Covariance for X = 11, 13, 15, 17 & 14 and Y = 12, 23, 14, 16 & 15
Covariance calculation summary for two random variables X = 11, 13, 15, 17 & 14 and Y = 12, 23, 14, 16 & 15 to estimate the strength of linear inter-dependence between them.
| Calculation Summary | |
|---|---|
| Dataset X | 11, 13, 15, 17 & 14 |
| Dataset Y | 12, 23, 14, 16 & 15 |
| COV(X, Y) | 0.6 |
Example with Steps for COV(X, Y) = 0.6
The below workout with step by step calculation may help grade school students, beginners or learners to understand how to estimate the covariance(X, Y) for random variables X = 11, 13, 15, 17 & 14 and Y = 12, 23, 14, 16 & 15
Workout :
step 1 Address the formula, input parameters and values
X = 11, 13, 15, 17 & 14
Y = 12, 23, 14, 16 & 15
Number of inputs = 5
step 2 Formula for Covariance(X, Y)
COV (X, Y) = 1/n n ∑ i = 1 (xi - x)(yi - y)
step 3 Apply the values in above formula
COV (X, Y) = 1/n{ (11 - 14) x (12 - 16) + (13 - 14) x (23 - 16) + . . . . + (14 - 14) x (15 - 16) }
= 1/5{ (-3) x (-4) + (-1) x (7) + . . . . + (0) x (-1) }
= 1/5{ (12) + (-7) + . . . . + (-0) }
=3/5
COV(X, Y) = 0.6
0.6 is the covariance for X = 11, 13, 15, 17 & 14 and Y = 12, 23, 14, 16 & 15
step 1 Address the formula, input parameters and values
X = 11, 13, 15, 17 & 14
Y = 12, 23, 14, 16 & 15
Number of inputs = 5
step 2 Formula for Covariance(X, Y)
COV (X, Y) = 1/n n ∑ i = 1 (xi - x)(yi - y)
step 3 Apply the values in above formula
COV (X, Y) = 1/n{ (11 - 14) x (12 - 16) + (13 - 14) x (23 - 16) + . . . . + (14 - 14) x (15 - 16) }
= 1/5{ (-3) x (-4) + (-1) x (7) + . . . . + (0) x (-1) }
= 1/5{ (12) + (-7) + . . . . + (-0) }
=3/5
COV(X, Y) = 0.6
0.6 is the covariance for X = 11, 13, 15, 17 & 14 and Y = 12, 23, 14, 16 & 15
