Original subtitles

Instructor: Correlation adjusts covariance

so that the relationship between

the two variables becomes easy

and intuitive to interpret.

The formulas

for the correlation coefficient are the covariance divided

by the product of the standard deviations

of the two variables.

This is either sample or population,

depending on the data you are working with.

We already have the standard deviations

of the two data sets.

Now, we'll use the formula

in order to find the sample correlation coefficient.

Mathematically,

there is no way to obtain a correlation value greater

than one or a less than minus one.

Remember, the coefficient of variation we talked

about a couple of lessons ago,

well, this concept is similar.

We manipulated the strange covariance value

in order to get something intuitive.

Let's examine it for a bit.

We got a sample correlation coefficient of 0.87,

so there is a strong relationship between the two values.

The correlation of one, also known

as perfect positive correlation,

means that the entire variability

of one variable is explained by the other variable.

However, logically we know that size determines the price.

On average, the bigger house you build,

the more expensive it will be.

This relationship goes only this way.

Once a house is built,

if for some reason it becomes more expensive,

its size doesn't increase,

although there is a positive correlation.

Okay, a correlation of zero between two variables means

that they are absolutely independent from each other.

We would expect a correlation of zero

between the price of coffee in Brazil

and the price of houses in London, right?

The two variables don't have anything in common.

Finally, we can have a negative correlation coefficient.

It can be perfect negative correlation of minus one

or much more likely an imperfect negative correlation

of a value between minus one and zero.

Think of the following businesses.

A company producing ice cream

and a company selling umbrellas.

Ice cream tends to be sold more when the weather is very

good and people buy umbrellas when it's rainy.

Obviously there is a negative correlation between the two,

and hence, when one of the companies makes more money,

the other won't.

All right, before we continue, we must note

that the correlation between two variables X

and Y is the same as the correlation between Y and X.

The formula is completely symmetrical with respect

to both variables.

Therefore, the correlation of price and size is the same

as the one of size and price.

This leads us to causality.

It is very important for any analyst or researcher

to understand the direction of causal relationships.

In the housing business, size causes the price,

and not vice versa.

We will explore this topic in much more detail

in the regression analysis section later on.

For now, it is only needed

that you realize that correlation does not imply causation.

Okay, very good.

With this example,

we conclude the section on descriptive statistics.

In the next lesson,

you will see a real life database example

that applies all the knowledge you acquired in this section.

You definitely don't wanna miss it.