MATLAB Examples

# Evaluate a Surface Fit

This example shows how to work with a surface fit.

## Load Data and Fit a Polynomial Surface

surffit = fit([x,y],z,'poly23','normalize','on')
Linear model Poly23:
surffit(x,y) = p00 + p10*x + p01*y + p20*x^2 + p11*x*y + p02*y^2 + p21*x^2*y
+ p12*x*y^2 + p03*y^3
where x is normalized by mean 1982 and std 868.6
and where y is normalized by mean 0.4972 and std 0.2897
Coefficients (with 95% confidence bounds):
p00 =      0.4253  (0.3928, 0.4578)
p10 =      -0.106  (-0.1322, -0.07974)
p01 =     -0.4299  (-0.4775, -0.3822)
p20 =     0.02104  (0.001457, 0.04062)
p11 =     0.07153  (0.05409, 0.08898)
p02 =    -0.03084  (-0.05039, -0.01129)
p21 =     0.02091  (0.001372, 0.04044)
p12 =     -0.0321  (-0.05164, -0.01255)
p03 =      0.1216  (0.09929, 0.1439)

The output displays the fitted model equation, the fitted coefficients, and the confidence bounds for the fitted coefficients.

## Plot the Fit, Data, Residuals, and Prediction Bounds

plot(surffit,[x,y],z)

Plot the residuals fit.

plot(surffit,[x,y],z,'Style','Residuals')

Plot prediction bounds on the fit.

plot(surffit,[x,y],z,'Style','predfunc')

## Evaluate the Fit at a Specified Point

Evaluate the fit at a specific point by specifying a value for x and y , using this form: z = fittedmodel(x,y).

surffit(1000,0.5)
ans =

0.5673

## Evaluate the Fit Values at Many Points

xi = [500;1000;1200];
yi = [0.7;0.6;0.5];
surffit(xi,yi)
ans =

0.3771
0.4064
0.5331

Get prediction bounds on those values.

[ci, zi] = predint(surffit,[xi,yi])
ci =

0.0713    0.6829
0.1058    0.7069
0.2333    0.8330

zi =

0.3771
0.4064
0.5331

## Get the Model Equation

Enter the fit name to display the model equation, fitted coefficients, and confidence bounds for the fitted coefficients.

surffit
Linear model Poly23:
surffit(x,y) = p00 + p10*x + p01*y + p20*x^2 + p11*x*y + p02*y^2 + p21*x^2*y
+ p12*x*y^2 + p03*y^3
where x is normalized by mean 1982 and std 868.6
and where y is normalized by mean 0.4972 and std 0.2897
Coefficients (with 95% confidence bounds):
p00 =      0.4253  (0.3928, 0.4578)
p10 =      -0.106  (-0.1322, -0.07974)
p01 =     -0.4299  (-0.4775, -0.3822)
p20 =     0.02104  (0.001457, 0.04062)
p11 =     0.07153  (0.05409, 0.08898)
p02 =    -0.03084  (-0.05039, -0.01129)
p21 =     0.02091  (0.001372, 0.04044)
p12 =     -0.0321  (-0.05164, -0.01255)
p03 =      0.1216  (0.09929, 0.1439)

To get only the model equation, use formula.

formula(surffit)
ans =

'p00 + p10*x + p01*y + p20*x^2 + p11*x*y + p02*y^2 + p21*x^2*y + p12*x*y^2 + p03*y^3'

## Get Coefficient Names and Values

Specify a coefficient by name.

p00 = surffit.p00
p03 = surffit.p03
p00 =

0.4253

p03 =

0.1216

Get all the coefficient names. Look at the fit equation (for example, f(x,y) = p00 + p10*x...) to see the model terms for each coefficient.

coeffnames(surffit)
ans =

9x1 cell array

{'p00'}
{'p10'}
{'p01'}
{'p20'}
{'p11'}
{'p02'}
{'p21'}
{'p12'}
{'p03'}

Get all the coefficient values.

coeffvalues(surffit)
ans =

Columns 1 through 7

0.4253   -0.1060   -0.4299    0.0210    0.0715   -0.0308    0.0209

Columns 8 through 9

-0.0321    0.1216

## Get Confidence Bounds on the Coefficients

Use confidence bounds on coefficients to help you evaluate and compare fits. The confidence bounds on the coefficients determine their accuracy. Bounds that are far apart indicate uncertainty. If the bounds cross zero for linear coefficients, this means you cannot be sure that these coefficients differ from zero. If some model terms have coefficients of zero, then they are not helping with the fit.

confint(surffit)
ans =

Columns 1 through 7

0.3928   -0.1322   -0.4775    0.0015    0.0541   -0.0504    0.0014
0.4578   -0.0797   -0.3822    0.0406    0.0890   -0.0113    0.0404

Columns 8 through 9

-0.0516    0.0993
-0.0126    0.1439

## Find Methods

List every method that you can use with the fit.

methods(surffit)
Methods for class sfit:

argnames       dependnames    indepnames     predint        sfit
category       differentiate  islinear       probnames      type
coeffnames     feval          numargs        probvalues
confint        formula        plot           setoptions

Use the help command to find out how to use a fit method.

QUAD2D  Numerically integrate a surface fit object.
Q = QUAD2D(FO, A, B, C, D) approximates the integral of the surface fit
object FO over the planar region A <= x <= B and C(x) <= y <= D(x). C and D
may each be a scalar, a function handle or a curve fit (CFIT) object.

[Q,ERRBND] = QUAD2D(...) also returns an approximate upper bound on the
absolute error, ERRBND.