Bivariate Measures: Linear Correlation Coefficient

00:01 Correlation adjusts covariance so that the relationship between the two variables becomes easy and intuitive to interpret.

00:08 The formulas for the correlation coefficient are the covariance divided by the product of the standard deviations of the two variables.

00:16 This is either sample or population, depending on the data you are working with.

00:20 We already have the standard deviations of the two data sets.

00:24 Now we'll use the formula in order to find the sample correlation coefficient.

00:30 Mathematically, there is no way to obtain a correlation value greater than one or less than minus one. Remember the coefficient of variation we talked about a couple of lessons ago? Well, this concept is similar.

00:43 We manipulated the strange covariance value in order to get something intuitive.

00:48 Let's examine it for a bit.

00:50 We got a sample correlation coefficient of 0.87.

00:53 So there is a strong relationship between the two values.

00:57 A correlation of one also known as perfect positive correlation means that the entire variability of one variable is explained by the other variable.

01:06 However, logically, we know that size determines the price.

01:10 On average, the bigger house you build, the more expensive it will be.

01:15 This relationship goes only this way.

01:18 Once a house is built, if for some reason it becomes more expensive, its size doesn't increase, although there is a positive correlation.

01:27 Ok a correlation of zero between two variables means that they are absolutely independent from each other.

01:33 We would expect a correlation of zero between the price of coffee and Brazil and the price of houses in London.

01:39 Right. The two variables don't have anything in common.

01:44 Finally, we can have a negative correlation coefficient.

01:48 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.

01:57 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.

02:08 Obviously, there is a negative correlation between the two and hence when one of the companies makes more money, the other won't.

02:17 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.

02:26 The formula is completely symmetrical with respect to both variables.

02:30 Therefore, the correlation of price and size is the same as the one of size and price. This leads us to causality.

02:38 It is very important for any analyst or researcher to understand the direction of causal relationships in the housing business.

02:45 Size causes the price and not vice versa.

02:49 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.

03:01 Okay. Very good.

03:03 With this example, we conclude the section on descriptive statistics.

03:08 In the next lesson, you will see a real life database example that applies all the knowledge you acquired in this section.

03:15 You definitely don't want to miss it.