Model fitting by least squares |

An important concept is that when energy is minimum,
the residual is orthogonal to the fitting functions.
The fitting functions are the column vectors
, , and .
Let us verify only that the dot product
vanishes;
to do so, we show
that those two vectors are orthogonal.
Energy minimum is found by:

The basic least-squares equations are often called
the ``normal'' equations.
The word ``normal'' means perpendicular.
We can rewrite equation
(39)
to emphasize the perpendicularity.
Bring both terms to the right,
and recall the definition of the residual
from equation (23):

Equation (44) says that the

Model fitting by least squares |

2014-12-01