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11.2: Coefficient of Correlation

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Coefficient of Correlation

11.2: Coefficient of Correlation

The correlation coefficient, r, developed by Karl Pearson in the early 1900s, is numerical and provides a measure of strength and direction of the linear association between the independent variable x and the dependent variable y.

If you suspect a linear relationship between x and y, then r can measure how strong the linear relationship is.

What the VALUE of r tells us:

The value of r is always between –1 and +1: –1 ≤ r ≤ 1.

The size of the correlation r indicates the strength of the linear relationship between x and y. Values of r close to –1 or to +1 indicate a stronger linear relationship between x and y.

If r = 0, there is likely no linear correlation. It is important to view the scatterplot because data that exhibit a curved or horizontal pattern may have a correlation of 0.

If r = 1, there is a perfect positive correlation. If r = –1, there is a perfect negative correlation. In both these cases, all of the original data points lie in a straight line. Of course, in the real world, this will not generally happen.

What the SIGN of r tells us

A positive value of r means that when x increases, y tends to increase, and when x decreases, y tends to decrease (positive correlation).

A negative value of r means that when x increases, y tends to decrease, and when x decreases, y tends to increase (negative correlation).

The sign of r is the same as the sign of the slope, b, of the best-fit line.

This text is adapted from Openstax, Introductory Statistics, Section 12.3, The Regression Equation

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