**Covariance **is a measure of how changes in one variable are associated with changes in a second variable. Specifically, it’s a measure of the degree to which two variables are linearly associated.

A **covariance matrix** is a square matrix that shows the covariance between many different variables. This can be a useful way to understand how different variables are related in a dataset.

The following example shows how to create a covariance matrix in R.

**How to Create a Covariance Matrix in R**

Use the following steps to create a covariance matrix in R.

**Step 1: Create the data frame.**

First, we’ll create a data frame that contains the test scores of 10 different students for three subjects: math, science, and history.

#create data frame data <- data.frame(math = c(84, 82, 81, 89, 73, 94, 92, 70, 88, 95), science = c(85, 82, 72, 77, 75, 89, 95, 84, 77, 94), history = c(97, 94, 93, 95, 88, 82, 78, 84, 69, 78)) #view data frame data math science history 1 84 85 97 2 82 82 94 3 81 72 93 4 89 77 95 5 73 75 88 6 94 89 82 7 92 95 78 8 70 84 84 9 88 77 69 10 95 94 78

**Step 2: Create the covariance matrix.**

Next, we’ll create the covariance matrix for this dataset using the **cov() **function:

#create covariance matrix cov(data) math science history math 72.17778 36.88889 -27.15556 science 36.88889 62.66667 -26.77778 history -27.15556 -26.77778 83.95556

**Step 3: Interpret the covariance matrix.**

The values along the diagonals of the matrix are simply the variances of each subject. For example:

- The variance of the math scores is 72.18
- The variance of the science scores is 62.67
- The variance of the history scores is 83.96

The other values in the matrix represent the covariances between the various subjects. For example:

- The covariance between the math and science scores is 36.89
- The covariance between the math and history scores is -27.16
- The covariance between the science and history scores is -26.78

A **positive number** for covariance indicates that two variables tend to increase or decrease in tandem. For example, math and science have a positive covariance (36.89), which indicates that students who score high on math also tend to score high on science. Conversely, students who score low on math also tend to score low on science.

A **negative number** for covariance indicates that as one variable increases, a second variable tends to decrease. For example, math and history have a negative covariance (-27.16), which indicates that students who score high on math tend to score low on history. Conversely, students who score low on math tend to score high on history.

*You can find more R tutorials here.*