# Linear Correlation Coefficient Formula

To find out the relation between two variables in a population, linear correlation is used. To see how the variables are connected we will use the formula. Also known as “Pearson’s Correlation”, linear correlation can be denoted by r” and the value will be between -1 and 1.

The elements denotes a strong relation if the product is 1. Similarly, if the coefficient comes close to -1, it has negative relation. If the Linear coefficient is zero means there is no relation between the data given.

Where, n is the number of observations, x_{i} and y_{i} are the variables.

### Solved Examples

**Question 1: **Calculate the linear correlation coefficient for the following data. X = 4, 8 ,12, 16 and Y = 5, 10, 15, 20.

**Solution:**

Given variables are,

X = 4, 8 ,12, 16 and Y = 5, 10, 15, 20

For finding the linear coefficient of these data, we need to first construct a table for the required values.

x | y | $x^{2}$ | $y^{2}$ | XY |

4 | 5 | 16 | 25 | 20 |

8 | 10 | 64 | 100 | 80 |

12 | 15 | 144 | 225 | 180 |

16 | 20 | 256 | 400 | 320 |

$\sum x$ = 40 | $\sum y$ =50 | 480 | 750 | 600 |

According to the formula we have,

$r(xy)=\frac{4\times 600-40\times 50}{\sqrt{4}\times 40^{2}\sqrt{4}\times 750 \times 50^{2}}=0.00008$