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. 

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
- 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).
- 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.  ($|r|$ is closer to 0)
## 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 |