Correlaçoes matematica

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Values of the Pearson Correlation
Erin Maloney
This work is produced by The Connexions Project and licensed under the Creative Commons Attribution License

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The Pearson product-moment correlation coecient is a measure of the strength of the linear relationIt is referred to as Pearson's correlation or simply as the correlation coecient. If the relationship between the variables is not linear, then the correlation coecient does not adequately represent the strength of the relationship between the variables. The symbol for Pearson's correlation is "ρ" when it is measured in the population and "r" when it is measured in a sample. Because we will be dealing almost exclusively with samples, we will use r to to represent Pearson's correlation unless otherwise noted. Pearson's r can range from −1 to 1. An r of −1 indicates a perfect negative linear relationship between variables, an r of 0 indicates no linear relationship between variables, and an r of 1 indicates a perfect positive relationship between variables. Figure 1 shows a scatter plot for which r = 1. ship between two variables.

Figure 1:

A perfect linear relationship,

r = 1.

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Figure 2 shows a perfect negative linear relationship. Notice that as X increases, Y decreases.

Figure 2:

A perfect negative linear relationship,

r = −1.

Figure 3 shows a scatter plot for which r = 0. Notice that there is no relationship between X and Y .

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Figure 3:

There is no linear relationship between the variables,

r = 0.

With real data, you would not expect to get values of r of exactly −1, 0, or 1. The data for spousal ages shown in Figure 4 and described in the introductory section has an r of 0.97.
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