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education/statistics/Correlation and Regression.md
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@ -106,6 +106,10 @@ $$ y = mx + b $$
Where $y$ is the predicted value, $m$ is the slope, $x$ is the given value and the $b$ is the intercept. Where $y$ is the predicted value, $m$ is the slope, $x$ is the given value and the $b$ is the intercept.
$$ slope = \frac{r * \sigma_y}{\sigma_x} $$ $$ slope = \frac{r * \sigma_y}{\sigma_x} $$
#### Residual plots
A plot of the differences from the line. Makes it easier to see if the data is football shaped.
If a residual plot has a strong pattern, it may not be suitable for making predictions.
### 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.