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Correlation Coefficient Calculator

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Correlation coefficients determines how two variables are associated. Correlation coefficient is denoted by "r". Correlation coefficient r ranges between 1 and -1. If r = 1, then its perfect positive correlation and when r = -1, then its perfect negative correlation. If r = 0, then there is no correlation coefficient.

Perfect Positive Correlation No Correlation Perfect Negative Correlation

Correlation Coefficient Calculator finds the correlation coefficient when you plug in the two sets of variables into the calculator.
 

Steps

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Step 1 : Observe and note the number of sample (n).

Step 2 : Determine the value of XY, $X^2$ and $Y^2$.

Step 3 : Find the sum($\Sigma $) of X, $X^2$, Y, $Y^2$ and XY.

Step 4 : Plug in these values into the correlation coefficient formula given below and you will get the correlation value(r).
$r = \frac{n(\Sigma XY)-(\Sigma X)(\Sigma Y)}{\sqrt{[n(\Sigma X^{2})-(\Sigma X)^{2}][n(\Sigma Y^{2})-(\Sigma Y)^{2}]}}$

Problems

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Given below are the problems based on correlation coefficient.

Solved Examples

Question 1: Find the value of correlation coefficient for

X valueY value
21 65
42 75
59 81
43 98
26 79


Solution:
 
Solution :
Step 1 : Number of sample, n = 5

Step 2 :
X values
Y values
XY $X^2$ $Y^2$
21 65 1365 441 4225
42 75 3150
1764 5625
59 81 4779 3481 6561
43 98 4214
1849 9604
26 79 2054 676 6241

Step 3 :
$\Sigma X$ = 21+42+59+43+26 = 191
$\Sigma Y$ = 65+75+81+98+79 = 398
$\Sigma XY$ = 1365+3150+4779+4214+2054 = 15562
$\Sigma X^2$ = 441+1764+3481+1849+676 = 8211
$\Sigma Y^2$ = 4225+5625+6561+9604+6241 = 32256

Step 4 :
Correlation r = $\frac{n(\Sigma XY)-(\Sigma X)(\Sigma Y)}{\sqrt{[n(\Sigma X^{2})-(\Sigma X)^{2}][n(\Sigma Y^{2})-(\Sigma Y)^{2}]}}$

r = $\frac{5(15562)-(191)(398)}{\sqrt{[5(8211)-(191)^{2}][5(32256)-(398)^{2}]}}$

$r = 0.4941$

 

Question 2: Find the value of correlation coefficient for

X valueY value
1 2
3 4
5 6
7 8
9 0

Solution:
 
Solution :
Step 1 : Number of sample, n = 5

Step 2 :
X values
Y values
XY $X^2$ $Y^2$
1 2 2
1
4
3 4 12
9
16
5 6
30
25
36
7
8  56
49 64
9
0
0
81
0

Step 3 :
$\Sigma X$ =1+3+5+7+9 = 25
$\Sigma Y$ = 2+4+6+8+0 = 20
$\Sigma XY$ = 2+12+30+56+0 = 100
$\Sigma X^2$ = 1+9+25+49+81 = 165
$\Sigma Y^2$ = 4+16+36+64+0 =120

Step 4 :
Correlation r = $\frac{n(\Sigma XY)-(\Sigma X)(\Sigma Y)}{\sqrt{[n(\Sigma X^{2})-(\Sigma X)^{2}][n(\Sigma Y^{2})-(\Sigma Y)^{2}]}}$

r = $\frac{5(100)-(25)(20)}{\sqrt{[5(165)-(25)^{2}][5(120)-(20)^{2}]}}$

$r = 0$