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113 Math

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113.034 Statistics - Coefficient of determination and Squared error

# Coefficient of determination and Squared error

`r^2`

= **coefficient of determination**

- Always between zero and one: `0 >= r^2 <= 1`

- `r^2`

is literally just `r`

squared, it's that easy

- $$r^2 = 1 - \frac{SE_{regression}}{SE_\bar{y}}$$

- Reads: r squared = 1 minus the squared error of the regression line divided by the squared error of the average of all y values

- If **squared error** is small, it means that the residuals of all points along the regression line are small and they fit the line pretty well

- If **squared error** is big, it means that the residuals of the points along the regression line are big and they don't fit the line very well

- So, `r^2`

close to 1 is a good fit and `r^2`

close to zero is a bad fit

##### Tags:

- statistics