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 Test
$ F=\frac{Variance\ of\ set\ 1}{Variance \ of \ set \ 2} = \frac{\sigma _{1}^{2}}{\sigma _{2}^{2}} $
See Variance.
Chi-Square
$ \chi ^2 = \sum{\frac{(O-E)^2}{E}} $
Population Mean
$ \mu = \frac{\sum{X_i}}{N} $
Mean
$ \overline{x} = \frac{\sum{x}}{n} $
Variance
$ \sigma ^2 = \frac{\sum{(x-\overline{x})^2}}{n} $
Standard Deviation
$ S=\sigma=\sqrt{\frac{\sum{(x-\overline{x})^2}}{n}} $
Linear Regression
$ 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}} $