Least squares fit, unknown intercerpt

Question

I have three data points through which I have to fit a straight line of the form Y=m*X+C. I want the line to have pre-determined slope 'm' but the constant'C' can change to get the least error while fitting using matlab. Can someone help me out?

What error metric? absolute difference? – Daniel Sep 02 '14 at 18:05 — Daniel, Sep 02 '14 at 18:05
The standard error. Sum (Ymeasured-Ypredicted).^2 – labalala Sep 02 '14 at 18:06 — labalala, Sep 02 '14 at 18:06

score 2 · Accepted Answer · answered Sep 02 '14 at 18:04

2

Just do the math:

C= mean(Y)-m*mean(X)

assuming Y is the vector containing the y coordinates, and X the x coordinates.

Reference: http://hotmath.com/hotmath_help/topics/line-of-best-fit.html

answered Sep 02 '14 at 18:04

BCartolo

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Jommy · Answer 2 · 2014-09-02T20:53:48.533

If you opt to use the Curve Fitting Toolbox the solution is as follows.

To start generate some data

m = 3;
x = (1:10).';
y = m*x + 2 + randn(size(x));

then select the model to fit and set the bounds for its coefficients

ft = fittype('poly1');
opts = fitoptions('Method', 'LinearLeastSquares');
opts.Lower = [m -Inf];
opts.Upper = [m  Inf];

finally call the fitting routine

[fitresult, gof] = fit(x, y, ft, opts);

The intercept is stored in fitresult.p2.

Least squares fit, unknown intercerpt

2 Answers2