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

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Albert Bing
Albert Bing on 22 Jul 2021
Answered: Star Strider on 22 Jul 2021
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')

Accepted Answer

Star Strider
Star Strider on 22 Jul 2021
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';
.

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