Furuya Gosei showed how to get Maxima to solve the linear regression
equations.
Let me add two comments:
1. Getting Maxima to do this calculation requires either luck or
adroitness; the first time I tried, I discovered a bug in simpsum:
(C1) sum(a+x[i],i,1,n),simpsum;
(D1) a n
(C2) sum(1+sqrt(i),i,1,n), simpsum;
(D2) n
(C3)
Maybe this bug has already been reported and fixed? (The culprit maybe in
the
function sumsum.)
2. As Maxima presents them, the formulae for the slope and the intercept
are
poorly suited for numerical evaluation. (They involve differences of
numbers
that might be close together.) To fix this, you'll need to do some
algebraic
tricks that would be far easier to do by hand than by Maxima. In the end,
it isn't worth the trouble; there are lots of software tools (a
garden-variety
spreadsheet or gnuplot are two that I have used) that will do linear
regression accurately without the hassle.
Currently, Maxima lacks the tools to build a good linear regression
function;
to do a decent job, we'd at least need a good numerical LU and SVD
functions.
It seems that there is interest in adding tools for fitting data to
curves;
for now, Maxima isn't up to the task.
Barton