In the previous lecture on scatter plots, we made a scatter plot for some sample bivariate data and concluded that the two variables were probably related.
We can use this data to calculate Pearson's r
Pearsonís r measures the strength of the linear relationship between two variables. Pearsonís r is always between -1 and 1.
Here is a perfect positive relationship. r is equal to 1.0:
Here is a perfect negative relationship. r is equal to -1.0:
Here is an example of data that has no relationship. r is somewhere close to 0.0:
Pearson's r is calculated with the following equation:
Plugging in the values from our original example with ages and yearly incomes, we can calculate the following r:
This r is almost 1.0, so we can conclude that x(Age) and y(Yearly Income) have a strong positive relationship. As one increases, the other tends to increase as well.