Consider fitting a line
so that at the points 
the line is close to the corresponding values 
in sense that we minimize the sum of
squared deviations
over the values of 
.
In matrix notation, we let y be the vector whose elements are the 
and X be a matrix whose columns contain K explanatory
variable vectors with elements 
in the 
column. The method of OLS computes a coefficient vector 
so
that the fitted vector 
minimizes the sum of squared elements
from the deviation vector 
. If the rank of X equals K,
then the solution can be written
