion of Variance 0.3076002 0.1037272 0.08986605 0.08452267
## Cumulative Proportion 0.3076002 0.4113275 0.50119350 0.58571617
## Comp.5 Comp.6 Comp.7 Comp.8
## Standard deviation 1.05474697 0.98896025 0.92446247 0.8486356
## Proportion of Variance 0.07946365 0.06986017 0.06104506 0.0514416
## Cumulative Proportion 0.66517982 0.73503999 0.79608505 0.8475266
## Comp.9 Comp.10 Comp.11 Comp.12
## Standard deviation 0.8157148 0.73601495 0.59873921 0.57699523
## Proportion of Variance 0.0475279 0.03869414 0.02560633 0.02378025
## Cumulative Proportion 0.8950545 0.93374869 0.95935502 0.98313527
## Comp.13 Comp.14
## Standard deviation 0.40382579 0.270242343
## Proportion of Variance 0.01164823 0.005216495
## Cumulative Proportion 0.99478351 1.000000000
##
## Loadings:
## Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 Comp.7 Comp.8
## 食品烟酒 -0.430 -0.183 -0.292
## 粮食 -0.183 -0.328 0.325 -0.282 0.218 -0.490 0.125
## 肉禽及其制品 -0.300 0.191 0.154 0.257 0.242 0.204 -0.155
## 蛋类 -0.181 0.439 0.284 -0.197 -0.134 0.393 -0.166 0.423
## 水产品 -0.365 -0.199 0.197 0.354 -0.115 -0.179
## 鲜菜 -0.276 -0.343 -0.505 -0.158 0.264 0.203
## 鲜果 -0.172 -0.558 -0.359 -0.181 0.181
## 衣着 0.134 0.197 0.585 -0.495 0.223 0.464
## 居住 0.230 -0.415 0.526 0.382
## 生活用品及服务 -0.270 -0.228 0.318 -0.230 -0.347 -0.320 -0.132
## 交通和通信 -0.221 -0.231 0.526 0.106 -0.217 0.399 -0.207
## 教育文化和娱乐 -0.271 0.153 0.397 -0.173 0.386 0.379
## 医疗保健 -0.219 0.255 -0.131 0.454 -0.203 -0.225 -0.375 0.322
## 其他用品和服务 -0.326 -0.113 0.313 0.411 0.275
## Comp.9 Comp.10 Comp.11 Comp.12 Comp.13 Comp.14
## 食品烟酒 0.824
## 粮食 0.337 -0.457 -0.149 0.124
## 肉禽及其制品 -0.526 -0.417 0.411 -0.158
## 蛋类 0.270 0.306 -0.300
## 水产品 0.370 -0.126 0.658 -0.163
## 鲜菜 0.189 0.109 -0.362 0.139 -0.136 -0.442
## 鲜果 -0.344 -0.175 0.424 -0.329 -0.165
## 衣着 -0.202 0.128 -0.126
## 居住 -0.189 0.257 -0.311 0.345 0.159
## 生活用品及服务 -0.142 0.440 0.200 0.413 -0.215
## 交通和通信 -0.123 -0.391 -0.427
## 教育文化和娱乐 0.421 -0.149 0.240 0.320 0.226
## 医疗保健 -0.277 -0.198 -0.433 -0.147
## 其他用品和服务 0.285 0.152 0.102 -0.119 -0.630
## 可以看出5个主成分的累计贡献率为66.5%
## 碎石图
screeplot(pca_2,type = "line",main = "碎石图",npcs = length(pca_2$sdev))
## 主成分双标散点图
biplot(pca_2,main = "主成分分析",cex = 0.7)
## 标准载荷矩阵（旋转后的）
pca_2$loadings[1:14,1:14]
## Comp.1 Comp.2 Comp.3 Comp.4
## 食品烟酒 -0.4297951 0.01128479 -0.182514318 -0.292455045
## 粮食 -0.1828897 -0.32772223 0.325075362 -0.282456078
## 肉禽及其制品 -0.2997557 0.19078525 0.154138486 -0.078427250
## 蛋类 -0.1808412 0.43930051 0.283538072 -0.196712128
## 水产品 -0.3650635 -0.03602757 -0.199280609 0.196791347
## 鲜菜 -0.2757534 0.04341014 -0.343129149 -0.504942283
## 鲜果 -0.1719884 -0.55807778 -0.358924873 0.009727364
## 衣着 0.1344033 -0.03927725 0.197418687 -0.094830384
## 居住 0.2302924 -0.41476594 0.003681783 0.083614223
## 生活用品及服务 -0.2704610 -0.22758524 0.317928190 -0.086742090
## 交通和通信 -0.2208387 -0.23094881 0.526281053 0.106354778
## 教育文化和娱乐 -0.2706186 -0.04511232 0.153173457 0.396917452
## 医疗保健 -0.2187936 0.25537391 -0.131318070 0.453698952
## 其他用品和服务 -0.3259699 -0.04996773 -0.113314894 0.312806775
## Comp.5 Comp.6 Comp.7 Comp.8
## 食品烟酒 0.01691091 -0.0466481532 0.07966491 0.02336223
## 粮食 0.21825816 0.0531323959 -0.48972578 0.12485553
## 肉禽及其制品 0.25715883 0.2417681259 0.20386589 -0.15497303
## 蛋类 -0.13424643 0.3927781530 -0.16636163 0.42270291
## 水产品 0.35444424 0.0005232331 -0.11492233 -0.17925325
## 鲜菜 -0.15846204 -0.0457505583 0.26385554 0.20297477
## 鲜果 -0.18133505 -0.0028873405 0.01681135 0.18113323
## 衣着 0.58516417 -0.4948198637 0.22258011 0.46404607
## 居住 0.03688833 0.5261233942 -0.01618158 0.38197364
## 生活用品及服务 -0.23022328 -0.3469650086 -0.31972306 -0.13190133
## 交通和通信 -0.21692188 0.0584834142 0.39892220 -0.20729914
## 教育文化和娱乐 -0.17345669 -0.0925039308 0.38639396 0.37875733
## 医疗保健 -0.20275171 -0.2249837827 -0.37482780 0.32207410
## 其他用品和服务 0.41142448 0.2748462113 -0.02266001 -0.07892288
## Comp.9 Comp.10 Comp.11 Comp.12
## 食品烟酒 -0.04512819 0.005323663 -0.0608217277 -0.04311046
## 粮食 0.33720160 -0.457360630 -0.1488738350 -0.05203458
## 肉禽及其制品 -0.52573865 -0.416985347 0.0925450048 0.41149063
## 蛋类 -0.07579387 0.270273033 0.3063586999 -0.29959667
## 水产品 -0.04121830 0.370311502 -0.1260884521 -0.03947073
## 鲜菜 0.18931826 0.108695307 -0.3616929999 0.13854043
## 鲜果 -0.34378241 -0.174770802 0.4237015731 -0.32946530
## 衣着 -0.20214724 0.127747588 -0.0002473008 -0.12564636
## 居住 -0.18872341 0.257440785 -0.3114300908 0.34545849
## 生活用品及服务 -0.14228622 0.439574605 0.2004320967 0.41313307
## 交通和通信 -0.12287838 0.064237756 -0.3907310220 -0.42706092
## 教育文化和娱乐 0.42054755 -0.149292234 0.2401641747 0.31980929
## 医疗保健 -0.27695681 -0.197831317 -0.4331043943 -0.04911051
## 其他用品和服务 0.28459829 0.151675908 0.1018977627 -0.11905486
## Comp.13 Comp.14
## 食品烟酒 -0.010347707 0.82415003
## 粮食 0.124495821 -0.06752970
## 肉禽及其制品 -0.025928073 -0.15760167
## 蛋类 0.091542121 -0.07606114
## 水产品 0.658154791 -0.16299591
## 鲜菜 -0.136429025 -0.44166192
## 鲜果 0.009792176 -0.16482542
## 衣着 -0.084430650 -0.01353132
## 居住 0.005880239 0.15918637
## 生活用品及服务 -0.214574185 -0.05549560
## 交通和通信 -0.032163008 -0.04136119
## 教育文化和娱乐 0.226102179 0.04578076
## 医疗保健 -0.147430202 -0.01742342
## 其他用品和服务 -0.629577226 -0.06386849
# write.xlsx(data.frame(pca_2$loadings[1:14,1:14]),file = "主成分载荷.xlsx")
## 标准载荷可视化
pca_load <- data.frame(pca_2$loadings[1:14,1:14])
par(mfcol = c(1,2),family = "STKaiti",cex = 0.6)
plot(pca_load$Comp.1,pca_load$Comp.2,type = "n",xla = "Comp 1",
ylab = "Comp 2",main = "PCA Loading",xlim = c(-.6,.6),ylim = c(-.6,.6))
text(pca_load$Comp.1,pca_load$Comp.2,row.names(pca_load))
abline(h = 0)
abline(v = 0)
plot(pca_load$Comp.3,pca_load$Comp.4,type = "n",xla = "Comp 3",
ylab = "Comp 4",main = "PCA Loading",xlim = c(-.6,.6),ylim = c(-.6,.6))
text(pca_load$Comp.3,pca_load$Comp.4,row.names(pca_load))
abline(h = 0)
abline(v = 0)
par(mfcol = c(1,1),family = "STKaiti")
## 主成分得分
pca_2$scores
## Comp.1 Comp.2 Comp.3 Comp.4 Comp.5
## [1,] -0.907008805 2.260218256 0.747449168 -0.53131318 -1.378609845
## [2,] -0.006439092 2.380540445 -0.373307462 0.90313182 -1.369548871
## [3,] 0.866146000 1.342964662 -0.222255744 0.45877909 -0.715735631
## [4,] 1.036475013 -0.460860512 -1.222313116 0.70360205 -0.353069399
## [5,] -0.106444366 0.121218769 -0.687449243 1.66436659 0.001499362
## [6,] 2.472690608 0.445636101 -1.118263553 1.02614160 1.017292635
## [7,] 1.811654727 -0.546865709 -2.472525125 0.12814779 0.294100185
## [8,] -4.724768813 -2.129073823 1.791893951 2.73480398 -1.883189307
## [9,] -0.540995337 -0.804428436 0.635858281 0.36666247 -1.296919313
## [10,] 1.071547003 0.602150919 -0.530939229 -0.43176695 0.684221336
## [11,] 1.956415689 0.310665831 -0.458099241 0.14997859 0.092638320
## [12,] -1.076565979 0.093704290 0.043456825 0.37738445 -0.291428360
## [13,] 0.921194618 1.751350299 -1.873860426 -0.59703495 -0.095074550
## [14,] -0.855408949 0.717365257 -1.010113115 2.50990698 -0.803801827
## [15,] 0.305380751 0.467390295 1.144313622 2.29999090 -0.957080876
## [16,] 1.464222856 0.464799538 1.147912916 1.94387413 0.559455318
## [17,] 0.817402740 0.525398558 0.423332900 1.45739319 0.176975916
## [18,] 3.733297322 1.045194728 -2.705690512 0.61723119 1.762147035
## [19,] -4.984480095 -0.632196236 -2.128159740 -1.14870248 0.029428377
## [20,] -1.652973468 0.635943393 -1.400208455 0.70417631 -1.036717103
## [21,] -0.373836040 0.238597231 -1.185901824 -1.25839302 -0.421200238
## [22,] 1.106362136 -1.015866134 0.011057081 -0.54321673 -0.617337530
## [23,] 2.005125078 -1.024564451 -0.173861434 0.73044461 0.209006605
## [24,] 0.798688458 0.555024918 -0.002443265 0.31691135 -0.705968519
## [25,] -0.476254510 2.287622805 0.039133686 -2.00738937 0.069321855
## [26,] -0.533804208 2.445147824 0.050956606 0.36482167 0.290996424
## [27,] 1.175318789 1.242071440 1.330540547 -0.22984304 2.684597929
## [28,] 1.923158832 0.134149150 1.526566765 0.64576155 3.381354947
## [29,] 1.450343554 -0.155755748 -0.064474629 1.10390498 -0.087073578
## [30,] 3.535565326 -0.631453143 -1.472010543 0.76901307 1.131863108
## [31,] -4.359904705 -1.309258670 -0.167577912 0.08749331 -2.300603567
## [32,] -0.537122500 -0.524025691 -0.564772607 -0.06266172 -0.780153213
## [33,] -0.051264796 -0.304837397 -0.944712621 -1.22921965 -0.432384546
## [34,] 2.017011512 -0.747799405 -0.185673436 -1.03029241 -0.006794525
## [35,] 1.063813907 -0.951842775 0.313849019 -0.19312671 0.198515472
## [36,] 0.031441937 0.051889177 -0.766654823 -0.05361298 -0.238864958
## [37,] 0.126604068 0.180633287 -1.399978638 -1.02899243 -0.241006898
## [38,] 0.154285753 1.220955996 -0.490317753 1.17316541 -0.776657672
## [39,] 0.567641549 0.158048118 0.166734581 0.06472442 -0.310704477
## [40,] -0.123232453 -0.236820037 0.183784713 -0.69474991 -0.344430972
## [41,] 0.383363097 0.912435943 0.671067180 -0.06575764 -0.112649854
## [42,] 1.654233737 0.703145072 0.836629526 -0.70249751 0.629696545
## [43,] 0.099493838 0.019455791 0.212599660 -0.73883375 0.775895988
## [44,] -2.908308959 1.183494909 1.542776101 0.55599418 -1.773936659
## [45,] -0.390653037 -0.070787717 -0.283008082 -0.35653634 -0.091894404
## [46,] 1.780557011 -0.656914892 0.485355733 -1.13459871 -0.219629818
## [47,] 1.659109550 -1.816361294 -1.034730143 0.48790258 -1.778386275
## [48,] -3.029536111 -1.235318121 -1.707465921 1.48346260 0.937881723
## [49,] -2.508875795 -0.008803607 -0.611585287 0.71420573 1.697824794
## [50,] -0.196802072 0.832078408 -0.390660016 1.38030098 -0.544659883
## [51,] 0.928007717 0.825740067 0.037853323 -0.23733976 -0.869744882
## [52,] 3.234203641 -0.292170625 0.464370308 -1.80035899 -2.800173229
## [53,] -0.148318004 0.100428870 -1.075373709 0.66555968 0.913480284
## [54,] 6.123870376 -0.255638116 1.039822004 -1.81788623 -2.812135653
## [55,] -4.416258530 0.745778019 -0.038200139 0.56872379 0.956426063
## [56,] -4.934912496 -0.429111973 -0.182349747 0.38799066 2.523674320
## [57,] -1.391394808 0.377546859 -0.712176445 -2.38681437 0.542549679
## [58,] 0.786247133 -1.297770066 0.528639599 -1.47774837 0.224036459
## [59,] 1.196757742 -1.472665538 0.545931343 1.10907664 0.472768672
## [60,] -0.472185292 -0.971310171 1.893784208 -0.01840468 0.329150581
## [61,] -1.158807012 1.429213473 0.443101366 -1.82166306 0.116672675
## [62,] -0.065497312 0.947317424 -0.093245353 0.41907143 -0.084457199
## [63,] 1.660684764 2.187683812 1.761034216 0.15674503 0.030477700
## [64,] 1.332434701 -0.059079266 0.274832634 0.09171161 0.201707118
## [65,] 0.478981001 -0.629108436 0.491712938 1.65287943 -0.537748899
## [66,] 0.611751949 -0.397171684 -0.709893546 0.09839410 0.268668610
## [67,] 0.832161534 -1.209898466 0.023867947 -0.07578773 0.582483399
## [68,] -4.980592683 0.401462461 -1.589227094 -1.12692735 -0.750524082
## [69,] 0.575951345 -0.361389738 -1.692947591 -1.38719654 0.214944306
## [70,] 1.853141470 -3.326602954 0.332093841 -0.25208782 -0.118861406
## [71,] 1.661853534 -2.273557159 -0.601039270 0.04028153 0.777071592
## [72,] -0.022097973 -1.251417185 0.542225002 -1.41274659 0.973525515
## [73,] -0.894432894 0.383416714 2.279982862 -0.60914267 -0.078557601
## [74,] -1.504016407 2.097611340 1.558791476 -0.48136213 0.584024966
## [75,] -0.870057412 2.475926235 2.385104000 -0.90496068 1.067010405
## [76,] -0.274730180 -0.341920908 2.597302212 0.08052605 0.330174654
## [77,] -0.296807179 -1.707687455 1.308815468 1.24320433 0.338053714
## [78,] 0.724982896 -3.101534988 2.169777453 -0.85898437 1.228708332
## [79,] -4.102493196 -0.925518563 -0.521024249 -2.04100750 0.710115645
## [80,] -4.112293796 -1.734029594 0.880179976 -1.68888352 0.007277055
## Comp.6 Comp.7 Comp.8 Comp.9 Comp.10
## [1,] 1.61891146 -0.3497120639 1.18686102 -0.46039078 1.024288006
## [2,] 0.11845490 0.2123054190 0.77581444 1.82437617 0.286148130
## [3,] 0.37681828 -1.0280256522 0.69745007 1.25420897 0.501055371
## [4,] -1.20216340 -1.1308275976 -0.12886977 -0.42762886 0.273820321
## [5,] -0.89157509 -0.7649817900 0.63929555 0.18900370 0.433115695
## [6,] -1.28465491 -0.7941451556 0.57128786 0.04558882 -0.033464524
## [7,] 0.27712489 -1.7029031950 -1.25112004 -0.72977747 -0.477225480
## [8,] 0.43632019 2.6753427076 -0.32282086 0.41708201 0.218141046
## [9,] -0.39448371 -0.0287335214 -0.30121051 -0.61103716 -0.218046813
## [10,] -0.77636731 0.0568495611 0.72652522 -0.07248579 0.117274734
## [11,] -1.72662246 -0.3879365062 0.46188999 -0.60114904 0.051005972
## [12,] -0.41991138 2.6215460021 2.94007911 0.24424318 0.266581862
## [13,] 0.44360405 -0.8301223986 0.79568213 0.65664883 0.161190320
## [14,] 0.46585617 0.8476990258 0.30100770 1.87984097 -0.114403673
## [15,] 0.56846522 0.9439935228 -1.18255264 -0.33409556 -0.361958607
## [16,] 0.53429555 0.0066009090 -1.02398269 -0.82199031 -0.521788247
## [17,] 0.03576719 0.1771722715 -0.58422246 -0.92825553 -0.195425403
## [18,] -0.50377060 -0.3450148194 -0.06306262 -0.20499212 -0.695145505
## [19,] 1.25245971 1.8086086961 -0.06479328 0.37304342 -0.305901713
## [20,] 0.82486538 0.8343920160 0.23093321 0.06295620 0.329782124
## [21,] 0.22976686 0.9660604253 -0.17830525 0.02235389 0.308023754
## [22,] 0.59915964 1.2389227808 -0.76007998 -0.05016285 1.094388604
## [23,] 0.10903183 0.9559848226 -0.86017398 0.26027951 -0.117163220
## [24,] 1.02882435 -0.3066919309 0.06124477 -1.09540972 0.716330278
## [25,] 1.38359118 0.3040906068 -0.21204826 -1.15166790 0.046834054
## [26,] -0.35746145 0.3689539192 -0.47636364 -0.67481635 -1.159854433
## [27,] -2.44512302 1.6168174681 0.78272349 -0.93664572 0.847962410
## [28,] -2.25615438 2.0033834431 2.21300150 -0.72763419 0.340770526
## [29,] -0.01629724 0.1771509654 -0.46497005 0.35041390 -0.469449697
## [30,] 1.35365310 1.0208334624 -0.22081112 0.92707419 -0.892661598
## [31,] -2.02736811 -0.4291986740 -0.22562606 -1.26683695 1.113682629
## [32,] -1.14141687 0.0002512136 -1.25504556 -0.83730715 0.388760581
## [33,] -0.14052210 0.7528339684 -0.71412054 -0.18273582 0.497141956
## [34,] 1.10746191 0.0801991032 -1.23022203 -0.38014243 0.959035056
## [35,] 0.41229832 -0.4774635142 -0.28091104 -0.23743146 0.588833408
## [36,] 1.27107834 -1.0446302018 1.08191034 -0.93581097 -0.740771614
## [37,] 0.02828798 0.7639456652 -0.91078268 0.23038391 0.002237209
## [38,] -1.07346720 0.1715012543 -0.09229852 0.33643738 -0.993287122
## [39,] -0.42672940 0.0506492319 -0.91515040 0.73675326 -0.588251832
## [40,] 0.69865674 0.0193276187 0.07789081 0.13496506 -0.474498595
## [41,] 1.26296608 -0.5598933055 0.77475476 -0.40957922 -0.002961045
## [42,] 1.56699321 0.0553695199 -0.00979641 0.54446936 0.574256865
## [43,] -0.03142207 0.6281627197 -1.63884912 0.75277037 -1.047195768
## [44,] -0.28525503 -1.3755731896 0.17421147 -1.10151479 -0.087464405
## [45,] 0.34294113 0.3504194396 0.24444770 0.73436901 -0.290011615
## [46,] 0.47263877 0.2555249364 -0.21172758 0.57403403 0.316300369
## [47,] -0.22399728 -1.4357172733 1.40104699 -0.29026336 0.347190441
## [48,] 2.38671389 0.1822545923 0.77199780 -2.19183081 -1.121849674
## [49,] 0.79638915 0.6543917847 -1.23849916 -1.26019424 -0.712742597
## [50,] -1.33124565 -0.7427401244 -0.16689483 0.35194776 -0.463477757
## [51,] -0.24646005 0.2006695647 -0.55844244 0.24529128 -0.566978978
## [52,] -0.22326277 0.4687799040 0.05633926 -0.98690874 -1.363256351
## [53,] 0.45715036 -1.3810793251 -0.31457036 0.16366137 2.153537030
## [54,] -1.27433406 0.0122281688 0.46868283 1.21601173 -0.772873263
## [55,] 0.19653781 -0.8099467142 -0.01345378 2.37515905 0.857383576
## [56,] 0.34252628 -2.2395869411 -0.61991309 1.38766504 0.801232215
## [57,] 0.20921033 0.3447820671 0.19966741 -0.07468244 -0.001603484
## [58,] 0.80168164 0.2673355727 -0.68863606 -0.10836088 1.635761058
## [59,] 0.79169432 -0.2679476812 0.15656419 -0.22087035 -1.257934768
## [60,] 2.13689576 -1.0022409862 1.70057797 0.48947618 -1.637724184
## [61,] 0.75763364 -0.0511633798 1.02345124 1.17011074 -0.643418924
## [62,] -1.29247872 -0.9939646967 -0.95757220 -0.23161982 -0.078529918
## [63,] 1.00539847 -1.1691021095 -0.23326349 -0.40807361 1.211122192
## [64,] -0.19360223 -0.3813344476 -0.52660567 -0.05331514 0.465380471
## [65,] -0.69879314 -0.3982153201 0.58827516 0.25958804 0.606444737
## [66,] -0.00986861 0.7164703164 0.29164535 1.18909989 0.511663286
## [67,] -0.98058533 1.3866833437 -1.83291903 1.25631912 0.138822751
## [68,] -2.55422417 -0.1080909810 0.08320312 -0.69098203 -0.019042712
## [69,] -0.15655973 1.0296571323 0.45233628 0.14210819 0.380980497
## [70,] 0.25185543 0.1041668502 -0.11759251 -0.48568765 1.647535031
## [71,] 0.46746969 -0.7224041225 1.33474445 -1.01519220 0.009724619
## [72,] 0.63272587 0.3890213839 1.17498133 -0.45891138 0.132790116
## [73,] 0.03206606 0.0319308793 -0.32242981 0.04753058 0.010224135
## [74,] -0.87957990 -0.0908778296 -0.95556644 -0.23200575 -0.671567050
## [75,] 0.24870373 0.2858498558 -1.24781146 -0.60698323 0.032321384
## [76,] 0.32770157 -0.6452116283 0.08731267 -0.37006617 0.584055538
## [77,] -0.14303177 -0.6975158130 0.61536462 -0.19108212 -0.596720683
## [78,] -0.49285124 -1.5475845657 -0.65283837 1.78524947 -0.975187441
## [79,] -1.05014424 -0.5670822204 -0.01887762 -0.22241105 -1.492767086
## [80,] -1.51086180 -1.2314544358 0.90260161 0.64842452 -0.820524581
## Comp.11 Comp.12 Comp.13 Comp.14
## [1,] -0.542522995 -0.636235678 -0.34090312 -0.0055901009
## [2,] 0.124704359 2.000885567 0.62330655 0.1405643012
## [3,] 0.664478951 0.515075146 0.32203564 -0.0751735255
## [4,] 0.918373670 0.347350420 0.27567431 0.0204114843
## [5,] 0.865669380 0.443541234 -0.32339600 -0.0575709081
## [6,] 0.151343119 -0.006888342 -0.01397712 -0.0256188040
## [7,] -0.054616194 -0.084790803 0.18804028 0.0822470022
## [8,] -0.765484082 -0.130296147 -0.27446107 -0.0913191079
## [9,] -0.531910538 -0.282824867 0.26004970 -0.0793999577
## [10,] -0.845278126 -0.491648499 -0.26620860 0.0004360375
## [11,] -0.649465263 0.134571845 -0.13336443 0.0207276929
## [12,] 0.826440864 -0.549685707 0.32662922 0.0463503137
## [13,] 0.464725662 0.688084096 0.02364578 0.0078503093
## [14,] -0.129326709 0.379932329 -0.58652846 -0.0903768295
## [15,] -0.650514911 -0.745560718 0.52701679 0.0628058138
## [16,] 0.588351438 -0.703089447 0.22947853 -0.1251482087
## [17,] 0.586752440 0.444207465 0.18377805 -0.0102702781
## [18,] -0.012244556 0.153342647 -0.77763528 0.1076838514
## [19,] -0.349524114 0.562966806 -0.34686251 0.1833499216
## [20,] 1.017998161 0.423597514 0.08317532 0.0957686074
## [21,] -0.292955389 -0.830249498 0.25835605 -0.0032318310
## [22,] 0.036278717 -0.435115246 -0.04204820 0.0451772549
## [23,] -0.263381799 0.188140591 0.18698454 0.0775304642
## [24,] -0.670199498 -0.037341345 -0.48928159 0.1388529779
## [25,] 0.505432381 -0.817379883 -0.07100312 0.1209709081
## [26,] -0.614068246 0.288382361 -0.15172004 0.0554099579
## [27,] -0.586227021 0.055169685 -0.36339885 -0.0250880243
## [28,] 0.516856004 -0.260295036 0.05420294 0.0406336285
## [29,] -1.173821392 0.229742401 -0.12355832 0.0215423798
## [30,] 0.395909115 -0.455100822 0.32084492 0.1591052225
## [31,] 0.052082196 0.641055465 0.16831851 -0.0655178167
## [32,] -0.471902691 -0.894375822 -0.14083443 -0.2285400201
## [33,] -0.304540143 -0.272544877 0.08757402 0.0036392368
## [34,] 0.097989291 0.075850908 -0.06324611 0.1069337439
## [35,] -0.672760424 0.957947986 -0.51249472 0.1718248071
## [36,] -1.206343867 0.114049507 -0.19619289 0.2656559116
## [37,] -0.083873425 -0.612164844 0.10116542 -0.3409642336
## [38,] -0.026872088 -0.604606384 0.04069449 -0.0560261617
## [39,] 0.097049830 0.271421628 0.08374408 -0.1982176371
## [40,] 0.381373119 0.258491843 0.24919942 -0.2681671201
## [41,] 0.154968220 0.586204842 0.06018837 -0.9667281562
## [42,] -0.348654073 0.104710655 0.09835729 -0.8003567278
## [43,] 0.314285530 -0.416817730 0.12228933 1.0631202693
## [44,] 1.336981311 -0.105178155 -0.20408990 1.0026684752
## [45,] 0.768567986 0.255957022 -0.42747509 -0.0552581005
## [46,] 0.208271381 0.162250410 -0.17689783 0.2584491346
## [47,] -0.671183396 -1.217988415 -0.20247332 0.2012456179
## [48,] -0.503499141 0.475456942 -0.10734979 -0.4313491653
## [49,] 1.312722267 0.453394485 0.48961618 -0.3737589191
## [50,] 0.413831480 -0.533561105 0.60034859 0.0607263536
## [51,] 0.916669101 0.037768405 -0.70023608 0.2017406038
## [52,] 1.189522424 -0.269592662 -0.87159874 -0.4971644155
## [53,] -1.189373437 -0.357673434 1.50483513 0.0514516795
## [54,] -0.977710807 0.290766608 0.65554616 -0.0234410793
## [55,] -0.079965177 -1.145589245 -1.02213658 0.0749077903
## [56,] 0.147757160 -0.544864268 -0.26382045 -0.0528946861
## [57,] -0.050245460 0.138755954 0.22533363 0.0460106490
## [58,] 0.469971690 1.227651676 -0.36642039 0.2078781216
## [59,] -0.210042448 0.058560020 0.14928990 0.2305207176
## [60,] -0.379904530 -0.139554161 0.50318238 0.2520551962
## [61,] -0.182652120 -0.609681202 -0.18438176 -0.1018063947
## [62,] -0.537572379 -0.214411981 -1.08702527 -0.3044232577
## [63,] 1.024227273 -1.110194843 0.25151284 -0.2190734786
## [64,] 0.448993139 -0.638743057 0.22308293 -0.1478853550
## [65,] -0.175133998 0.169524415 0.05832361 -0.1032731884
## [66,] -0.408668817 -0.258174790 0.20314222 0.0401751027
## [67,] 0.417105457 -0.220158363 0.04652788 -0.1675373480
## [68,] -0.324173449 0.712478122 0.19420469 -0.1121764262
## [69,] -0.070436439 0.047791180 0.40183278 0.0922481584
## [70,] 0.848868938 0.405554392 -0.11869623 0.0808869968
## [71,] -0.344925439 0.520959382 -0.36680926 0.3154647410
## [72,] 0.006731905 -0.122282462 -0.08530887 0.2212901468
## [73,] -0.413440277 -0.548702092 -0.19330277 0.0168105947
## [74,] -1.089666879 0.873745505 -0.14402898 0.0626094623
## [75,] -0.618680103 1.383241191 0.39556360 0.2282926666
## [76,] 0.315379147 0.318912284 0.10123703 0.0193581661
## [77,] 0.283664486 0.049637074 0.14434585 0.0314927774
## [78,] -0.006561166 0.705372950 -0.42125642 -0.2980760611
## [79,] 0.270852544 -0.661891058 0.81344843 -0.0420682806
## [80,] 0.339142873 -0.187247973 0.32429919 -0.2913836448
# write.xlsx(data.frame(pca_2$scores),file = "主成分得分.xlsx")
## 样本得分可视化
pca_scores <- data.frame(pca_2$scores)
par(mfcol = c(1,2),family = "STKaiti",cex = 0.8)
plot(pca_scores$Comp.1,pca_scores$Comp.2,type = "n",xla = "Comp 1",
ylab = "Comp 2",main = "sample PCA",col = "red")
text(pca_scores$Comp.1,pca_scores$Comp.2,row.names(pca_scores))
abline(h = 0)
abline(v = 0)
plot(pca_scores$Comp.3,pca_scores$Comp.4,type = "n",xla = "Comp 3",
ylab = "Comp 4",main = "sample PCA",col = "red")
text(pca_scores$Comp.3,pca_scores$Comp.4,row.names(pca_scores))
abline(h = 0)
abline(v = 0)
par(mfcol = c(1,1),family = "STKaiti")
## 主成分回归分析，使用前8个主成分，能够保留约84％的原始数据信息
lmpcadf <- pca_scores[,1:8]
lmpcadf$Y <- mydata$居民消费价格指数
lm1 <- lm(Y~.,data = lmpcadf)
summary(lm1)
##
## Call:
## lm(formula = Y ~ ., data = lmpcadf)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.36245 -0.06233 0.00801 0.05831 0.37195
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 100.188750 0.014115 7098.126 < 2e-16 ***
## Comp.1 -0.216077 0.006802 -31.768 < 2e-16 ***
## Comp.2 -0.012048 0.011713 -1.029 0.30716
## Comp.3 -0.064102 0.012584 -5.094 2.78e-06 ***
## Comp.4 -0.079734 0.012976 -6.145 4.16e-08 ***
## Comp.5 -0.006134 0.013382 -0.458 0.64809
## Comp.6 -0.018681 0.014272 -1.309 0.19480
## Comp.7 0.036709 0.015268 2.404 0.01882 *
## Comp.8 0.062931 0.016632 3.784 0.00032 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1262 on 71 degrees of freedom
## Multiple R-squared: 0.9392, Adjusted R-squared: 0.9323
## F-statistic: 137 on 8 and 71 DF, p-value: < 2.2e-16
## 对回归结果进行逐步回归进一步筛选重要的主成分
lm2 <- step(lm1)
## Start: AIC=-322.67
## Y ~ Comp.1 + Comp.2 + Comp.3 + Comp.4 + Comp.5 + Comp.6 + Comp.7 +
## Comp.8
##
## Df Sum of Sq RSS AIC
## - Comp.5 1 0.0033 1.1350 -324.43
## - Comp.2 1 0.0169 1.1485 -323.49
## - Comp.6 1 0.0273 1.1589 -322.76
## <none> 1.1316 -322.67
## - Comp.7 1 0.0921 1.2237 -318.41
## - Comp.8 1 0.2282 1.3598 -309.98
## - Comp.3 1 0.4136 1.5452 -299.75
## - Comp.4 1 0.6018 1.7335 -290.55
## - Comp.1 1 16.0850 17.2166 -106.89
##
## Step: AIC=-324.43
## Y ~ Comp.1 + Comp.2 + Comp.3 + Comp.4 + Comp.6 + Comp.7 + Comp.8
##
## Df Sum of Sq RSS AIC
## - Comp.2 1 0.0169 1.1518 -325.25
## - Comp.6 1 0.0273 1.1623 -324.53
## <none> 1.1350 -324.43
## - Comp.7 1 0.0921 1.2271 -320.19
## - Comp.8 1 0.2282 1.3631 -311.78
## - Comp.3 1 0.4136 1.5485 -301.58
## - Comp.4 1 0.6018 1.7368 -292.40
## - Comp.1 1 16.0850 17.2200 -108.88
##
## Step: AIC=-325.25
## Y ~ Comp.1 + Comp.3 + Comp.4 + Comp.6 + Comp.7 + Comp.8
##
## Df Sum of Sq RSS AIC
## - Comp.6 1 0.0273 1.1791 -325.38
## <none> 1.1518 -325.25
## - Comp.7 1 0.0921 1.2440 -321.10
## - Comp.8 1 0.2282 1.3800 -312.80
## - Comp.3 1 0.4136 1.5654 -302.71
## - Comp.4 1 0.6018 1.7537 -293.63
## - Comp.1 1 16.0850 17.2369 -110.80
##
## Step: AIC=-325.38
## Y ~ Comp.1 + Comp.3 + Comp.4 + Comp.7 + Comp.8
##
## Df Sum of Sq RSS AIC
## <none> 1.1791 -325.38
## - Comp.7 1 0.0921 1.2713 -321.36
## - Comp.8 1 0.2282 1.4073 -313.23
## - Comp.3 1 0.4136 1.5927 -303.33
## - Comp.4 1 0.6018 1.7810 -294.39
## - Comp.1 1 16.0850 17.2642 -112.67
summary(lm2)
##
## Call:
## lm(formula = Y ~ Comp.1 + Comp.3 + Comp.4 + Comp.7 + Comp.8,
## data = lmpcadf)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.39634 -0.04943 0.01993 0.04901 0.36754
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 100.188750 0.014113 7099.026 < 2e-16 ***
## Comp.1 -0.216077 0.006801 -31.772 < 2e-16 ***
## Comp.3 -0.064102 0.012582 -5.095 2.58e-06 ***
## Comp.4 -0.079734 0.012974 -6.146 3.67e-08 ***
## Comp.7 0.036709 0.015266 2.405 0.018694 *
## Comp.8 0.062931 0.016630 3.784 0.000311 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1262 on 74 degrees of freedom
## Multiple R-squared: 0.9366, Adjusted R-squared: 0.9323
## F-statistic: 218.7 on 5 and 74 DF, p-value: < 2.2e-16