How to Create a Covariance Matrix in R?

A covariance matrix is a square matrix that displays the covariance between each pair of variables in a dataset. It helps us understand how two variables change together. A positive value means both variables increase or decrease together, while a negative value means one increases as the other decreases. In R programming language, we can use the cov() function to create this matrix.

Syntax: 

cov( df )

Parameter:

• df: determines the data frame for creating covariance matrix.

A positive value for the covariance matrix indicates that two variables tend to increase or decrease sequentially. A negative value for the covariance matrix indicates that as one variable increases, the second variable tends to decrease.

Example 1: Covariance Matrix from Static Data

We create a data frame with three numeric variables and pass it to the cov() function to generate the covariance matrix.

• data.frame: Creates a structured table with named numeric vectors.
• var1, var2, var3: Column names representing different numeric variables.
• cov(): Calculates pairwise covariances between columns in the data frame.

sample_data <- data.frame(
  var1 = c(86, 82, 79, 83, 66),
  var2 = c(85, 83, 80, 84, 65),
  var3 = c(107, 127, 137, 117, 170)
)

cov(sample_data)

Output:

• Diagonal values show variances of var1, var2 and var3.
• 63.9 shows strong positive relation between var1 and var2.
• -185.9 and -192.8 show negative relation between var3 and var1 or var2.

Example 2: Covariance Matrix from Random Data

We use the rnorm() function to generate two columns of random numeric data and pass them to the cov() function to compute the matrix.

• rnorm(): Generates random numbers from a normal distribution.
• n = 20: Number of observations.
• mean, sd: Mean and standard deviation for each column.
• cov(): Computes covariances between the generated variables.

sample_data <- data.frame(
  var1 = rnorm(20, 5, 23),
  var2 = rnorm(20, 8, 10)
)

cov(sample_data)

Output:

• Diagonal values show variances of var1 and var2.
• -14.66 shows weak negative relation between var1 and var2.
• Values change on every run as data is random.