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education/statistics/Correlation and Regression.md
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@ -86,4 +86,7 @@ Given a scatter diagram where the average of each set lies on the point $(75, 70
- 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.
$$ z_x = \frac{x-\bar{x}}{\sigma_x} * r * \sigma_y + \bar{y} $$
$$ z_x = \frac{x-\bar{x}}{\sigma_x} * r * \sigma_y + \bar{y} $$
This formula finds the $z$ score for $x$, transforms by $r$, and uses the equation $x = z * \sigma + \bar{x}$ to predict a value for one axis given another axis.