Correlation Analyses in R
mohammad yasir (Roll No: 5121151) Data Science
2024-01-03
Correlation Test Between Two Variables in R
Install and load required R packages
install.packages(“ggpubr”) library(“ggpubr”)
Import your data into R
my_data <- mtcars
head(my_data, 6)## 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 1Visualize your data using scatter plots
library("ggpubr")## Warning: package 'ggpubr' was built under R version 4.3.2## Loading required package: ggplot2## Warning: package 'ggplot2' was built under R version 4.3.2ggscatter(my_data, x = "mpg", y = "wt",
add = "reg.line", conf.int = TRUE,
cor.coef = TRUE, cor.method = "pearson",
xlab = "Miles/(US) gallon", ylab = "Weight (1000 lbs)")
Preleminary test to check the test assumptions
# Shapiro-Wilk normality test for mpg
shapiro.test(my_data$mpg) # => p = 0.1229##
## Shapiro-Wilk normality test
##
## data: my_data$mpg
## W = 0.94756, p-value = 0.1229# Shapiro-Wilk normality test for wt
shapiro.test(my_data$wt) # => p = 0.09##
## Shapiro-Wilk normality test
##
## data: my_data$wt
## W = 0.94326, p-value = 0.09265# mpg
ggqqplot(my_data$mpg, ylab = "MPG")
# wt
ggqqplot(my_data$wt, ylab = "WT")
Pearson correlation test
res <- cor.test(my_data$wt, my_data$mpg,
method = "pearson")
res##
## Pearson's product-moment correlation
##
## data: my_data$wt and my_data$mpg
## t = -9.559, df = 30, p-value = 1.294e-10
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.9338264 -0.7440872
## sample estimates:
## cor
## -0.8676594Interpretation of the result
### The p-value of the test is 1.29410^{-10}, which is less than the significance level alpha = 0.05. We can conclude that wt and mpg are significantly correlated with a correlation coefficient of -0.87 and p-value of 1.29410^{-10} .Kendall rank correlation test
res2 <- cor.test(my_data$wt, my_data$mpg, method="kendall")## Warning in cor.test.default(my_data$wt, my_data$mpg, method = "kendall"):
## Cannot compute exact p-value with tiesres2##
## Kendall's rank correlation tau
##
## data: my_data$wt and my_data$mpg
## z = -5.7981, p-value = 6.706e-09
## alternative hypothesis: true tau is not equal to 0
## sample estimates:
## tau
## -0.7278321Spearman rank correlation coefficient
res2 <-cor.test(my_data$wt, my_data$mpg, method = "spearman")## Warning in cor.test.default(my_data$wt, my_data$mpg, method = "spearman"):
## Cannot compute exact p-value with tiesres2##
## Spearman's rank correlation rho
##
## data: my_data$wt and my_data$mpg
## S = 10292, p-value = 1.488e-11
## alternative hypothesis: true rho is not equal to 0
## sample estimates:
## rho
## -0.886422Correlation Matrix: Analyze, Format and Visualize
Compute correlation matrix in R
# Load data
data("mtcars")
my_data <- mtcars[, c(1,3,4,5,6,7)]
# print the first 6 rows
head(my_data, 6)## mpg disp hp drat wt qsec
## Mazda RX4 21.0 160 110 3.90 2.620 16.46
## Mazda RX4 Wag 21.0 160 110 3.90 2.875 17.02
## Datsun 710 22.8 108 93 3.85 2.320 18.61
## Hornet 4 Drive 21.4 258 110 3.08 3.215 19.44
## Hornet Sportabout 18.7 360 175 3.15 3.440 17.02
## Valiant 18.1 225 105 2.76 3.460 20.22res <- cor(my_data)
round(res, 2)## mpg disp hp drat wt qsec
## mpg 1.00 -0.85 -0.78 0.68 -0.87 0.42
## disp -0.85 1.00 0.79 -0.71 0.89 -0.43
## hp -0.78 0.79 1.00 -0.45 0.66 -0.71
## drat 0.68 -0.71 -0.45 1.00 -0.71 0.09
## wt -0.87 0.89 0.66 -0.71 1.00 -0.17
## qsec 0.42 -0.43 -0.71 0.09 -0.17 1.00cor(my_data, use = "complete.obs")## mpg disp hp drat wt qsec
## mpg 1.0000000 -0.8475514 -0.7761684 0.68117191 -0.8676594 0.41868403
## disp -0.8475514 1.0000000 0.7909486 -0.71021393 0.8879799 -0.43369788
## hp -0.7761684 0.7909486 1.0000000 -0.44875912 0.6587479 -0.70822339
## drat 0.6811719 -0.7102139 -0.4487591 1.00000000 -0.7124406 0.09120476
## wt -0.8676594 0.8879799 0.6587479 -0.71244065 1.0000000 -0.17471588
## qsec 0.4186840 -0.4336979 -0.7082234 0.09120476 -0.1747159 1.00000000Prerequisites
Install Package
install.packages(“corrplot”)
To use the rquery.cormat function, you can source it as follow :
source("http://www.sthda.com/upload/rquery_cormat.r")# Example of data
mydata <- mtcars[, c(1,3,4,5,6,7)]
head(mydata)## mpg disp hp drat wt qsec
## Mazda RX4 21.0 160 110 3.90 2.620 16.46
## Mazda RX4 Wag 21.0 160 110 3.90 2.875 17.02
## Datsun 710 22.8 108 93 3.85 2.320 18.61
## Hornet 4 Drive 21.4 258 110 3.08 3.215 19.44
## Hornet Sportabout 18.7 360 175 3.15 3.440 17.02
## Valiant 18.1 225 105 2.76 3.460 20.22Computing the correlation matrix
rquery.cormat(mydata)## Warning: package 'corrplot' was built under R version 4.3.2## corrplot 0.92 loaded
## $r
## hp disp wt qsec mpg drat
## hp 1
## disp 0.79 1
## wt 0.66 0.89 1
## qsec -0.71 -0.43 -0.17 1
## mpg -0.78 -0.85 -0.87 0.42 1
## drat -0.45 -0.71 -0.71 0.091 0.68 1
##
## $p
## hp disp wt qsec mpg drat
## hp 0
## disp 7.1e-08 0
## wt 4.1e-05 1.2e-11 0
## qsec 5.8e-06 0.013 0.34 0
## mpg 1.8e-07 9.4e-10 1.3e-10 0.017 0
## drat 0.01 5.3e-06 4.8e-06 0.62 1.8e-05 0
##
## $sym
## hp disp wt qsec mpg drat
## hp 1
## disp , 1
## wt , + 1
## qsec , . 1
## mpg , + + . 1
## drat . , , , 1
## attr(,"legend")
## [1] 0 ' ' 0.3 '.' 0.6 ',' 0.8 '+' 0.9 '*' 0.95 'B' 1Upper triangle of the correlation matrix
rquery.cormat(mydata, type="upper")
## $r
## hp disp wt qsec mpg drat
## hp 1 0.79 0.66 -0.71 -0.78 -0.45
## disp 1 0.89 -0.43 -0.85 -0.71
## wt 1 -0.17 -0.87 -0.71
## qsec 1 0.42 0.091
## mpg 1 0.68
## drat 1
##
## $p
## hp disp wt qsec mpg drat
## hp 0 7.1e-08 4.1e-05 5.8e-06 1.8e-07 0.01
## disp 0 1.2e-11 0.013 9.4e-10 5.3e-06
## wt 0 0.34 1.3e-10 4.8e-06
## qsec 0 0.017 0.62
## mpg 0 1.8e-05
## drat 0
##
## $sym
## hp disp wt qsec mpg drat
## hp 1 , , , , .
## disp 1 + . + ,
## wt 1 + ,
## qsec 1 .
## mpg 1 ,
## drat 1
## attr(,"legend")
## [1] 0 ' ' 0.3 '.' 0.6 ',' 0.8 '+' 0.9 '*' 0.95 'B' 1Full correlation matrix
rquery.cormat(mydata, type="full")
## $r
## hp disp wt qsec mpg drat
## hp 1.00 0.79 0.66 -0.710 -0.78 -0.450
## disp 0.79 1.00 0.89 -0.430 -0.85 -0.710
## wt 0.66 0.89 1.00 -0.170 -0.87 -0.710
## qsec -0.71 -0.43 -0.17 1.000 0.42 0.091
## mpg -0.78 -0.85 -0.87 0.420 1.00 0.680
## drat -0.45 -0.71 -0.71 0.091 0.68 1.000
##
## $p
## hp disp wt qsec mpg drat
## hp 0.0e+00 7.1e-08 4.1e-05 5.8e-06 1.8e-07 1.0e-02
## disp 7.1e-08 0.0e+00 1.2e-11 1.3e-02 9.4e-10 5.3e-06
## wt 4.1e-05 1.2e-11 0.0e+00 3.4e-01 1.3e-10 4.8e-06
## qsec 5.8e-06 1.3e-02 3.4e-01 0.0e+00 1.7e-02 6.2e-01
## mpg 1.8e-07 9.4e-10 1.3e-10 1.7e-02 0.0e+00 1.8e-05
## drat 1.0e-02 5.3e-06 4.8e-06 6.2e-01 1.8e-05 0.0e+00
##
## $sym
## hp disp wt qsec mpg drat
## hp 1
## disp , 1
## wt , + 1
## qsec , . 1
## mpg , + + . 1
## drat . , , , 1
## attr(,"legend")
## [1] 0 ' ' 0.3 '.' 0.6 ',' 0.8 '+' 0.9 '*' 0.95 'B' 1Change the colors of the correlogram
col<- colorRampPalette(c("blue", "white", "red"))(20)
cormat<-rquery.cormat(mydata, type="full", col=col)
Draw a heatmap
cormat<-rquery.cormat(mydata, graphType="heatmap")
Format the correlation table
rquery.cormat(mydata, type="flatten", graph=FALSE)## $r
## row column cor p
## 1 hp disp 0.790 7.1e-08
## 2 hp wt 0.660 4.1e-05
## 3 disp wt 0.890 1.2e-11
## 4 hp qsec -0.710 5.8e-06
## 5 disp qsec -0.430 1.3e-02
## 6 wt qsec -0.170 3.4e-01
## 7 hp mpg -0.780 1.8e-07
## 8 disp mpg -0.850 9.4e-10
## 9 wt mpg -0.870 1.3e-10
## 10 qsec mpg 0.420 1.7e-02
## 11 hp drat -0.450 1.0e-02
## 12 disp drat -0.710 5.3e-06
## 13 wt drat -0.710 4.8e-06
## 14 qsec drat 0.091 6.2e-01
## 15 mpg drat 0.680 1.8e-05
##
## $p
## NULL
##
## $sym
## NULL