Calculating

Regression Lines


In statistics we write the equation for a line as 

\[y'=\alpha+bx\]

Example:

line example

Formula for the Regression Line \(y'=\alpha+bx\):

\[\alpha=\frac{\left(\sum y\right)\left(\sum x^2\right)-\left(\sum x\right)\left(\sum xy\right)}{n\left(\sum x^2\right)-\left(\sum x\right)^2}\]

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

where \(\alpha\) is the \(y'\) intercept and \(b\) is the slope of the line.