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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


Coefficient Of Correlation Correlation Coefficient Strength Direction Linear Association Independent Variable Dependent Variable Linear Relationship Value Of R Size Of Correlation Scatterplot Positive Correlation Negative Correlation Best-fit Line

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