How do I use MatLab to find a line of best fit with a predetermined y intercept using regression.

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Chris Joyce 2022-12-18

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评论： Star Strider 2022-12-18

I have data on changes in cardiac output with temperature changes from several studies. This data is expressed as CO at Tn / CO at T0, so at baseline temperature the result = 1. I want to find a line of best fit for this data, but the y intercept must be 1 for it to make sense.

How do I use Matlab find a line of best fit with least squares regression for this data, with the y intercept constrained to 1? It is easily done with Microsoft Excel, but I am trying to become more familiar with stats on Matlab.

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Answer 1

Star Strider 2022-12-18

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在 MATLAB Online 中打开

Perhaps —

x = 0:250;

y = randn(size(x));

B0 = x(:) \ (y(:)-1)

B0 = -0.0054

fitline = x(:) * B0 + 1;

figure

plot(x, y, '.')

hold on

plot(x, fitline, '-r')

hold off

grid

.

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John D'Errico 2022-12-18

编辑：John D'Errico 2022-12-18

在 MATLAB Online 中打开

@Chris Joyce

You misunderstand. Let me show the help for sym/backslash.

help sym/mldivide
 MLDIVIDE Symbolic matrix left division.
    MLDIVIDE(A,B) overloads symbolic A \ B.
    X = A\B solves the symbolic linear equations A*X = B.
    Warning messages are produced if X does not exist or is not unique.
    Rectangular matrices A are allowed, but the equations must be
    consistent; a least squares solution is not computed.
 
    See also SYM/MRDIVIDE, SYM/LDIVIDE, SYM/RDIVIDE, SYM/QUOREM.

And, Yes, it states that the symbolic version of backslash does not produce a least squares solution, but that is only because this is the symbolic solver. The symbolic toolbox does not generate least squares solutions in any case, since they are essentially never an exact solution to a system of equations.

HOWEVER...

What @Star Strider wrote is indeed exactly the solution you need. It solves for the linear least squares solution to the problem

y = 1 + B0*x

where the y-intercept is fixed at 1.

Just because the symbolic solver does not produce that result is not relevant, since this is a problem of numerical linear algebra. And that is what MLDIVIDE does when applied here. So you can happily trust what Star has given you. Of course, you might not trust me either. (We could go down a long way into this rabbit hole.) But honestly, Star was correct. Trust him. Would I buy a used car from him? Well, that might be another question completely. :)

Chris Joyce 2022-12-18

It works perfectly, giving me exactly the same answers as EXCEL.

Thanks again

Star Strider 2022-12-18

My pleasure!

If my Answer helped you solve your problem, please Accept it!

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