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.

Figure 1. |
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We can use this data to calculate Pearson's r

Pearson’s r |
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Pearson’s r measures the strength of the linear relationship between two variables. Pearson’s r is always between -1 and 1. |

Here is a perfect positive relationship. r is equal to 1.0:

Figure 2. |
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Here is a perfect negative relationship. r is equal to -1.0:

Figure 3. |
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Here is an example of data that has no relationship. r is somewhere close to 0.0:

Figure 4. |
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Pearson's r is calculated with the following equation:

Figure 5. |
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Plugging in the values from our original example with ages and yearly incomes, we can calculate the following r:

Figure 6. |
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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.