*R*^2 tells us just how approximate it is). We then saw that we could use the equation that describes this straight line to explore the relationship between the two variables in a few different ways. In particular, we could use it to predict the scores associated with new cases in the future.

Multiple regression is just the same, except instead of using a one-dimensional line to describe the data, we use an

*n*-dimensional hyperplane (lawks!). Simple linear regression placed a one-dimensional line in a two-dimensional space (these two dimensions are of course the ones represented on a graph as

*x*and

*y*). Multiple regression takes this further by placing an

*n*-dimensional hyperplane in an (

*n*+1)-dimensional space. So linear regression is just the simplest possible form of multiple regression, where

*n*= 1.

Recall that the straight-line formula we used was:

*y = ax + b*

This is saying that

*y*, the dependent variable, is reached by multiplying

*x*, the observed variable, by a certain number,

*a*, and then adding another number,

*b*.

If we want to take this further and predict

*y*from more than one independent variable, then we need a different regression coefficient for each. Let's say we want to predict y from two other variables,

*x1*and

*x2*, we would have two different coefficients,

*b1*and

*b2*. Our regression formula would therefore be:

*y = a + b1x1 + b2x2*

and would therefore describe a two-dimensional slice of three-dimensional space. (These three dimensions can still just about be plotted on a graph, but beyond this point you can no longer easily visualize what is going on.) More

*x*'s can be added to the equation - as many as we want, in fact. So you could quite easily have a situation where y is predicted from five other variables, giving this equation:

*y = a + b1x1 + b2x2 + b3x3 + b4x4 + b5x5*

As with simple regression, the computer will calculate the

*a*and

*b*values for you. However, there are various ways in which they can be added to the equation. All of these are accessed from the

**analyze > regression > linear**menu.