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education/statistics/Correlation and Regression.md
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@ -103,9 +103,10 @@ $$ \hat{y} = \frac{x-\bar{x}}{\sigma_x} * r * \sigma_y + \bar{y} $$
- In a test-retest situation, people with low scores tend to improve, and people with high scores tend to do worse. This means that individuals score closer to the average as they retest.
- The regression *fallacy* is contributing this to something other than chance error.
### R.M.S Error for Regression
The distance of an individual point from the regression line.
The distance of an individual point from the regression line. This only applies for a football shaped scatter diagram.
- If a point is below the line, the error is negative.
- If a point is above the line, the error is positive.
- "Give or take"
- `residual = observed - predicted` for a given $x$ value
- The r.m.s error is the r.m.s size of the errors
$$ \sqrt{1-r^2}(\sigma_y) $$