Covariance and Correlation are terms used in statistics to measure relationships between two random variables. Both of these terms measure linear dependency between a pair of random variables or bivariate data.
In this article, we are going to discuss cov()
, cor()
and cov2cor()
functions in R which use covariance and correlation methods of statistics and probability theory.
Covariance
In R programming, covariance can be measured using cov()
function. Covariance is a statistical term used to measures the direction of the linear relationship between the data vectors. Mathematically,
where,
x represents the x data vector
y represents the y data vector
represents mean of x data vector
represents mean of y data vector
N represents total obeservations
Syntax:
cov(x, y, method)
where,
x and y represents the data vectors method defines the type of method to be used to compute covariance. Default is "pearson".
Example:
# Data vectors x < - c( 1 , 3 , 5 , 10 ) y < - c( 2 , 4 , 6 , 20 ) # Print covariance using different methods print (cov(x, y)) print (cov(x, y, method = "pearson" )) print (cov(x, y, method = "kendall" )) print (cov(x, y, method = "spearman" )) |
Output:
[1] 30.66667 [1] 30.66667 [1] 12 [1] 1.666667
Correlation
cor()
function in R programming measures the correlation coefficient value. Correlation is a relationship term in statistics that uses the covariance method to measure how strong the vectors are related. Mathematically,
where,
x represents the x data vector
y represents the y data vector
represents mean of x data vector
represents mean of y data vector
Syntax:
cor(x, y, method)
where,
x and y represents the data vectors method defines the type of method to be used to compute covariance. Default is "pearson".
Example:
# Data vectors x < - c( 1 , 3 , 5 , 10 ) y < - c( 2 , 4 , 6 , 20 ) # Print correlation using different methods print (cor(x, y)) print (cor(x, y, method = "pearson" )) print (cor(x, y, method = "kendall" )) print (cor(x, y, method = "spearman" )) |
Output:
[1] 0.9724702 [1] 0.9724702 [1] 1 [1] 1
Conversion of Covariance to Correlation
cov2cor()
function in R programming converts a covariance matrix into corresponding correlation matrix.
Syntax:
cov2cor(X)
where,
X and y represents the covariance square matrix
Example:
# Data vectors x < - rnorm( 2 ) y < - rnorm( 2 ) # Binding into square matrix mat < - cbind(x, y) # Defining X as the covariance matrix X < - cov(mat) # Print covariance matrix print (X) # Print correlation matrix of data vector print (cor(mat)) # Using function cov2cor() # To convert covariance matrix to correlation matrix print (cov2cor(X)) |
Output:
x y x 0.0742700 -0.1268199 y -0.1268199 0.2165516 x y x 1 -1 y -1 1 x y x 1 -1 y -1 1