## Least squares fitting where we pre-determine the slope

Asked by Barbara Wortham

### Barbara Wortham (view profile)

on 16 May 2018
Latest activity Commented on by Ameer Hamza

### Ameer Hamza (view profile)

on 13 Aug 2018
Accepted Answer by Ameer Hamza

### Ameer Hamza (view profile)

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!

### Ameer Hamza (view profile)

Answer by Ameer Hamza

### Ameer Hamza (view profile)

on 16 May 2018
Edited by Ameer Hamza

### Ameer Hamza (view profile)

on 16 May 2018

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 (view profile)

on 12 Aug 2018
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?
Ameer Hamza

### Ameer Hamza (view profile)

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.