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education/statistics/Correlation and Regression.md
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@ -87,5 +87,9 @@ Given a scatter diagram where the average of each set lies on the point $(75, 70
$$ slope = r(\frac{\sigma_y}{\sigma_x}) $$ $$ slope = r(\frac{\sigma_y}{\sigma_x}) $$
- 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.
$$ z_x = \frac{x-\bar{x}}{\sigma_x} * r * \sigma_y + \bar{y} $$ The below formula can be used to predict a y value given a 5 number summary of a set.
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. $$ \hat{y} = \frac{x-\bar{x}}{\sigma_x} * r * \sigma_y + \bar{y} $$
# Terminology
| Term | Definition |
| -- | -- |
| $\hat{y}$ | The predicted value |