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education/statistics/Correlation and Regression.md
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@ -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. 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 ### Association
- Positive association is demonstrated when the dots are trend upward as $x$ increases ($r$ is positive). - 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). - 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
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. 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 # Terminology
| Term | Definition | | Term | Definition |
| -- | -- | | -- | -- |