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R Squared Calculator
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The coefficent of determination is given by R2 decides how well the given data fits a line or a curve.The correlation R formula is
R= $\frac{N \sum{XY} - \sum{X} \sum{Y}}{\sqrt{[N \sum X^2 - (\sum X)^2][N \sum Y^2 -(\sum Y)^2]}}$
Here R : Correlation that lies between -1 and +1
N : total no of scores given
$\sum$ XY = Sum of scores of paired product
$\sum$ X = sum of X scores
$\sum$ Y = sum of Y scores
$\sum$ X2 = sum of X scores square
$\sum$ Y2 = sum of Y scores square

R square Calculator is a online tool to calculate the R square.You just have to enter the value of X scores and Y scores and get the value of correlation R and R2 instantly.
 

Steps for R Squared Calculator

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Step 1 :  

Read the problem and note down the data given



Step 2 :  

Make a table out of X score, Y score, XY score, X2 and Y2 score.Calculate $\sum$ X, $\sum$ Y, $\sum$ XY, $\sum$ X2, $\sum$ Y2.



Step 3 :  

Calculate correlation using formula


R= $\frac{n \sum{XY} - \sum{X} \sum{Y}}{\sqrt{[N \sum X^2 - (\sum X)^2][N \sum Y^2 -(\sum Y)^2]}}$


Now find the value R2 to find the coefficient of determination. 



Problems on R Squared Calculator

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  1. Determine the coefficient of correlation for the following data:

    X Y
    1 3
    3 5
    5 7
    7 10


    Step 1 :  

    Given data is

    XY
    13
    35
    57
    710


    Step 2 :  

    Create the table out of it

    XYXYX2Y2
    13319
    3515925
    57352549
    7107049100

     

    Here N = 4
    $\sum$ X = 16
    $\sum$ Y = 25
    $\sum$ XY = 123
    $\sum$ X2 = 84
    $\sum$ Y2 = 183



    Step 3 :  

    Calculate correlation using formula


    R= $\frac{n \sum{XY} - \sum{X} \sum{Y}}{\sqrt{[N \sum X^2 - (\sum X)^2][N \sum Y^2 -(\sum Y)^2]}}$


      = $\frac{4 \times 123 - 16 \times 25}{\sqrt{[4 \times 84 - (16)^2][4 \times 183 - (25)^2]}}$
     = $\frac{92}{92.52}$
     = 0.997
    R2 = 0.994





    Answer  :  

    The coefficient of determination R2 = 0.994.



  2. Determine the coefficient of correlation for the score of two students X and Y in various sujects:

    Subjects X Y
    History 39 44
    English 42 40
    Maths 67 60
    Science 76 84


    Step 1 :  

    Given data is

    SubjectsXY
    History3944
    English4240
    Maths6760
    Science7684


    Step 2 :  

    Create the table out of it

    XYXYX2Y2
    3944171615211936
    4240168017641600
    6760402044893600
    7684638457767056

    Here N = 4
    $\sum$ X = 224
    $\sum$ Y = 228
    $\sum$ XY = 13800
    $\sum$ X2 = 13550
    $\sum$ Y2 = 14192



    Step 3 :  

    Calculate correlation using formula


    R = $\frac{N \sum{XY} - \sum{X} \sum{Y}}{\sqrt{[N \sum X^2 - (\sum X)^2][N \sum Y^2 -(\sum Y)^2]}}$
       = $\frac{4 \times 123 - 16 \times 25}{\sqrt{[4 \times 84 - (16)^2][4 \times 183 - (25)^2]}}$
       = 0.9408


    R2 = 0.885.



    Answer  :  

    The coefficient of determination R2 = 0.885.



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