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education/statistics/Correlation and Regression.md
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@ -97,6 +97,8 @@ $$ \hat{y} = \frac{x-\bar{x}}{\sigma_x} * r * \sigma_y + \bar{y} $$
4. Add the average of $y$ 4. Add the average of $y$
- For a positive association, for every $\sigma_x$ above average we are in $x$, the line predicts $y$ to be $\sigma_y$ standard deviations above y.x - For a positive association, for every $\sigma_x$ above average we are in $x$, the line predicts $y$ to be $\sigma_y$ standard deviations above y.x
- There are two separate regression lines, one for predicting $y$ from $x$, and one for predicting $x$ from $y$
- Do not extrapolate outside of the graph
### The Regression Effect ### The Regression Effect
- 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. - 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. - The regression *fallacy* is contributing this to something other than chance error.