Correlation between {1, 2, 3, 4 & 5} & {2, 1, 4, 3 & 7}
Solved example problem, work with steps & calculation summary for correlation (r) between {1, 2, 3, 4 & 5} & {2, 1, 4, 3 & 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 | {1, 2, 3, 4 & 5} |
| Data set y | {2, 1, 4, 3 & 7} |
| Correlation Coefficient (r) | 0.8242 |
Work with Steps for Correlation r = 0.8242
Users may refer the below example workout with steps to find if any correlation between dataset x = {1, 2, 3, 4 & 5} & y = {2, 1, 4, 3 & 7} or to learn the input parameters & values are being used in the calculation.
Workout :
step 1 Address the formula, input parameters and values
data set x = {1, 2, 3, 4 and 5}
data set y = {2, 1, 4, 3 and 7}
Total number of elements (n) = 5
step 2 Find x̄ & ȳ
x̄ = 15/5
x̄ = 3
ȳ = 17/5
ȳ = 3
step 3 To find coefficient correlation follow below the table
step 4 Substitute ∑x, ∑y, ∑xy, ∑x2 & ∑y2 value in the below correlation coefficient formula
r = ∑XY√∑X2. ∑Y2
∑XY = 12, ∑X2 = 10, ∑Y2 = 21.2
r = 12√10 x 21.2
step 5 Simplify above expression
= 12√212
= 1214.5602
r = 0.8242
Thus 0.8242 is the correlation between x = {1, 2, 3, 4 and 5} & y = {2, 1, 4, 3 and 7}
step 1 Address the formula, input parameters and values
data set x = {1, 2, 3, 4 and 5}
data set y = {2, 1, 4, 3 and 7}
Total number of elements (n) = 5
step 2 Find x̄ & ȳ
x̄ = 15/5
x̄ = 3
ȳ = 17/5
ȳ = 3
step 3 To find coefficient correlation follow below the table
| x | y | X = x - x̄ | Y = y - ȳ | X2 | Y2 | XY |
| 1 | 2 | -2 | -1.4 | 4 | 1.96 | 2.8 |
| 2 | 1 | -1 | -2.4 | 1 | 5.76 | 2.4 |
| 3 | 4 | 0 | 0.6 | 0 | 0.36 | 0 |
| 4 | 3 | 1 | -0.4 | 1 | 0.16 | -0.4 |
| 5 | 7 | 2 | 3.6 | 4 | 12.96 | 7.2 |
| ∑x = 15 | ∑y = 17 | ∑X = 0 | ∑Y = 0 | ∑X2 = 10 | ∑Y2 = 21.2 | ∑XY = 12 |
step 4 Substitute ∑x, ∑y, ∑xy, ∑x2 & ∑y2 value in the below correlation coefficient formula
r = ∑XY√∑X2. ∑Y2
∑XY = 12, ∑X2 = 10, ∑Y2 = 21.2
r = 12√10 x 21.2
step 5 Simplify above expression
= 12√212
= 1214.5602
r = 0.8242
Thus 0.8242 is the correlation between x = {1, 2, 3, 4 and 5} & y = {2, 1, 4, 3 and 7}
