|
Fitting (multiple regression) Estimates
the parameters for fitting to a "general" model. |
|
|
| [X(nx ×
nvar)]T |
|
Independent variable(s) values.
Transposed
X matrix (see next entry); or x vector. • |
| Transpose ? |
|
Transposing the X matrix. • |
| yT |
|
Dependent variable values. • |
| Model to fit |
|
Univariate polynomial or (below) partic. function. • |
| Parameters |
|
Initial guess for parameters. • |
| Scale factors |
|
Scale factors for parameters. • |
| Criterion |
∞ (minimax)
1
2 (min. sq.)
3 |
Criterion (power of
|ycalc−y|). |
| tol, maxit, mon |
(tol = 0 ⇒ εmach) |
Tolerance, max. num. of iterations, monitoring. |
| Graph abscissa |
(−1, no sort; 0, by y;
j, by xj, 1 ≤ j ≤ nvar) |
Graph abscissa to sort by. |
| Graph |
|
Plots the initial or final graph. • |
| Show values ? |
|
Shows the graph coordinates. |
Estimates the parameters
in the underlying (fixed) model, from the given parameter values
(initial guesses). The model is: either a particular function mentioned below
for the base data; or, in order to make it as general as (in this context)
possible, a polynomial,
y = Σi pixi−1,
i = 1..n, with n the number of (given) parameters.
(NB: for a polynomial, only univariate, "x1",
data are used, others ignored.)
The order of the polynomial is deduced from the number of given parameters,
e.g., a parabola if three parameters are given. The Nelder-Mead algorithm
is used to optimize fit.
A plot is shown for the experimental
and calculated points.
The base data are from (sheet) 'particular' in
generalfitting.xlsx,
the data coming from y =
p1x1 +
p2x2 +
p3x3 cos(x4), giving
P ≅ (4, 1, 6).
In (sheet) 'polynomial', are data (from electrical conductivity)
for the adjustment of a polynomial. |
| References: |
Plate: GeneralFitting |
• Herz, Richard, Reactor Lab
(UC San Diego) — Google fitting equations to data.
• Wikipedia: Matrix (mathematics) (notation)
• 1735-02-28: Vandermonde, Alexandre-Théophile
(1796-01-01) |
