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?
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
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 = 82.875√650.875 x 1814.875
step 5 Simplify above expression
= 82.875√1181256.7656
= 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}
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 = 82.875√650.875 x 1814.875
step 5 Simplify above expression
= 82.875√1181256.7656
= 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}
