# R 相关性分析

### 1. 相关性矩阵计算：

• 加载mtcars数据
```> setwd("E:\\Rwork")
> data("mtcars")
mpg cyl disp  hp drat    wt  qsec vs am gear carb
Mazda RX4         21.0   6  160 110 3.90 2.620 16.46  0  1    4    4
Mazda RX4 Wag     21.0   6  160 110 3.90 2.875 17.02  0  1    4    4
Datsun 710        22.8   4  108  93 3.85 2.320 18.61  1  1    4    1
Hornet 4 Drive    21.4   6  258 110 3.08 3.215 19.44  1  0    3    1
Hornet Sportabout 18.7   8  360 175 3.15 3.440 17.02  0  0    3    2
Valiant           18.1   6  225 105 2.76 3.460 20.22  1  0    3    1```
• 计算两两相关系数
```> cor(mtcars\$mpg,mtcars\$cyl)
[1] -0.852162```
• 计算矩阵相关系数
```> matcar.cor <- cor(mtcars)
> matcar.cor
mpg        cyl       disp         hp        drat         wt
mpg   1.0000000 -0.8521620 -0.8475514 -0.7761684  0.68117191 -0.8676594
cyl  -0.8521620  1.0000000  0.9020329  0.8324475 -0.69993811  0.7824958
disp -0.8475514  0.9020329  1.0000000  0.7909486 -0.71021393  0.8879799
hp   -0.7761684  0.8324475  0.7909486  1.0000000 -0.44875912  0.6587479
drat  0.6811719 -0.6999381 -0.7102139 -0.4487591  1.00000000 -0.7124406
wt   -0.8676594  0.7824958  0.8879799  0.6587479 -0.71244065  1.0000000
qsec  0.4186840 -0.5912421 -0.4336979 -0.7082234  0.09120476 -0.1747159
vs    0.6640389 -0.8108118 -0.7104159 -0.7230967  0.44027846 -0.5549157
am    0.5998324 -0.5226070 -0.5912270 -0.2432043  0.71271113 -0.6924953
gear  0.4802848 -0.4926866 -0.5555692 -0.1257043  0.69961013 -0.5832870
carb -0.5509251  0.5269883  0.3949769  0.7498125 -0.09078980  0.4276059
qsec         vs          am       gear        carb
mpg   0.41868403  0.6640389  0.59983243  0.4802848 -0.55092507
cyl  -0.59124207 -0.8108118 -0.52260705 -0.4926866  0.52698829
disp -0.43369788 -0.7104159 -0.59122704 -0.5555692  0.39497686
hp   -0.70822339 -0.7230967 -0.24320426 -0.1257043  0.74981247
drat  0.09120476  0.4402785  0.71271113  0.6996101 -0.09078980
wt   -0.17471588 -0.5549157 -0.69249526 -0.5832870  0.42760594
qsec  1.00000000  0.7445354 -0.22986086 -0.2126822 -0.65624923
vs    0.74453544  1.0000000  0.16834512  0.2060233 -0.56960714
am   -0.22986086  0.1683451  1.00000000  0.7940588  0.05753435
gear -0.21268223  0.2060233  0.79405876  1.0000000  0.27407284
carb -0.65624923 -0.5696071  0.05753435  0.2740728  1.00000000```

### 2. 相关系数的显著性水平

• 使用Hmisc 包，计算矩阵相关系数及其对应的显著性水平
```> library(Hmisc)
> res <- rcorr(as.matrix(mtcars))
> res
mpg   cyl  disp    hp  drat    wt  qsec    vs    am  gear  carb
mpg   1.00 -0.85 -0.85 -0.78  0.68 -0.87  0.42  0.66  0.60  0.48 -0.55
cyl  -0.85  1.00  0.90  0.83 -0.70  0.78 -0.59 -0.81 -0.52 -0.49  0.53
disp -0.85  0.90  1.00  0.79 -0.71  0.89 -0.43 -0.71 -0.59 -0.56  0.39
hp   -0.78  0.83  0.79  1.00 -0.45  0.66 -0.71 -0.72 -0.24 -0.13  0.75
drat  0.68 -0.70 -0.71 -0.45  1.00 -0.71  0.09  0.44  0.71  0.70 -0.09
wt   -0.87  0.78  0.89  0.66 -0.71  1.00 -0.17 -0.55 -0.69 -0.58  0.43
qsec  0.42 -0.59 -0.43 -0.71  0.09 -0.17  1.00  0.74 -0.23 -0.21 -0.66
vs    0.66 -0.81 -0.71 -0.72  0.44 -0.55  0.74  1.00  0.17  0.21 -0.57
am    0.60 -0.52 -0.59 -0.24  0.71 -0.69 -0.23  0.17  1.00  0.79  0.06
gear  0.48 -0.49 -0.56 -0.13  0.70 -0.58 -0.21  0.21  0.79  1.00  0.27
carb -0.55  0.53  0.39  0.75 -0.09  0.43 -0.66 -0.57  0.06  0.27  1.00

n= 32

P
mpg    cyl    disp   hp     drat   wt     qsec   vs     am     gear
mpg         0.0000 0.0000 0.0000 0.0000 0.0000 0.0171 0.0000 0.0003 0.0054
cyl  0.0000        0.0000 0.0000 0.0000 0.0000 0.0004 0.0000 0.0022 0.0042
disp 0.0000 0.0000        0.0000 0.0000 0.0000 0.0131 0.0000 0.0004 0.0010
hp   0.0000 0.0000 0.0000        0.0100 0.0000 0.0000 0.0000 0.1798 0.4930
drat 0.0000 0.0000 0.0000 0.0100        0.0000 0.6196 0.0117 0.0000 0.0000
wt   0.0000 0.0000 0.0000 0.0000 0.0000        0.3389 0.0010 0.0000 0.0005
qsec 0.0171 0.0004 0.0131 0.0000 0.6196 0.3389        0.0000 0.2057 0.2425
vs   0.0000 0.0000 0.0000 0.0000 0.0117 0.0010 0.0000        0.3570 0.2579
am   0.0003 0.0022 0.0004 0.1798 0.0000 0.0000 0.2057 0.3570        0.0000
gear 0.0054 0.0042 0.0010 0.4930 0.0000 0.0005 0.2425 0.2579 0.0000
carb 0.0011 0.0019 0.0253 0.0000 0.6212 0.0146 0.0000 0.0007 0.7545 0.1290
carb
mpg  0.0011
cyl  0.0019
disp 0.0253
hp   0.0000
drat 0.6212
wt   0.0146
qsec 0.0000
vs   0.0007
am   0.7545
gear 0.1290
carb
> signif(res\$r, 2)
mpg   cyl  disp    hp   drat    wt   qsec    vs     am  gear   carb
mpg   1.00 -0.85 -0.85 -0.78  0.680 -0.87  0.420  0.66  0.600  0.48 -0.550
cyl  -0.85  1.00  0.90  0.83 -0.700  0.78 -0.590 -0.81 -0.520 -0.49  0.530
disp -0.85  0.90  1.00  0.79 -0.710  0.89 -0.430 -0.71 -0.590 -0.56  0.390
hp   -0.78  0.83  0.79  1.00 -0.450  0.66 -0.710 -0.72 -0.240 -0.13  0.750
drat  0.68 -0.70 -0.71 -0.45  1.000 -0.71  0.091  0.44  0.710  0.70 -0.091
wt   -0.87  0.78  0.89  0.66 -0.710  1.00 -0.170 -0.55 -0.690 -0.58  0.430
qsec  0.42 -0.59 -0.43 -0.71  0.091 -0.17  1.000  0.74 -0.230 -0.21 -0.660
vs    0.66 -0.81 -0.71 -0.72  0.440 -0.55  0.740  1.00  0.170  0.21 -0.570
am    0.60 -0.52 -0.59 -0.24  0.710 -0.69 -0.230  0.17  1.000  0.79  0.058
gear  0.48 -0.49 -0.56 -0.13  0.700 -0.58 -0.210  0.21  0.790  1.00  0.270
carb -0.55  0.53  0.39  0.75 -0.091  0.43 -0.660 -0.57  0.058  0.27  1.000```
• 提取矩阵相关及其P值
```> CorMatrix <- function(cor,p) {
+                               ut <- upper.tri(cor)
+                               data.frame(row = rownames(cor)[row(cor)[ut]] ,
+                               column = rownames(cor)[col(cor)[ut]],
+                               cor =(cor)[ut],
+                               p = p[ut] )
+ }
>
>
> res <- rcorr(as.matrix(mtcars))
> CorMatrix (res\$r, res\$P)
row column         cor            p
1   mpg    cyl -0.85216196 6.112688e-10
2   mpg   disp -0.84755138 9.380328e-10
3   cyl   disp  0.90203287 1.803002e-12
4   mpg     hp -0.77616837 1.787835e-07
5   cyl     hp  0.83244745 3.477861e-09
6  disp     hp  0.79094859 7.142679e-08
7   mpg   drat  0.68117191 1.776240e-05
8   cyl   drat -0.69993811 8.244636e-06
9  disp   drat -0.71021393 5.282022e-06
10   hp   drat -0.44875912 9.988772e-03
11  mpg     wt -0.86765938 1.293958e-10
12  cyl     wt  0.78249579 1.217567e-07
13 disp     wt  0.88797992 1.222311e-11
14   hp     wt  0.65874789 4.145827e-05
15 drat     wt -0.71244065 4.784260e-06
16  mpg   qsec  0.41868403 1.708199e-02
17  cyl   qsec -0.59124207 3.660533e-04
18 disp   qsec -0.43369788 1.314404e-02
19   hp   qsec -0.70822339 5.766253e-06
20 drat   qsec  0.09120476 6.195826e-01
21   wt   qsec -0.17471588 3.388683e-01
22  mpg     vs  0.66403892 3.415937e-05
23  cyl     vs -0.81081180 1.843018e-08
24 disp     vs -0.71041589 5.235012e-06
25   hp     vs -0.72309674 2.940896e-06
26 drat     vs  0.44027846 1.167553e-02
27   wt     vs -0.55491568 9.798492e-04
28 qsec     vs  0.74453544 1.029669e-06
29  mpg     am  0.59983243 2.850207e-04
30  cyl     am -0.52260705 2.151207e-03
31 disp     am -0.59122704 3.662114e-04
32   hp     am -0.24320426 1.798309e-01
33 drat     am  0.71271113 4.726790e-06
34   wt     am -0.69249526 1.125440e-05
35 qsec     am -0.22986086 2.056621e-01
36   vs     am  0.16834512 3.570439e-01
37  mpg   gear  0.48028476 5.400948e-03
38  cyl   gear -0.49268660 4.173297e-03
39 disp   gear -0.55556920 9.635921e-04
40   hp   gear -0.12570426 4.930119e-01
41 drat   gear  0.69961013 8.360110e-06
42   wt   gear -0.58328700 4.586601e-04
43 qsec   gear -0.21268223 2.425344e-01
44   vs   gear  0.20602335 2.579439e-01
45   am   gear  0.79405876 5.834043e-08
46  mpg   carb -0.55092507 1.084446e-03
47  cyl   carb  0.52698829 1.942340e-03
48 disp   carb  0.39497686 2.526789e-02
49   hp   carb  0.74981247 7.827810e-07
50 drat   carb -0.09078980 6.211834e-01
51   wt   carb  0.42760594 1.463861e-02
52 qsec   carb -0.65624923 4.536949e-05
53   vs   carb -0.56960714 6.670496e-04
54   am   carb  0.05753435 7.544526e-01
55 gear   carb  0.27407284 1.290291e-01```

### 3. 可视化相关性分析

##### 1. symnum() function
```> cor_matr <- cor(mtcars)
> symnum(cor_matr)
m cy ds h dr w q v a g cr
mpg  1
cyl  + 1
disp + *  1
hp   , +  ,  1
drat , ,  ,  . 1
wt   + ,  +  , ,  1
qsec . .  .  ,      1
vs   , +  ,  , .  . , 1
am   . .  .    ,  ,     1
gear . .  .    ,  .     , 1
carb . .  .  ,    . , .     1
attr(,"legend")
[1] 0 ‘ ’ 0.3 ‘.’ 0.6 ‘,’ 0.8 ‘+’ 0.9 ‘*’ 0.95 ‘B’ 1```

#### 2. corrplot() function to plot a correlogram

```library(corrplot)
matcar.cor <- cor(mtcars)

round(matcar.cor, 2)
class(matcar.cor)

corrplot(matcar.cor)```
```corrplot(matcar.cor, order = "AOE", method = "color",
`corrplot.mixed(matcar.cor, order = "AOE")`
`corrplot(matcar.cor, method = "ellipse")`

#### 3. scatter plots

```library(PerformanceAnalytics)
chart.Correlation(mtcars,histogram = TRUE,pch=19)```

#### 4. heatmap

```matcar.cor <- cor(mtcars)
col<- colorRampPalette(c("blue", "white", "red"))(20)#调用颜色版自定义颜色
heatmap(x = matcar.cor, col = col, symm = TRUE)#symm表示是否对称```

#### 5.ggcorrplot

• 添加P值，不显著用白色显示
```setwd("E:\\Rwork")
data("mtcars")
library(ggcorrplot)
#计算相关矩阵(cor()计算结果不提供p-value)
data("mtcars")
corr <- round(cor(mtcars), 2)

#用ggcorrplot包提供的函数cor_pmat()
p.mat <- cor_pmat(mtcars)

ggcorrplot(corr, hc.order = TRUE, type = "lower", p.mat = p.mat)```

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