### 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*