  In this review article we consider linear regression analysis from a
geometric perspective, looking at standard methods and outputs in terms of the
lengths of the relevant vectors and the angles between these vectors. We show
that standard regression output can be written in terms of the lengths and
angles between the various input vectors, such that this geometric information
is sufficient in linear regression problems. This allows us to obtain a
standard formula for multiple correlation and give a geometric interpretation
to this. We examine how multicollinearity affects the total explanatory power
of the data, and we examine a counter-intuitive phenomena called "enhancement"
where the total information from the explanatory vectors is greater than the
sum of the marginal parts.
