Correlation Coefficient Example

The worksheet for correlation coefficient helps you to understand how to correlation coefficient. The step by step procedure explains how to perform such calculations easily.

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:
σ_x=
√(1/(N-1)*((x₁-x_m)²+(x₂-x_m)²+..+(x_n-x_m)²))

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

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

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

=√(308.7)

=17.5699


Step 3: Standard Deviation for X Inputs:

σ_x=
√(1/(N-1)*((x₁-x_m)²+(x₂-x_m)²+..+(x_n-x_m)²))

=√(1/(5-1)((1-3)²+(2-3)²+(3-3)²+(4-3)²+(5-3)²))

=√(1/4((-2)²+(-1)²+(0)²+(1)²+(2)²))

=√(1/4((4)+(1)+(0)+(1)+(4)))

=√(2.5)

=1.5811

Σ((X - μ_x) (Y - μ_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 correlation coefficient between the two given data set is 0.9989

When you attempt to solve such on your own, use this correlation coefficient Calculator to verify your answers.