# 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()**,

**and**

`cor()`

**functions in R which use covariance and correlation methods of statistics and probability theory.**

`cov2cor()`

#### Covariance

In R programming, covariance can be measured using

function. Covariance is a statistical term used to measures the direction of the linear relationship between the data vectors. Mathematically,**cov()**

**where,**

xrepresents the x data vectoryrepresents the y data vector

represents mean of x data vector

represents mean of y data vectorNrepresents total obeservations

**Syntax:**

cov(x, y, method)

**where,**

xandyrepresents the data vectorsmethoddefines 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

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,**cor()**

**where,**

xrepresents the x data vectoryrepresents the y data vector

represents mean of x data vector

represents mean of y data vector

**Syntax:**

cor(x, y, method)

**where,**

xandyrepresents the data vectorsmethoddefines 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

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

**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