A simple linear regression

A simple linear regression uses the following notation:

• \(y\) is the outcome/dependent variable,
• \(x\) is the explanatory/independent variable,
• \(\beta\) is the slope, also called a coefficient,
• \(\beta_0\) is the y-intercept, and
• \(\epsilon\) is the error term that captures our uncertainty over the estimated values.

The equation can be expressed as:

\[\begin{align} y &= \beta x + \beta_0 + \epsilon. \end{align}\]

This is similar to a standard linear equation, with new notation (i.e. \(\beta_0\) instead of \(c\) or \(b\) for the y-intercept/constant).

Note that there are many nonlinear regression functions that are more complex than a straight line in one dimension. A slightly more complex function, called multiple linear regression, will be covered in the second part of this document.