Correlation Coefficient Example

This worksheet may help you to know about the correlation coefficient of two given data sets. The formula for calculating Correlation Coefficient

Correlation Coefficient formula

Correlation Coefficient Formula

Find Correlation coefficient

Find Correlation coefficient for X and Y values are given below
X= (1,2,3,4,5)
Y= {11,22,34,43,56}

Solution:
Step 1: Find Mean for X and Y
X=15/5=3
Y=166/5=33.2

Step 2: Calculate Standard Deviation for Y inputs:
σx=
&radic(1/(N-1)*((x1-xm)2+(x2-xm)2+..+(xn-xm)2))

=&radic(1/(5-1)((11-33.2)2+(22-33.2)2+(34-33.2)2+(43-33.2)2+(56-33.2)2))

=&radic(1/4((-22.2)2+(-11.2)2+(0.8)2+(9.8)2+(22.8)2))

=&radic(1/4((492.84)+(125.44)+(0.64)+(96.04)+(519.84)))

=&radic(308.7)

=17.5699


Step 3: Standard Deviation for X Inputs:

σx=
&radic(1/(N-1)*((x1-xm)2+(x2-xm)2+..+(xn-xm)2))

=&radic(1/(5-1)((1-3)2+(2-3)2+(3-3)2+(4-3)2+(5-3)2))

=&radic(1/4((-2)2+(-1)2+(0)2+(1)2+(2)2))

=&radic(1/4((4)+(1)+(0)+(1)+(4)))

=&radic(2.5)

=1.5811

Σ((X-X)* (Y-Y)
=(1-3)*(11-33.2)+(2-3)(22-33.2)+(3-3)(34-33.2)+(4-3)(43-33.2)+(5-3)(56-33.2)
=-2*-22.2+ -1*-11.2 + 0* 0.8 + 1 *9.8 + 2* 22.8
=44.4 +11.2+0 + 9.8 + 45.6
=111
Correlation Coefficient=111/((5-1)*1.5811*17.5699)
Correlation Coefficient (r)=0.9989

Hence the required Correlation coefficient is 0.9989.

The above worksheet is a walk through to understand the concept of correlation co efficient. When it comes to online calculation this online Correlation coefficient Calculator is an efficient tool to make the calculation easy.

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