# Correlation between {7000, 7500, 6500, 5000, . . . , 12000} & {5200, 5500, 5750, 4300, . . . , 8300} Solved example problem, work with steps & calculation summary for correlation (r) between {7000, 7500, 6500, 5000, . . . , 12000} & {5200, 5500, 5750, 4300, . . . , 8300} 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{7000, 7500, 6500, 5000, 7500, 9000, 9500 & 12000}
Data set y{5200, 5500, 5750, 4300, 6000, 8900, 7200 & 8300}
Correlation Coefficient (r)0.8572

## Work with Steps for Correlation r = 0.8572

Question:
Find the correlation between this below income & expense report.
 Income 7000 7500 6500 5000 7500 9000 9500 12000 Expense 5200 5500 5750 4300 6000 8900 7200 8300

Workout :

step 1 Address the formula, input parameters and values
data set x = {7000, 7500, 6500, 5000, 7500, 9000, 9500 and 12000}
data set y = {5200, 5500, 5750, 4300, 6000, 8900, 7200 and 8300}
Total number of elements (n) = 8

step 2 Find x̄ & ȳ
x̄ = 64000/8
x̄ = 8000
ȳ = 51150/8
ȳ = 6394

step 3 To find coefficient correlation follow below the table

 x y X = x - x̄ Y = y - ȳ X2 Y2 XY 7000 5200 -1000 -1193.75 1000000 1425039.0625 1193750 7500 5500 -500 -893.75 250000 798789.0625 446875 6500 5750 -1500 -643.75 2250000 414414.0625 965625 5000 4300 -3000 -2093.75 9000000 4383789.0625 6281250 7500 6000 -500 -393.75 250000 155039.0625 196875 9000 8900 1000 2506.25 1000000 6281289.0625 2506250 9500 7200 1500 806.25 2250000 650039.0625 1209375 12000 8300 4000 1906.25 16000000 3633789.0625 7625000 ∑x = 64000 ∑y = 51150 ∑X = 0 ∑Y = 0 ∑X2 = 32000000 ∑Y2 = 17742187.5 ∑XY = 20425000

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

r = ∑XY∑X2. ∑Y2

∑XY = 20425000, ∑X2 = 32000000, ∑Y2 = 17742187.5

r = 2042500032000000 x 17742187.5

step 5 Simplify above expression

= 204250005.6775E+14

= 2042500023827505.1149

r = 0.8572

Thus 0.8572 is the correlation between x = {7000, 7500, 6500, 5000, 7500, 9000, 9500 and 12000} & y = {5200, 5500, 5750, 4300, 6000, 8900, 7200 and 8300} 