From 139a665a12cd6781bdaf61b83fa228f09145daae Mon Sep 17 00:00:00 2001 From: zleyyij Date: Fri, 15 Dec 2023 13:14:23 -0700 Subject: [PATCH] vault backup: 2023-12-15 13:14:23 --- education/statistics/Correlation and Regression.md | 6 ++++-- 1 file changed, 4 insertions(+), 2 deletions(-) diff --git a/education/statistics/Correlation and Regression.md b/education/statistics/Correlation and Regression.md index e35e119..19cc306 100644 --- a/education/statistics/Correlation and Regression.md +++ b/education/statistics/Correlation and Regression.md @@ -76,11 +76,13 @@ $$\pm \frac{\sigma_y}{\sigma_x}$$ - It'll go through the middle of the "football" - $(ave_x, ave_y)$ is on the line - 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. 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) - 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 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. \ No newline at end of file