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education/statistics/Correlation and Regression.md
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@ -76,11 +76,13 @@ $$\pm \frac{\sigma_y}{\sigma_x}$$
- It'll go through the middle of the "football" - It'll go through the middle of the "football"
- $(ave_x, ave_y)$ is on the line - $(ave_x, ave_y)$ is on the line
- Visually looks like a line of best fit - Visually looks like a line of best fit
- The SD line is not used for prediction because it overpredicts - The SD line is not used for prediction because it over-predicts
- 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. - 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.
### The Regression Line/Least Squared Regression Line (LSRL) ### The Regression Line/Least Squared Regression Line (LSRL)
- This line has a more moderate slope than the SD line. it does not go through the peaks of the "football" - This line has a more moderate slope than the SD line. it does not go through the peaks of the "football"
- The regression line is *used to predict* the y variable when the x variable is given - The regression line is *used to predict* the y variable when the x variable is given
- The rgre - The regression line also goes through the point of averages
$$ slope = r(\frac{\sigma_y}{\sigma_x}) $$
- You can find the regression line by multiplying $\sigma_y$ by $r$, for the rise, then using $\sigma_x$ for the run from the point of averages.