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education/statistics/Correlation and Regression.md
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@ -83,7 +83,8 @@ Given a scatter diagram where the average of each set lies on the point $(75, 70
### 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 regression line goes through the point of averages - In regression, the $x$ variable is the known variable, and $y$ is the value being solved for.
- The regression line goes through the point of averages, and can be positive or negative
$$ slope = r(\frac{\sigma_y}{\sigma_x}) $$ $$ slope = r(\frac{\sigma_y}{\sigma_x}) $$
- 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. - 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.