Asked by Barbara Wortham
on 16 May 2018

Hello all,

I have a set of data, say on a scatter plot, and I have a line that has a pre-determined slope (i.e. not determined by the data on the scatter plot but determined by ideal calculations). I would like to move the line through the data until it has the least amount of offset (like least-squares fitting) but without changing the slope of the line. Is there a least-squares fitting function that lets you pre-determine the slope?

Cheers!

Answer by Ameer Hamza
on 16 May 2018

Edited by Ameer Hamza
on 16 May 2018

Accepted Answer

Yes, you can do that following the pattern of the linear regression fitting with little modification. In linear regression, we fit the equation

a*x+b = y

and in MATLAB we write it as

[x_vector ones(size(x_vector))]\y_vector

to get a and b. But since you already know slope a, your equation become

b = y-a*x

so in MATLAB use

ones(size(x_vector))\[y_vector-a*x_vector]

it will give you the value of b which minimize the least square error.

Barbara Wortham
on 17 May 2018

Thanks everyone!

Curtis Baden
on 12 Aug 2018

Ameer Hamza
on 13 Aug 2018

For weighted least square you can use lscov(). In term of the backslash operator, you can use the following

(X.'*W*X)\(X.'*W*y)

where W is a diagonal matrix containing the weights.

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