How to calculate the standard error estimation when using fit from curve fitting toolbox?

Is is possible to calculate the standard error estimation when using fit from curve fitting toolbox as in polyfit?

Suppose I have 2 vector (x, y). Using polyfit and polyval gives the standard error estimation for all predictions.

How to calculate delta in fit? I need the prediction interval like examples below.

I assume the delta in polyval is not a scalar but varies with x. (Purhaps it is not?)

Example from the documention,

x = 1:100; 
y = -0.3*x + 2*randn(1,100); 
[p,S] = polyfit(x,y,1); 
[y_fit,delta] = polyval(p,x,S);
plot(x,y,'bo')
hold on
plot(x,y_fit,'r-')
plot(x,y_fit+2*delta,'m--',x,y_fit-2*delta,'m--')
title('Linear Fit of Data with 95% Prediction Interval')
legend('Data','Linear Fit','95% Prediction Interval')

Answer 1

[Star Strider]

Yes. Use the predint function.

x = linspace(0, 100, 100); 
y = -0.3*x + 2*randn(1,100);

[f,gof,out] = fit(x(:), y(:), 'poly1')

f = 
     Linear model Poly1:
     f(x) = p1*x + p2
     Coefficients (with 95% confidence bounds):
       p1 =     -0.2946  (-0.3081, -0.2811)
       p2 =     -0.5298  (-1.311, 0.251)

gof = struct with fields:
           sse: 384.9559
       rsquare: 0.9504
           dfe: 98
    adjrsquare: 0.9499
          rmse: 1.9819

out = struct with fields:
        numobs: 100
      numparam: 2
     residuals: [100×1 double]
      Jacobian: [100×2 double]
      exitflag: 1
     algorithm: 'QR factorization and solve'
    iterations: 1

ci = predint(f, x);

figure
plot(f, x, y)
hold on
plot(x, ci, '--')
hold off
grid
hl = legend;
hl.String{3} = 'Lower 95% CI';
hl.String{4} = 'Upper 95% CI';

.