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education/statistics/Correlation and Regression.md
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@ -73,5 +73,8 @@ https://www.thoughtco.com/how-to-calculate-the-correlation-coefficient-3126228
- The $\sigma$ line will always always have a slope of: - The $\sigma$ line will always always have a slope of:
$$\pm \frac{\sigma_y}{\sigma_x}$$ $$\pm \frac{\sigma_y}{\sigma_x}$$
- The SD line always passes through the averages for each axis. - 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 - It'll go through the middle of the "football"
- $(ave_x, ave_y)$ is on the line
- Visually looks like a line of best fit
- Someone who is *exactly on* the SD line is the same number of SDs above or below the average in the y axis as they are in the x axis.
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. 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.