Overview
On this page, we discuss the concepts of Correlation and Linear Regression of two quantitative random variables.
Basic learning objectives
These are the tasks you should be able to perform with reasonable fluency when you arrive at your next class meeting. Important new vocabulary words are indicated in italics.
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Understand the concept of correlation and the correlation coefficient \(r\) (also called Pearson’s correlation coefficient).
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Understand the concept of a linear regression line, and how its slope is in fact determined by the correlation coefficient \(R\).
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Understand that Correlation does not imply Causation!
Advanced learning objectives
In addition to mastering the basic objectives, here are the tasks you should be able to perform after class, with practice:
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Understand that the slope of the linear least-squares regression line is essentially determined by the correlation coefficient \(r\). In fact, if \(y=mx+b\), then \(m=r\cdot \frac{s_y}{s_x}\) and \(b=\overline{y}-m\cdot \overline{x}\).
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Understand that the coefficient of determination \(R^2\), which is a measure of “quality” of the linear regression, is in fact equal to \(r^2\), i.e. the square of the correlation coefficient.
To prepare for class
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Watch the following video (3min, by 3-Minute Data Science) which introduces the concepts of the correlation coefficient \(r\), and the coefficient of determination \(r^2\):
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Watch the following video (4min, by 3-Minute Data Science) which introduces the concept of linear regression:
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Watch the following video (2min, by Cody Baldwin) which explains the difference between Correlation and Causation:
After class
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Watch the following video (7min, by jbstatistics) which explains in more detail how the least-squares regression line is defined:
