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education/statistics/Correlation and Regression.md
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@ -113,9 +113,14 @@ $$ \sqrt{1-r^2}(\sigma_y) $$
- On a least squared regression line, the 1 r.m.s error away will contain $2\sigma$ of the data, and it should loosely mirror a normal curve. - On a least squared regression line, the 1 r.m.s error away will contain $2\sigma$ of the data, and it should loosely mirror a normal curve.
- To approximate the R.M.S error for a scatter diagram, take a high value and a low value for a given $x$ coordinate, and divide by 4, because r.m.s error is within $2\sigma$ of either side of the line. - To approximate the R.M.S error for a scatter diagram, take a high value and a low value for a given $x$ coordinate, and divide by 4, because r.m.s error is within $2\sigma$ of either side of the line.
- 68% = $2\sigma$, 95% = $4\sigma$ - 68% = $2\sigma$, 95% = $4\sigma$
- RMS can help determine which observations are outliers. Typically if a value is more than *2 r.m.s* away from the prediction estimate, it is considered to be an outlier. - RMS can help determine which observations are outliers. Typically if a value is more than *2 r.m.s* away from the prediction estimate, it is considered to be an outlier
- Heteroscedastic scatter diagrams should not be used to make a prediction
- homoscedastic scatter diagrams can be used to make predictions, because they follow
--- ---
# Terminology # Terminology
| Term | Definition | | Term | Definition | |
| -- | -- | | ---- | ---- | ---- |
| $\hat{y}$ | The predicted value | | $\hat{y}$ | The predicted value | |
| Homoscedastic | The scatter diagram will look the same above and below the LSRL | |
| Heteroscedastic | Will have more variability on one side of the regression line | |