Adding extra variables

A simple linear model for a single explanatory variable,

y  =  b0 + b1 x

can be easily extended to describe the effect of a second explanatory variable, Z, with an extra linear term,

y  =  b0 + b1 x + b2 z

and so on with more explanatory variables,

y  =  b0 + b1 x + b2 z + b3 w + ...

This type of model is called a multiple regression model.

Coefficients

Despite our use of the same symbols (b0, b1, ...) for all three models above, their 'best' values are often different for the different models. An example will be given in the next page.