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Pearson Correlation Calculator
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Correlation is that what tells about how two linear data are associated with each other. It lies between -1 and +1 and is given by formula

$r$ = $\frac{N(\sum{XY})-(\sum{X})(\sum{Y})}{\sqrt{(N\sum{X^{2}}-(\sum{X})^{2})(N\sum{Y^{2}}-(\sum{Y})^{2})}}$

The correlation calculator is a online tool to calculate the correlation (r) for the given data. You just have to enter the values of x and y and can get the correlation instantly. This helps you a lot in saving your time as it gives you out instant solutions.
Default x and y values is given in the calculator below. The calculator will calculate XY,X^2,Y^2 and substitute in the correlation formula. You can see correlation for the given data when you click on "Pearson Correlation Calculator".

## Steps for Pearson Correlation Calculator

Step 1 :

Count the number of elements given. Calculate XY,X2 and Y2. Form a table out of it

Step 2 :

Find $\sigma$ X, $\sigma$ Y, $\sigma$ XY, $\sigma$ X2 and $\sigma$ Y2.

Step 3 :

The correlation is given by
Correlation (r) = $\frac{N(\sum{XY})-(\sum{X})(\sum{Y})}{\sqrt{(N\sum{X^{2}}-(\sum{X})^{2})(N\sum{Y^{2}}-(\sum{Y})^{2})}}$

Substitute the values in the above formula and get the answer.

## Problems on Pearson Correlation Calculator

1. ### Find the correlation of X   Y2   3  4   4 6   8 8   5 10 6

Step 1 :

Given : No of elements = 5. Lets find XY, X2, Y2 and form a table out of it.
X   Y  XY X2   Y2
2   3  6   4    9
4   4  16 16  16
6   8  48 36  64
8   5  40 64  25
10 6  60 100 36

Step 2 :

$\sum$ X = 30
$\sum$ Y = 26
$\sum$ XY = 170
$\sum$ X2 = 220
$\sum$ Y2 = 150

Step 3 :

The Correlation is given by
Correlation (r) =$\frac{N(\sum{XY})-(\sum{X})(\sum{Y})}{\sqrt{(N\sum{X^{2}}-(\sum{X})^{2})(N\sum{Y^{2}}-(\sum{Y})^{2})}}$
= $\frac{5(170) - (30)(26)}{\sqrt{((5 \times 220) - (30)^2) (5 \times 150 - (26)^2)}}$
= $\frac{70}{121.655}$
= 0.575.

Correlation (r) = 0.575

2. ### Find the correlation of X  Y  4  5 8  710 6

Step 1 :

Given: No of elements = 3. Lets find XY, X2, Y2 and form a table out of it.

X  Y XY  X2    Y2
4  5 20  16    25
8  7 56  64    49
10 6 60  100   36

Step 2 :

$\Sigma$ X = 22
$\sigma$ Y = 18
$\Sigma$ XY = 136
$\Sigma$ X2 = 180
$\sigma$ Y2 = 110

Step 3 :

The correlation is given by
Corelation (r) = $\frac{N(\sum{XY})-(\sum{X})(\sum{Y})}{\sqrt{(N\sum{X^{2}}-(\sum{X})^{2})(N\sum{Y^{2}}-(\sum{Y})^{2})}}$
= $\frac{3(136) - (22)(18)}{\sqrt{((3 \times 180) - (22)^2) (3 \times 110 - (18)^2)}}$
= $\frac{12}{18.33}$
= 0.654.