All language subtitles for 01 - Visualize what covariance means

- [Instructor] When you analyze data,

it is often important to see how two sets of values

vary in relation to one another.

One way to do that

is to calculate the covariance of the data sets.

The covariance formula looks a little intimidating,

but I'll break it down for you step by step.

If you have two sets of values and columns,

you can find the average of each column.

And the average is indicated by a bar

above the variable name.

So you see X bar,

which is the average of all the X values, column one.

And Y bar is the average or mean of all of the Y values.

That would be your second column.

Then, to average the covariance of a pair of values,

you subtract the mean of column one

from the first value in column one,

and subtract the mean of column two

from the first value of column two,

and then multiply those values together

for each pair of data points.

You find the sum of all of those values

and then, finally, you divide by the number of data pairs.

So if you have 10 pairs of values,

you would divide that sum by 10.

And the result is given in terms of the original data,

such as dollars, per mile driven,

or perhaps customers versus dollar spent.

The next question is how you interpret covariance values.

If the value is zero, which is rare, but can happen,

the data sets don't vary together at all.

If you have a positive covariance,

the data sets tend to move in the same direction.

So if one value goes up,

such as personal income,

then the other value would go up,

such as amount spent at your store.

If the values show a negative covariance,

then they tend to move in opposite directions.

Finally, then, you can ask,

is my covariance significant?

And I have to admit

that this is a difficult question to answer.

In general, values close to zero

do indicate little relationship.

And also, large positive or negative values

can be significant.

So look at the covariance

in relation to the means of each data set.

If you have a positive covariance of 500 and a mean of 100,

then the covariance is five times greater than the mean,

and that might be significant.

But that kind of analysis does come down

to individual interpretation.

In practice, what most analysts do

is convert covariances to correlations.

But before we take that step,

I will show you how to calculate covariance

for different sets of values.