Equation to describe a regression line

A regression line could be drawn 'by eye' through a scatterplot, but we restrict attention to simple mathematical functions

y  =  ƒ ( x )

since they are easier and more objective to use.

Linear model

Some relationships must be described by curves, but a straight line is an adequate description of many bivariate data sets.

y  =  b0 + b1 x

The constant b0 is the intercept of the line and describes the y-value when x is zero. The constant b1 is the line's slope; it describes the change in y when x increases by one.

The predicted response at any x-value is

  =  b0 + b1 x