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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

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

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

 X Y 1 3 3 5 5 7 7 10

Step 2 :

Create the table out of it

 X Y XY X2 Y2 1 3 3 1 9 3 5 15 9 25 5 7 35 25 49 7 10 70 49 100

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

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

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

Step 2 :

Create the table out of it

 X Y XY X2 Y2 39 44 1716 1521 1936 42 40 1680 1764 1600 67 60 4020 4489 3600 76 84 6384 5776 7056

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.