Co-Variance in Statistics easily explained with Toy example
Co-Variance:
Lest take a random Variables [Heights , Weights]
height weight
120cm 50
130cm 60
150cm 80
.
.
.
140cm 75
130cm 65
Co-variance Quantify relationship between 2 Parameters i.e.
If Height Increase and Weight also Increase
If Height Decrease and Weight also Decrease
[Positive Co-Variance]
If Height Increase and Weight Decrease
If Height Decrease and Weight Increase
[Negative Co-Variance]
Mathematical Formula is represented as :
Co-Variance [2 variable] & Variance [1 variable]
So now lets focus on our height and weight example:
height weight
120cm 50
130cm 60
150cm 80
.
.
.
140cm 75
130cm 65
So first calculate mean of both features (height and weight): So ,mean of height = 135 , mean of weight = 66.25.
And mathematical formula of Co-Variance is:
Covariance (height, weight) = (xi-mean)*(yi -mean)
Covariance (height, weight) = (120–135)*(50–66.25) = (-15) * (-16.25)
i.e. Xi and Yi both are negative that means positive Co-Variance.
Drawback of Co-Variance:
X (increase) and Y (increase) = positive Co-Variance (But it do not says how much positive)X (Increase) and Y (Dec) = Negative Co-Variance (But it do not says how much Negative)