To get the best deal on Tutoring, call 1-855-666-7440 (Toll Free)
Top

Pearson Correlation Calculator
Top
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

Back to Top
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

Back to Top
  1. Find the correlation of
    X   Y
    2   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.



    Answer  :  

    Correlation (r) = 0.575



  2. Find the correlation of
    X  Y 
    4  5
    8  7
    10 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.



    Answer  :  

    Correlation (r) = 0.654.



*AP and SAT are registered trademarks of the College Board.