33 lines
2.0 KiB
Markdown
33 lines
2.0 KiB
Markdown
(Chapter 8, STAT 1040)
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# Correlation
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## Scatter Diagrams
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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.
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If a scatter diagram is football shaped, it can be summarized using the 5-number summary:
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| Variable | Description |
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| -- | -- |
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| $\mu_x$ | The average of the set graphed along the X axis |
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| $\sigma_x$| The standard deviation of set graphed along the X axis |
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| $\mu_y$ | The average of the set graphed along the Y axis |
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| $\sigma_y$ | The standard deviation of the set graphed along the Y axis |
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| $r$ | The correlation coefficient, or how closely clustered the datapoints are in a line |
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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.
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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 $\mu$.
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### Association
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- Positive association is demonstrated when the dots are trend upward as $x$ increases ($r$ is positive).
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- Negative association is demonstrated when the the dots trend downward as $x$ increases ($r$ is negative).
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- Strong association is demonstrated when dots are clustered tightly together along a line ($|r|$ is closer to 1).
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- Weak association is demonstrated when dots are not clustered tightly. ($|r|$ is closer to 0)
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## Correlation
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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.
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# Terminology
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| Term | Definition |
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| -- | -- |
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| $r$ | Correlation Coefficient |
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| Linear Correlation | Measures the strength of a line |
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