Maxima Function
lsquares_estimates_exact (MSE, a)
Estimate parameters a to minimize the mean square error MSE,
by constructing a system of equations and attempting to solve them symbolically via solve
.
The mean square error is an expression in the parameters a,
such as that returned by lsquares_mse
.
The return value is a list of lists of equations of the form [a = ..., b = ..., c = ...]
.
The return value may contain zero, one, or two or more elements.
If two or more elements are returned,
each represents a distinct, equivalent minimum of the mean square error.
See also
lsquares_estimates
,
lsquares_estimates_approximate
,
lsquares_mse
,
lsquares_residuals
,
and lsquares_residual_mse
.
Example:
(%i1) load (lsquares)$ (%i2) M : matrix ([1, 1, 1], [3/2, 1, 2], [9/4, 2, 1], [3, 2, 2], [2, 2, 1]); [ 1 1 1 ] [ ] [ 3 ] [ - 1 2 ] [ 2 ] [ ] (%o2) [ 9 ] [ - 2 1 ] [ 4 ] [ ] [ 3 2 2 ] [ ] [ 2 2 1 ] (%i3) mse : lsquares_mse (M, [z, x, y], (z + D)^2 = A*x + B*y + C); 5 ==== \ 2 2 > ((D + M ) - C - M B - M A) / i, 1 i, 3 i, 2 ==== i = 1 (%o3) --------------------------------------------- 5 (%i4) lsquares_estimates_exact (mse, [A, B, C, D]); 59 27 10921 107 (%o4) [[A = - --, B = - --, C = -----, D = - ---]] 16 16 1024 32