MATLAB Answers

0

Least squares fitting where we pre-determine the slope

Asked by Barbara Wortham on 16 May 2018
Latest activity Commented on by Ameer Hamza
on 13 Aug 2018 at 7:09

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!

  0 Comments

Sign in to comment.

1 Answer

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.

  5 Comments

Thank you for the thorough, concise explanation! I'm hoping to perform a similar calculation, except I'd like to employ a weighted least squares regression (using inverse variances associated with my dependent variable as weights). How will this calculation change in this case?

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.

Sign in to comment.