notes/education/statistics/Correlation and Regression.md

(Chapter 8, STAT 1040)

# Correlation
## 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. 
### Association
- Positive association is demonstrated when the dots are trend upward as $x$ increases. 
- Negative association is demonstrated when the the dots trend downward as $x$ increases.
- Strong association is demonstrated when dots are clustered tightly together along a line.
- Weak association is demonstrated when dots are not clustered tightly. 
## 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.

# Terminology
| Term | Definition |
| -- | -- |
| $r$ | Correlation Coefficient |
| Linear Correlation | Measures the strength of a line |