All language subtitles for 04 - Visualize what correlation means

- [Instructor] When you analyze business data,

you will often want to know

whether two sets of values are related.

One way to do that is to calculate correlation.

Previously, I showed you how to calculate core variance.

And as a reminder here is that formula.

The idea is that you multiply the differences

from the mean for each value pair,

so we have two columns of data

and we have an X and Y value that are matched up,

and you find the sum of that product.

You then divide that total by the number of data pairs.

Correlation is related

and here is the formula.

So you'll see that the top term is the same

but is divided by the term shown.

And it takes a while to explain,

so I will just ask you to accept the term as given

and use it in your calculations.

So the next question is

how do you interpret your correlation values?

You will get a value between 1 and - 1

data that is completely uncorrelated returns

a correlation value of 0.

In other words, the two sets of values

have nothing to do with each other.

Data that is positively correlated

will be between 0 and 1.

And if you have 1, that means

the data sets move and lockstep.

In other words, they move the same way

all the time, every time.

And if you have data that is negatively correlated

between minus 1 and 0

then the data moves in opposite directions.

So when one set of values goes up, the other one goes down.

And of course it's possible to have values

between 0 and 1 or 0 and -1,

and that means the correlation isn't quite as strong.

So let's take a look at a visual example

of data that is not correlated.

Here, I have five starting values

and those are 1, 2, 3, 4, and 5.

You can see those on the horizontal axis.

And 1 produces two results, 3 and -3.

And the same for the other values along the horizontal axis.

What this means is that the starting value

tells you nothing about the value that follows it,

the X says nothing about the Y,

so the correlation is 0.

If you have data with a perfect positive correlation

in other words, a correlation of 1,

then you'll see that it goes up

and the values exactly match.

1 gives you 1, 2 gives you 2, and so on.

It doesn't have to be this exact pattern

but you can see a visual example

of what a correlation of 1 looks like.

And data with a perfect negative correlation

goes in the opposite direction.

The next question you have to ask, of course is,

is my correlation significant?

And that depends on several factors.

You have the number of measurements

whether a value can be positive or negative.

And by that, I mean if you're looking

for a positive or negative value only,

in other words, one side,

then that's called a one-tailed test.

If your difference can be either positive or negative

then you have a two-tailed test.

And then you look up the correlation value

in a table, which you can find in statistics,

textbooks are online,

and see what that looks like.

And here is an example

of a two-tailed correlation lookup table.

And the leftmost column gives you the number

of samples that you have,

and then to the right you have different confidence levels.

And you subtract that confidence level from 1

to give you the value that you want.

So, for example, in the column next to N, 0.1

you subtract that from 1 for the 90% confidence interval

or a confidence level.

And then to the right of that, you have 0.05,

so that's 95%, 98%,

and the other two values you see there.

So if you have 10 values and you calculate the correlation

and you want to look at the 90% level

then you would need to have a correlation value

of at least 0.55,

and that's the value at the intersection

of 10 and 0.1

to have a 90% certainty or 90% confidence level

that the correlation is valid.

And the various other combinations are available here.

So again, there are a lot of moving parts to correlation

but it is a very useful way to look at your data.