12.1 Linear equations

Linear regression for two variables is based on a linear equation with one independent variable. It has the form:

where $a$ and $b$ are constant numbers.

$x$ is the independent variable, and $y$ is the dependent variable. Typically, you choose a value to substitute for the independent variable and then solve for the dependent variable.

The graph of a linear equation of the form $y=a+\text{bx}$ is a straight line . Any line that is not vertical can be described by this equation.

Linear equations of this form occur in applications of life sciences, social sciences, psychology, business, economics, physical sciences, mathematics, and other areas.