Covariance

The correlation measures the extent to which the value of one variable is related to the value of another variable.
The covariance measures the extend to which two variables change together


The variance (and standard deviation) are useful measures but they can only be used on a single variable.
When we are interested in a relationship between two variables we need to find the covariance


SS - equation


The covariance between 2 variables measures the strength of the linear association between them.
At times you need to compare two sets of data to see how they relate to each other.
COVAR() takes 2 arrays as its arguments
a positive result means the two arrays move in the same direction
a negative result means the two arrays move in opposite directions.
If = 0 then ther is no relationship between the 2 data sets.


One problem of the covariance is that the result depends on the actual units of the data sets.



The CORREL is similar to the COVAR except the result is always between -1 and 1.
This allows the result of one correlation to be easily compared with another.



Understanding Covariance

We need to calculate the difference between every point and its mean and then multiply these together.
Then take the average of all these products.
The covariance is the average of the difference between every point from the mean of the first series multiplied by the same thing for the second series.




What is wrong with the Covariance ?

There are two problems:
1) It depends on the units in which the variables are measured.
For example if I want to see if there is relationship between peoples heights and peoples weights.
I could calculate the covariance based on a height measurement in meters or feet and get two completely different values.


2) There is no upper limit nor a lower limit to the value
This makes it hard to identify a weak or a strong relationship.
We are able to tell if they are positively or negatively related but not how strong this relationship is.




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