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Coefficient of Determination Calculator
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If there are two data series are given, the Coefficient of Determination Calculator calculates the relationship between these series.
 

Steps for Coefficient of Determination Calculator

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Step 1 :   

Observe the no of values given in the problem. Take it value of n.



Step 2 :  Calculate the value of X, Y, XY, X2 and Y2.

Step 3 :   

Using the formula:
Correlation (r) = n(XY)(X)(Y)(n(X)2(X)2)(nY2Y22)
get the value of correlation (r).



Step 4 :  To get the value of coefficient of determination find the value of r2.
where r2 = r × r.



Problems on Coefficient of Determination Calculator

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  1. Find the correlation coefficient  of determination for given values:

    X value Y value
    30 5.5
    31 5.6
    32 5.8
    33 6.0
    34 6.2


    Step 1 :  

    Number of values = n = 5



    Step 2 :  
    X valueY ValueXYX2Y2
    40312012009
    414164168116
    425210176425
    436258184936


    Step 3 :  

    $\sum$ X = 160


    $\sum$ Y = 29.1


    $\sum$ XY = 933


    $\sum$ X2 = 5130


    $\sum$ Y2 = 169.69



    Step 4 :  

    Using the formula:
    Correlation (r) =  $\frac{n \sum{XY} - \sum{X} \sum{Y}}{\sqrt{(n \sum{x^2} - (\sum X)^{2} (n \sum {Y^2} - {\sum Y}^2)}}$


    $\frac{5(933) - (160) (29.1)}{\sqrt{(5 \times 5130 - (160)^{2})(5 (169.69) - {29.1}^{2})}}$.



    Answer  :  

    Corerelation(r) = 0.994

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

    Coefficient of Determination (r2) = r $\times$ r = 0.987.



  2. Find the Coefficient of determinant for given values:

    X Value  Y Value
    40 3
    41 4
    42 5
    43 6


    Step 1 :  

    No of values = n = 4



    Step 2 :  
    X valueY ValueXYX2Y2
    40312012009
    414164168116
    425210176425
    436258184936


    Step 3 :  

    $\sum$ X = 166


    $\sum$ Y = 18


    $\sum$ XY = 752


    $\sum$ X2 = 6494


    $\sum$ Y2 = 86



    Step 4 :  

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


    $\frac{4(752) - (166) (18)}{\sqrt{(4 \times 6494 - (166)^{2})(4 (18)^{2} - 86)}}$


    = $\frac{3008 - 2988}{\sqrt{20(344 - 324)}}$


    = $\frac{20}{20}$



    Answer  :  

    Correlation (r) = 1

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

    Coefficient of Determination (r2) = r $\times$ r = 1.



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