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# Facts About the Correlation Coefficient for Linear Regression

Module by: Kathy Chu. E-mail the author

Summary: This module provides an overview of Facts About the Correlation Coefficient for Linear Regression as a part of Collaborative Statistics collection (col10522) by Barbara Illowsky and Susan Dean.

• A positive rr means that when xx increases, yy increases and when xx decreases, yy decreases (positive correlation).
• A negative rr means that when xx increases, yy decreases and when xx decreases, yy increases (negative correlation).
• An rr of zero means there is absolutely no linear relationship between xx and yy (no correlation).
• High correlation does not suggest that xx causes yy or yy causes xx. We say "correlation does not imply causation." For example, every person who learned math in the 17th century is dead. However, learning math does not necessarily cause death!

If r=-1r=-1 or r=+1r=+1, then all the data points lie exactly on a straight line.

If the linear correlation is strong, then the line can be used to predict a yy value.

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#### Definition of a lens

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##### What is in a lens?

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