Common Statistical Formulas and Equations

R-Squared

$$ R^{2}=\frac{N\sum xy-\sum x \sum y}{\sqrt{\left[N\sum x^{2}-\left(\sum x\right)^{2}\right]\left[N\sum y^{2}-\left(\sum y\right)^{2}\right]}} $$

$$ F=\frac{Variance\ of\ set\ 1}{Variance \ of \ set \ 2} = \frac{\sigma _{1}^{2}}{\sigma _{2}^{2}} $$

$$ \chi ^2 = \sum{\frac{(O-E)^2}{E}} $$

$$ \mu = \frac{\sum{X_i}}{N} $$

$$ \overline{x} = \frac{\sum{x}}{n} $$

$$ \sigma ^2 = \frac{\sum{(x-\overline{x})^2}}{n} $$

$$ S=\sigma=\sqrt{\frac{\sum{(x-\overline{x})^2}}{n}} $$

$$ y=a+bx $$

Where a (or the intercept) is:

$$ a =\frac{\sum y \sum x^{2} – \sum x \sum xy} {(\sum x^{2}) – (\sum x)^{2}} $$

And b (or the slope) is:

$$ b=\frac{n\sum xy-\left(\sum x\right)\left(\sum y\right)}{n\sum x^{2}-\left(\sum x\right)^{2}} $$

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