As the weather is hotter, more people consume ice cream and more people swim in the ocean, making them susceptible to shark attacks. In this example, it is hot weather that is a common factor. This example demonstrates a common mistake that people make: assuming causation when they see correlation. They are triggered by a third factor: summer. For example, if ice cream sales at the beach are highly correlated with the number of shark attacks, it does not imply that increased ice cream sales cause increased shark attacks. It is possible that an unknown third variable C is causing both A and B to change. If variable A is highly correlated with variable B, it does not necessarily mean A causes B or vice versa. There are clear relationships but they are not linear and therefore cannot be determined with Pearson’s correlation coefficient. Notice the scatter plots below with a correlation equal to 0. It is possible that two variables have a perfect non-linear relationship when the correlation coefficient is low. Pearson’s correlation coefficient is only sensitive to the linear dependence between two variables. At 0.4 and −0.4, it looks like the scattering of data points is leaning to one direction or the other, but it is more difficult to see a relationship because of all the noise.At 0.8 and −0.8, notice how you can see a directional relationship, but there is some noise around where a line would be.At 0 the data points are completely random.Notice that at −1 and 1 the points form a perfectly straight line. This Figure demonstrates the relationships between variables as the Pearson r value ranges from 1 to 0 and to −1. The closer the correlation is to 0, the weaker the relationship. When the correlation is weak, the data points are spread apart more (loose). The closer r is to −1 or 1, the stronger the relationship. When the correlation is strong, the data points on a scatter plot will be close together (tight). If |r| = 1, there is a perfect linear correlation.If |r| > 0.5, there is a strong linear correlation.If |r| ≤ 0.5, there is a weak linear correlation.The absolute value of r describes the strength of the relationship: If r 0, there is a positive linear correlation.The sign of r indicates the direction of the relationship:.If r = 0, there is no linear relationship between the variables.It measures the linear relationship between two variables.Ĭorrelation coefficients range from −1 to 1. Of the different metrics to measure correlation, Pearson’s correlation coefficient is the most popular. What is Correlation?Ĭorrelation is a statistical technique that describes whether and how strongly two or more variables are related.Ĭorrelation analysis helps to understand the direction and degree of association between variables, and it suggests whether one variable can be used to predict another. Pearson’s correlation coefficient is also called Pearson’s r or coefficient of correlation and Pearson’s product moment correlation coefficient (r), where r is a statistic measuring the linear relationship between two variables.
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