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education/statistics/Correlation and Regression.md
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# Correlation # Correlation
## Scatter Diagrams ## Scatter Diagrams
A scatter diagram or scatter plot shows the relationship between two variables. One variable is on the X axis, the other on the Y axis. A scatter diagram or scatter plot shows the relationship between two variables. One variable is on the X axis, the other on the Y axis.
If a scatter diagram is football shaped, it can be summarized using the 5-number summary:
| Variable | Description |
| -- | -- |
| $ave_x$ | |
| $SD_x$| |
| $ave_y$ |
| $SD_y$ | |
| $r$ | |
### Association ### Association
- Positive association is demonstrated when the dots are trend upward as $x$ increases. - 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. - Negative association is demonstrated when the the dots trend downward as $x$ increases ($r$ is negative).
- Strong association is demonstrated when dots are clustered tightly together along a line. - Strong association is demonstrated when dots are clustered tightly together along a line ($|r|$ is closer to 1).
- Weak association is demonstrated when dots are not clustered tightly. - Weak association is demonstrated when dots are not clustered tightly. ($|r|$ is closer to 0)
## 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.