# Correlation between {6.1, 6.0, 5.9, 5.8, . . . , 4.8} & {5.9, 5.7, 6.1, 5.2, . . . , 5.7}

Solved example problem, work with steps & calculation summary for correlation (r) between {6.1, 6.0, 5.9, 5.8, . . . , 4.8} & {5.9, 5.7, 6.1, 5.2, . . . , 5.7} 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{6.1, 6.0, 5.9, 5.8, 5.5, . . . . , 4.9 & 4.8}
Data set y{5.9, 5.7, 6.1, 5.2, 5.7, . . . . , 4.1 & 5.7}
Correlation Coefficient (r)0.6328

## Work with Steps for Correlation r = 0.6328

Question:
The following data collected from the survey taken at 11 persons. The purpose of this survey is to estimate the height correlation between each father & son in the group. All the measurements are given in feet & inches.
All the measurement in feet & inches
Father 6.1 6.0 5.9 5.8 5.5 5.4 5.2 5.1 5.0 4.9 4.8
Son 5.9 5.7 6.1 5.2 5.7 4.8 5.5 4.3 4.3 4.1 5.7

Workout :

step 1 Address the formula, input parameters and values
data set x = {6.1, 6.0, 5.9, 5.8, 5.5, . . . . , 4.9 and 4.8}
data set y = {5.9, 5.7, 6.1, 5.2, 5.7, . . . . , 4.1 and 5.7}
Total number of elements (n) = 11

step 2 Find x̄ & ȳ
x̄ = 59.7/11
x̄ = 5
ȳ = 57.3/11
ȳ = 5

step 3 To find coefficient correlation follow below the table

 x y X = x - x̄ Y = y - ȳ X2 Y2 XY 6.1 5.9 0.6727 0.6909 0.4525 0.4773 0.4648 6.0 5.7 0.5727 0.4909 0.328 0.241 0.2811 5.9 6.1 0.4727 0.8909 0.2234 0.7937 0.4211 5.8 5.2 0.3727 -0.0091000000000001 0.1389 0.0001 -0.0034 5.5 5.7 0.0727 0.4909 0.0053 0.241 0.0357 5.4 4.8 -0.027299999999999 -0.4091 0.0007 0.1674 0.0112 5.2 5.5 -0.2273 0.2909 0.0517 0.0846 -0.0661 5.1 4.3 -0.3273 -0.9091 0.1071 0.8265 0.2975 5.0 4.3 -0.4273 -0.9091 0.1826 0.8265 0.3885 4.9 4.1 -0.5273 -1.1091 0.278 1.2301 0.5848 4.8 5.7 -0.6273 0.4909 0.3935 0.241 -0.3079 ∑x = 59.7 ∑y = 57.3 ∑X = -0.0003 ∑Y = -0.0001 ∑X2 = 2.1618 ∑Y2 = 5.1291 ∑XY = 2.1073

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

r = ∑XY∑X2. ∑Y2

∑XY = 2.1073, ∑X2 = 2.1618, ∑Y2 = 5.1291

r = 2.10732.1618 x 5.1291

step 5 Simplify above expression

= 2.107311.0882

= 2.10733.3299

r = 0.6328

Thus 0.6328 is the correlation between x = {6.1, 6.0, 5.9, 5.8, 5.5, . . . . , 4.9 and 4.8} & y = {5.9, 5.7, 6.1, 5.2, 5.7, . . . . , 4.1 and 5.7}