# Covariance and Correlation in R Programming

**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 Language

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, **

xrepresents the x data vectoryrepresents the y data vector

[Tex]\bar{x} [/Tex]represents mean of x data vector

[Tex]\bar{y} [/Tex]represents mean of y data vectorNrepresents total observations

### Covariance Syntax in R

Syntax:cov(x, y, method)

where,

xandyrepresents the data vectorsmethoddefines the type of method to be used to compute covariance. Default is “pearson”.

**Example:**

## R

`# 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 in R Programming Language

**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, **

xrepresents the x data vectoryrepresents the y data vector

[Tex]\bar{x} [/Tex]represents mean of x data vector

[Tex]\bar{y} [/Tex]represents mean of y data vector

### Correlation in R

Syntax:cor(x, y, method)

where,

xandyrepresents the data vectorsmethoddefines the type of method to be used to compute covariance. Default is “pearson”.

**Example:**

## R

`# 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 in R

**cov2cor()** function in R programming converts a covariance matrix into corresponding correlation matrix.

Syntax:cov2cor(X)

where,

Xandyrepresents the covariance square matrix

**Example:**

## R

`# 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