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Correlation Matrix in R Programming
  • Last Updated : 23 Oct, 2020

Correlation refers to the relationship between two variables. It refers to the degree of linear correlation between any two random variables. This relation can be expressed as a range of values expressed within the interval [-1, 1]. The value -1 indicates a perfect non-linear (negative) relationship, 1 is a perfect positive linear relationship and 0 is an intermediate between neither positive nor negative linear interdependency. However, a value of 0 doesn’t indicate the variables to be independent of each other completely. Correlation Matrices compute the linear relationship degree between a set of random variables, taking one pair at a time and performing for each set of pairs within the data.

Properties of Correlation Matrices

  1. All the diagonal elements of the correlation matrix must be 1 because the correlation of a variable with itself is always perfect, cii=1.
  2. It should be symmetric cij=cji.

Computing Correlation Matrix in R

In R programming, a correlation matrix can be completed using the cor( ) function, which has the following syntax:

 Syntax: cor (x, use = , method =    )

Parameters:

x: It is a numeric matrix or a data frame.
use: Deals with missing data.



  • all.obs: this parameter value assumes that the data frame has no missing values and throws an error in case of violation.
  • complete.obs: listwise deletion.
  • pairwise.complete.obs: pairwise deletion.

method: Deals with a type of relationship. Either Pearson, Spearman, or Kendall can be used for computation. The default method used is Pearson. 

The correlation matrix can be computed in R after loading the data. The following code snippet indicates the usage of the cor() function: 

R

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# loading dataset from the speicified url 
# storing the data into csv 
data = read.csv("https://people.sc.fsu.edu/~jburkardt/data/csv/ford_escort.csv"
                header = TRUE, fileEncoding = "latin1")
  
# printing the head of the data
print ("Original Data")
head(data)
  
# computing correlation matrix
cor_data = cor(data)
  
print("Correlation matrix")
print(cor_data)

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 Output:

[1] "Original Data"
  Year Mileage..thousands. Price
1 1998                  27  9991
2 1997                  17  9925
3 1998                  28 10491
4 1998                   5 10990
5 1997                  38  9493
6 1997                  36  9991

[1] "Correlation matrix"
                         Year Mileage..thousands.      Price
Year                 1.0000000          -0.7480982  0.9343679
Mileage..thousands. -0.7480982           1.0000000 -0.8113807
Price                0.9343679          -0.8113807  1.0000000

Computing Correlation Coefficients

R contains an in-built function rcorr() which generates the correlation coefficients and a table of p-values for all possible column pairs of a data frame. This function basically computes the significance levels for Pearson and spearman correlations.

Syntax:

rcorr (x, type = c(“pearson”, “spearman”))

In order to run this function in R, we need to download and load the “Hmisc” package into the environment. This can be done in the following way: 

install.packages(“Hmisc”) 

library(“Hmisc”)

The following code snippet indicates the computation of correlation coefficients in R:

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data = read.csv("https://people.sc.fsu.edu/~jburkardt/data/csv/ford_escort.csv"
                header = TRUE, fileEncoding = "latin1")
  
# printing the head of the data
print("Original Data")
head(data)
  
# installing the library of Hmisc 
install.packages("Hmisc")
library("Hmisc")
  
# computing p values of the data loaded
p_values <- rcorr(as.matrix(data))
print(p_values)

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Output:

[1] "Original Data"
Year Mileage..thousands. Price
1 1998                  27  9991
2 1997                  17  9925
3 1998                  28 10491
4 1998                   5 10990
5 1997                  38  9493
6 1997                  36  9991

Year Mileage..thousands. Price
Year                 1.00               -0.75  0.93
Mileage..thousands. -0.75                1.00 -0.81
Price                0.93               -0.81  1.00

n= 23 


P
                    Year Mileage..thousands. Price
Year                      0                   0   
Mileage..thousands.  0                        0   
Price                0    0                       

Visualize a Correlation Matrix

To visualize a correlation matrix refer to these articles:




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