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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

Step 1 :

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

Step 2 :  Calculate the value of X$\sum X$, Y$\sum Y$, XY$\sum XY$, X2$\sum X^{2}$ and Y2$\sum Y^{2}$.

Step 3 :

Using the formula:
Correlation (r) = n(XY)(X)(Y)(n(X)2(X)2)(nY2Y22)$\frac{n(\sum XY) - (\sum X) (\sum Y)}{\sqrt{(n \sum (X)^{2} - (\sum X)^{2})}(n \sum Y^{2} - {\sum Y^{2}}^{2})}$
get the value of correlation (r).

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

## Problems on Coefficient of Determination Calculator

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 value Y Value XY X2 Y2 40 3 120 1200 9 41 4 164 1681 16 42 5 210 1764 25 43 6 258 1849 36

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

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

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 value Y Value XY X2 Y2 40 3 120 1200 9 41 4 164 1681 16 42 5 210 1764 25 43 6 258 1849 36

Step 3 :

$\sum$ X = 166

$\sum$ Y = 18

$\sum$ XY = 752

$\sum$ X2 = 6494

$\sum$ Y2 = 86

Step 4 :

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

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

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

= $\frac{20}{20}$

Correlation (r) = 1

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

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