All language subtitles for 02 - Calculate covariance between two columns of data

- [Instructor] When you analyze data,

it's often important to see how two sets of value

vary in relation to one another.

For example, if people drive to get to your store,

you might be interested in knowing if the distance

they drive is related to how much they spend.

In this movie, I will show you how

to look at the relationship between two sets of values

by calculating covariance.

My sample file is 05_02_SingleCovariance.

And you can find it in the Chapter05 folder

of the Exercise Files collection.

I'll show you two different ways to calculate covariance.

The first is the long way.

So I will implement the formula that you see here

in this graphic as part of the worksheet.

And then once you understand what's going on,

I will show you how to use a built-in function

to perform the same calculation.

Rather than give an overview,

I will go ahead and start implementing the formula

that you see on the right in cell C2.

So this will be for our first pair of values.

So in C2, I will type an equal sign.

And the first thing I want to do is subtract the average

of the values in column one

from the specific value in cell A2.

So I'll type a left parentheses, A2,

minus, and then we want to find the average or mean

of the values in column one.

So that's AVERAGE.

And the range is A2 to A11.

And I don't want that reference to change.

I always want to refer to that set of values

for the average.

So I'll press F4 and I'll go back to A2.

Press F4 to make that an absolute reference.

So I have my range of values,

and I can type two right parentheses

to close out that part of the calculation.

Then I'll type in asterisk for multiplication,

and we'll do the same thing for the values in column two.

So I'll go a little faster.

We're going to multiply that by, left parentheses, B2

minus the average of the values in B2.

And again, that will be an absolute reference.

Colon B11.

And F4 again on the PC.

On Mac, its command + T.

Then two right parentheses, and I will press enter

to create our calculation.

And I have a covariance of 4.68.

And it is a small value because we're working

with small values in columns A and B.

Now I want to copy this formula down.

So it covers every row of values going down

to row 11 in the worksheet.

So I will click cell C2.

Double-click the fill handle at the bottom-right corner.

I know my mouse pointer is in the right place

when it changes to a black cross.

So I double-clicked,

and there I have covariances for each pair of values.

Now, I want to add all of that up,

so I will click in cell C12.

Type an equal sign.

And then, I'll do SUM, and that will be C2 to C11.

And I want to divide that by the number of pairs,

and I'll type in a forward slash for division,

10 'cause that's the number I have, and enter.

And I have an overall covariance of 0.48.

So that is the mechanics of how the calculation is done.

Now, I'll show you how to do it with a built-in function.

So I'll click in cell E3.

Type an equal sign.

And the function that we'll use is COVARIANCE.P.

COVARIANCE.P returns the covariance of a population.

And a population calculation assumes

that you have every possible value,

and you're working with them as part of the calculation.

And then you need to enter in the two arrays of value.

So I have A2 through A11, then a comma,

and B2 through B11.

Then a right parenthesis and enter.

And you see that once again,

we get the value of negative 0.48.

So this value is very close to zero.

And even though we're working with small numbers,

that indicates that there probably

isn't a very strong relationship

between these two sets of values.

I'll go back up to E3 and double-click.

And you might have noticed that when I was entering

in the formula, we had two options

for calculating covariance.

COVARIANCE.P, which is what I demonstrated here,

and COVARIANCE.S.

S assumes that you have a sample of your data.

So I will highlight that.

Press tab, and the function has been changed

in the formula.

I'll press enter.

And you can see that the value is slightly larger,

or at least farther away from zero

than the previous calculation.

And that's because we are dividing by n minus one

instead of just n.

so it's a slightly more conservative way

of doing the same calculation.