Regression coefficients:

$ \qquad a = \dfrac{\sum y - b \cdot \sum x}{n} $

$ \qquad b = \dfrac{n \cdot \sum xy - \sum x \cdot \sum y} {n \cdot \sum x^{2} - (\sum x)^2 } $

Auxiliary variables h1 and h2:

$ \qquad h_{1} = b \cdot \left( \sum xy - \dfrac{1}{n} \sum x \cdot \sum y \right) $

$ \qquad h_{2} = \sum y^{2} - \dfrac{1}{n} \sum y \cdot \sum y $

Coefficient of determination and correlation coefficient:

$ \qquad r^{2} = \dfrac{h_{1}}{h_{2}} \qquad \qquad r = \sqrt{r^{2}} $

Variance and standard deviation:

$ \qquad s^{2} = \dfrac{h_{2} - h_{1}}{n - 2} \qquad s = \sqrt{s^{2}} $

Abbreviated summation terms:

$ \qquad \displaystyle \Sigma x := \sum_{i=1}^{n} x_i $

$ \qquad \displaystyle \Sigma y := \sum_{i=1}^{n} y_i $

$ \qquad \displaystyle \Sigma xy := \sum_{i=1}^{n} x_i \cdot y_i$

$ \qquad \displaystyle \Sigma x^2 := \sum_{i=1}^{n} x_i^2$

$ \qquad \displaystyle \Sigma y^2 := \sum_{i=1}^{n} y_i^2$