vault backup: 2023-12-13 14:28:19

education/statistics/Correlation and Regression.md

@@ -16,7 +16,7 @@ If a scatter diagram is football shaped, it can be summarized using the 5-number
 
 The intersection of the averages of x and y will be the center of an oval shaped scatter diagram. Draw lines $2\sigma$ (will contain ~95% of all data) from the center along each axis to generalize the shape of a scatter plot.
 
-You can approximate the mean by trying to find the upper bound and the lower bound of $2\sigma$ deviation to either side of the mean, then finding the middle of those two points to find $\mu$.
+You can approximate the mean by trying to find the upper bound and the lower bound of $2\sigma$ deviation to either side of the mean, then finding the middle of those two points to find $\mu$. You can divide the range between the two points by 4 to find $\sigma$.
 ### Association
 - Positive association is demonstrated when the dots are trend upward as $x$ increases ($r$ is positive). 
 - Negative association is demonstrated when the the dots trend downward as $x$ increases ($r$ is negative).
@@ -25,6 +25,11 @@ You can approximate the mean by trying to find the upper bound and the lower bou
 ## Correlation
 Correlation is between `-1` and `1`. Correlation near 1 means tight clustering, and correlation near 0 means loose clustering.  $r$ is -1 if the points are on a line with negative slope, $r$ is positive 1 if the points are on a line with a positive slope. As $|r|$ gets closer to 1, the line points cluster more tightly around a line.
 
+## Calculating $r$ by hand
+Put the $x$ values into $L1$, put the $y$ values into $L2$. 
+
+Convert the $x$ values to standard units. Convert the $y$ values to standard units. Multiply the standard units for each x y pair. Find the average of the values from step 3, this is $r$.
+
 # Terminology
 | Term | Definition |
 | -- | -- |