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education/statistics/Correlation and Regression.md
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@ -83,12 +83,18 @@ 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 also goes through the point of averages - The regression line goes through the point of averages
$$ slope = r(\frac{\sigma_y}{\sigma_x}) $$ $$ slope = r(\frac{\sigma_y}{\sigma_x}) $$
- 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.
The below formula can be used to predict a y value given a 5 number summary of a set. The below formula can be used to predict a y value given a 5 number summary of a set.
$$ \hat{y} = \frac{x-\bar{x}}{\sigma_x} * r * \sigma_y + \bar{y} $$ $$ \hat{y} = \frac{x-\bar{x}}{\sigma_x} * r * \sigma_y + \bar{y} $$
1. Find $z_x$
2. Multiply $z_x$ by $r$
3. Multiply that by $\sigma_y$
4. Add the average of $y$
# Terminology # Terminology
| Term | Definition | | Term | Definition |
| -- | -- | | -- | -- |