# Correlation between {81, 85, 96, 75, . . . , 75} & {95, 96, 99, 82, . . . , 75} Solved example problem, work with steps & calculation summary for correlation (r) between {81, 85, 96, 75, . . . , 75} & {95, 96, 99, 82, . . . , 75} to estimate the linear relationship or to find if the data linearly, non-linearly, positively or negatively correlated in statistical experiments.
Calculation Summary
Data set x{81, 85, 96, 75, 65, 90, 82 & 75}
Data set y{95, 96, 99, 82, 85, 60, 57 & 75}
Correlation Coefficient (r)0.0763

## Work with Steps for Correlation r = 0.0763

Question:
Find the following data X & Y positively or negatively correlated?
 X 81 85 96 75 65 90 82 75 Y 95 96 99 82 85 60 57 75

Workout :

step 1 Address the formula, input parameters and values
data set x = {81, 85, 96, 75, 65, 90, 82 and 75}
data set y = {95, 96, 99, 82, 85, 60, 57 and 75}
Total number of elements (n) = 8

step 2 Find x̄ & ȳ
x̄ = 649/8
x̄ = 81
ȳ = 649/8
ȳ = 81

step 3 To find coefficient correlation follow below the table

 x y X = x - x̄ Y = y - ȳ X2 Y2 XY 81 95 -0.125 13.875 0.0156 192.5156 -1.7344 85 96 3.875 14.875 15.0156 221.2656 57.6406 96 99 14.875 17.875 221.2656 319.5156 265.8906 75 82 -6.125 0.875 37.5156 0.7656 -5.3594 65 85 -16.125 3.875 260.0156 15.0156 -62.4844 90 60 8.875 -21.125 78.7656 446.2656 -187.4844 82 57 0.875 -24.125 0.7656 582.0156 -21.1094 75 75 -6.125 -6.125 37.5156 37.5156 37.5156 ∑x = 649 ∑y = 649 ∑X = 0 ∑Y = 0 ∑X2 = 650.875 ∑Y2 = 1814.875 ∑XY = 82.875

step 4 Substitute ∑x, ∑y, ∑xy, ∑x2 & ∑y2 value in the below correlation coefficient formula

r = ∑XY∑X2. ∑Y2

∑XY = 82.875, ∑X2 = 650.875, ∑Y2 = 1814.875

r = 82.875650.875 x 1814.875

step 5 Simplify above expression

= 82.8751181256.7656

= 82.8751086.8564

r = 0.0763

Thus 0.0763 is the correlation between x = {81, 85, 96, 75, 65, 90, 82 and 75} & y = {95, 96, 99, 82, 85, 60, 57 and 75} 