Custom Nonlinear Census Fitting
This example shows how to fit a custom equation to census data, specifying bounds, coefficients, and a problem-dependent parameter.
Load and plot the data in census.mat:
load census plot(cdate,pop,'o') hold on
Create a fit options structure and a fittype object for the custom nonlinear model y = a(x-b)n, where a and b are coefficients and n is a problem-dependent parameter. See the fittype function page for more details on problem-dependent parameters.
s = fitoptions('Method','NonlinearLeastSquares',... 'Lower',[0,0],... 'Upper',[Inf,max(cdate)],... 'Startpoint',[1 1]); f = fittype('a*(x-b)^n','problem','n','options',s);
Fit the data using the fit options and a value of n = 2:
[c2,gof2] = fit(cdate,pop,f,'problem',2)
c2 = General model: c2(x) = a*(x-b)^n Coefficients (with 95% confidence bounds): a = 0.006092 (0.005743, 0.006441) b = 1789 (1784, 1793) Problem parameters: n = 2
gof2 = struct with fields:
sse: 246.1543
rsquare: 0.9980
dfe: 19
adjrsquare: 0.9979
rmse: 3.5994
Fit the data using the fit options and a value of n = 3:
[c3,gof3] = fit(cdate,pop,f,'problem',3)
c3 = General model: c3(x) = a*(x-b)^n Coefficients (with 95% confidence bounds): a = 1.359e-05 (1.245e-05, 1.474e-05) b = 1725 (1718, 1731) Problem parameters: n = 3
gof3 = struct with fields:
sse: 232.0058
rsquare: 0.9981
dfe: 19
adjrsquare: 0.9980
rmse: 3.4944
Plot the fit results and the data:
plot(c2,'m') plot(c3,'c') legend('data','fit with n=2','fit with n=3')