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Correlation Coefficient Calculator


  • Correlation Coefficient

How does Correlation Coefficient Calculator work?

  • Enter the data set of x & y In The Input Box.
  • Hit The Calculate Button.
  • Use The Reset Button To calculate New Values.




The Correlation Coefficient calculator solves the Correlation Coefficient (R), Mean of x, Mean of y, Difference of Data set x and x mean (x- x̄), Difference of Data set y and y mean (y- ȳ). It also calculates the Square of the differences i.e. (x- x̄)2 and (y- ȳ)2 respectively using two different data sets X and Y.

Both data sets must have an equal number of terms.


What is the Correlation Coefficient?


The correlation coefficient is the specific measure that quantifies the strength of the linear relationship between two variables in a correlation analysis.It is denoted by r


Correlation Coefficient formula:


The correlation coefficient formula is given below:

correlation coefficient formula                                           

Where

  • x and y are the two datasets.
  • x̄ And ȳ are the means.
  • x- x̄ & y-ȳ are deviation scores.
  • (x- x̄)2 & (y-ȳ)2 are squared deviations.
  • (x- x̄)(y-ȳ) product of deviation scores.

Types of Correlation Coefficient:


There are two different types of Correlation coefficients:

  1. Pearson’s correlation coefficient.
  2. Spearman’s rank correlation coefficient.

Generally, Pearson’s correlation coefficient is known as Pearson’s r or simply the correlation coefficient. Its range is -1 to 1.

Spearman's rank correlation coefficient or Spearman's ρ, named after Charles Spearman. It describes the relation between two monotonic variables.

The correlation coefficient is the ratio between the covariance of any two variables, say, X & Y to the product of their standard deviation.


How to find correlation coefficient r:


With the help of the following example, you will be able to find the correlation coefficient.

Example:

Let x be any data set having values 2, 7.5, 3, 34.2, 26, and y data set 21, 12.5, 3, 11, 17. Find the Correlation coefficient r.

Solution:

x = 2, 7.5, 3, 34.2, 26
y = 21, 12.5, 3, 11, 17

Step 1: Calculate the mean of the data sets
x̄ = (2 + 7.5 + 33 + 34.2 + 26)/5 = 14.540
ȳ = (21 + 12.5 + 3 + 11 + 17)/5 = 12.900
 

x y x-x̄ y-ȳ (x- x̄)2 (y-ȳ)2 (x- x̄)(y-ȳ)
2 21 -12.540 8.100 157.252 65.610 -101.574
7.5 12.5 -7.040 -0.400 49.562 0.160 2.816
33 3 -11.540 -9.900 133.172 98.010 114.246
 34.2 11 19.660 -1.900 386.516 3.610 -37.354
26 17 11.460 4.100 131.332 16.810 46.986
        857.832 184.200 25.120


Step2: Calculation of r
Correlation coefficient Formula = r = ∑ ((x - x̄) (y-ȳ)) / √(∑ (x-x̄)2 ∑ (y-ȳ)2)
Putting the values in the above formula.
r = 25.12 / √ ((857.832) (184.2))
r = 0.0632

How to verify whether the answer is correct or not.

As r = 0.0632, the answer is between -1 and 1, so the answer is correct because the range of the correlation coefficient is -1 to 1.


References:


Correlation coefficient | JMP. (n.d.).
Spearman's rank correlation coefficient.| Wikipedia.
Types of correlation coefficients. |  Ersoy, P.