Curve fit but only for the values that exists with defined values of x.

I wnat to fit the curve for the point but i only want the curve to fit from value suppose in given code x vary from 1800-1950 and shouldn't extend beyond it. Is there any way to do this?

load census
plot(cdate,pop,'o')

%Create a fit options object and a fit type for the custom nonlinear model , where a and b are coefficients and n is a problem-dependent parameter. 
fo = fitoptions('Method','NonlinearLeastSquares',...
               'Lower',[0,0],...
               'Upper',[Inf,max(cdate)],...
               'StartPoint',[1 1]);
ft = fittype('a*(x-b)^n','problem','n','options',fo);

%Fit the data using the fit options and a value of n = 2. 
[curve2,gof2] = fit(cdate,pop,ft,'problem',2)

curve2 = 
     General model:
     curve2(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. 
[curve3,gof3] = fit(cdate,pop,ft,'problem',3)

curve3 = 
     General model:
     curve3(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 with the data. 
hold on
plot(curve2,'m')
plot(curve3,'c')
legend('Data','n=2','n=3')
hold off

Answer 1

[Torsten]

load census
I = cdate >= 1850 & cdate <= 1950;
cdate1 = cdate(I);
pop1 = pop(I);
plot(cdate,pop,'o')

%Create a fit options object and a fit type for the custom nonlinear model , where a and b are coefficients and n is a problem-dependent parameter. 
fo = fitoptions('Method','NonlinearLeastSquares',...
               'Lower',[0,0],...
               'Upper',[Inf,max(cdate)],...
               'StartPoint',[1 1]);
ft = fittype('a*(x-b)^n','problem','n','options',fo);

%Fit the data using the fit options and a value of n = 2. 
[curve2,gof2] = fit(cdate1,pop1,ft,'problem',2)

curve2 = 
     General model:
     curve2(x) = a*(x-b)^n
     Coefficients (with 95% confidence bounds):
       a =    0.005544  (0.004984, 0.006103)
       b =        1784  (1777, 1790)
     Problem parameters:
       n =           2

gof2 = struct with fields:
           sse: 70.1612
       rsquare: 0.9963
           dfe: 9
    adjrsquare: 0.9959
          rmse: 2.7921

%Fit the data using the fit options and a value of n = 3. 
[curve3,gof3] = fit(cdate1,pop1,ft,'problem',3)

curve3 = 
     General model:
     curve3(x) = a*(x-b)^n
     Coefficients (with 95% confidence bounds):
       a =   1.326e-05  (1.023e-05, 1.63e-05)
       b =        1723  (1708, 1738)
     Problem parameters:
       n =           3

gof3 = struct with fields:
           sse: 151.9055
       rsquare: 0.9919
           dfe: 9
    adjrsquare: 0.9910
          rmse: 4.1083

%Plot the fit results with the data. 
hold on
plot(cdate1,curve2(cdate1),'m')
plot(cdate1,curve3(cdate1),'c')
legend('Data','n=2','n=3')
hold off

[Yashvardhan Bhati]

@Torsten I want to show the data(markers) for the other x values outside the limits, but have curve fit only for values between 1850 to 1950 lets suppose. how can i do that?

[Torsten]

I modified the code above accordingly.

[Yashvardhan Bhati]

@Torsten Thanks this works well.