Maxima Function
lsquares_residual_mse (D, x, e, a)
Returns the residual mean square error (MSE) for the equation e with specified parameters a and data D.
The residual MSE is defined as:
n ==== \ 2 > (lhs(e ) - rhs(e )) / i i ==== i = 1 -------------------------- n
where e[i]
is the equation e
evaluated with the variables in x assigned values from the i
-th datum, D[i]
,
and assigning any remaining free variables from a.
load(lsquares)
loads this function.
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) a : lsquares_estimates (M, [z, x, y], (z + D)^2 = A*x + B*y + C, [A, B, C, D]); 59 27 10921 107 (%o3) [[A = - --, B = - --, C = -----, D = - ---]] 16 16 1024 32 (%i4) lsquares_residual_mse (M, [z, x, y], (z + D)^2 = A*x + B*y + C, first (a)); 169 (%o4) ---- 2560