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education/statistics/Correlation and Regression.md
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@ -71,4 +71,7 @@ https://www.thoughtco.com/how-to-calculate-the-correlation-coefficient-3126228
- Just because a relationship exists between $x$ and $y$ *does not* mean that changes in $x$ *cause* changes in $y$.
- If the graph is given to you already set up, you already know the response and explanatory variables.
- The $\sigma$ line will always always have a slope of:
$$\frac{\sigma_x}{\sigma_y}$$
$$\pm \frac{\sigma_y}{\sigma_x}$$
- The SD line always passes through the averages for each axis.
- Someone who is *exactly on* the SD line is the same number of SDs above or below
Given a scatter diagram where the average of each set lies on the point $(75, 70)$, with a $\sigma_x$ of 10 and a $\sigma_y$ of 12, you can graph the SD line by going up $\sigma_y$ and right $\sigma_x$, then connecting that point (in this example, $(85, 82)$) with the mean points.