Take advantage of this free Linear Correlation Coefficient Calculator to find the linear correlation coefficient. Enter data points of x and y in the input boxes and press on the calculate button to generate the output in less amount of time.

**Linear Correlation Coefficient Calculator: **Gaining knowledge on math concepts will make you strong in attempting the board exams. We are proving the each and every step to get the linear correlation coefficient of data points in the below sections. Students who are searching for the best and easy procedure can read this entire page. The solved example problems are helpful for you in getting a clear idea on the concept.

The step by step guide given below will make you comfortable in solving the correlation coefficient. Feel free and follow these steps while solving the data points.

- Take the data points for two variables.
- The formula to get the linear correlation coefficient r is r = [(n ∑xy - ∑x ∑y) / {√(n ∑x
^{2}- (∑x)^{2}) √(n ∑y^{2}- (∑y)^{2})}]. - Find ∑x, ∑y, ∑xy, and ∑x
^{2}, ∑y^{2}. - Substitute the values in the formula and do calculation.
- After completing calculations, r value is the result.

Linear correlation coefficient is used to determine the strength of the linear relationship between two variables in the data set values. It is denoted by r. The formula to compute the linear correlation coefficient is given below.

**Example**

**Question: Calculate the linear correlation coefficient for the values X and Y? X = {4, 8 ,12, 16} and Y = {5, 10, 15, 20}.**

**Solution:**

Given that,

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

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 |

Σx = 40 | Σy = 50 | ∑x^{2} = 480 |
∑y^{2} = 750 |
∑xy = 600 |

Linear Correlation Coefficient formula is

r = [(n ∑xy - ∑x ∑y) / {√(n ∑x^{2} - (∑x)^{2}) √(n ∑y^{2} - (∑y)^{2})}]

Place all the values in the formula

r = [(4×600)−(40×50)]/ √[4(480) − 40^{2} * √4(750) − 50^{2}]

= [2400 − 2000] / [√(1920 − 1600) * √(3000 − 2500)]

= (400) / [√320 * √500]

= 400 / (17.89 × 22.36)

= 400 / 400

= 1

Linear correlation coefficient = r = 1.

**1. Define linear correlation coefficient?**

Linear correlation coefficient defines the linear relationship between two variables x and y of varying strengths. The coefficient for the collection of n pairs (x, y) of numbers in a sample is the number r. The sign of the linear correlation coefficient indicates the direction of the linear relationship between x and y. Its formula is

r = (SS_{xy}) / √(SS_{xx} * SS_{yy}

where,

SS_{xx} = ∑x^{2} - 1/n (∑x)^{2}

SS_{xy} = ∑xy - 1/n (∑x)*(∑y)

SS_{yy} = ∑y^{2} - 1/n (∑y)^{2}

**2. How do you find the linear correlation coefficient on a calculator?**

Just provide data values in the input sections and press on the calculate button next to the input fields to get the accurate and exact output in fraction of seconds.

**3. Where can I get the detailed explanation to solve the linear correlation coefficient?**

You can get the detailed step by step process to calculate the linear correlation coefficient r value along with the formula on this page.

**4. Where can I find the best tool to get the linear correlation coefficient value?**

You can find the best online tools for linear correlation coefficient taking the help from Onlinecalculator.guru a trustworthy and genuine site.