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Forum index » Science and Technology » Math
Regression equation using absolute errors
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draccarlawpet
science forum beginner


Joined: 09 Jan 2006
Posts: 41

PostPosted: Tue Jun 27, 2006 5:39 pm    Post subject: Regression equation using absolute errors Reply with quote
What would the regression formula using absolute errors and not least
squared errors?
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C6L1V@shaw.ca
science forum Guru


Joined: 23 May 2005
Posts: 628

PostPosted: Tue Jun 27, 2006 6:49 pm    Post subject: Re: Regression equation using absolute errors Reply with quote
draccarlawpet wrote:
Quote:
What would the regression formula using absolute errors and not least
squared errors?

There is no "formula", but you can set up and solve the problem using
linear programming (LP). For example, if your fit is of the form y = a
+ b*x, and you have observed values (x_i,y_i) for i = 1, 2, ..., n,
then you can minimize sum |y_i - a - b*x_i| by introducing new
variables z_i >= 0 and solving min sum z_i, subject to the constraints
z_i >= y_i - a - b*x_i and z_i >= a + b*x_i - y_i for i = 1,...,n.
(The variables in the LP are a,b and the z_i, and only the z_i are
restricted to being >= 0.). Alternatively, you can introduce 2n new
variables zp_i, zn_i >=0 and introduce constraints
zp_i - zn_i = y_i - a - b*x_i for i = 1, ..., n.
Then the problem is to minimize sum (zp_i + zn_i). The first
formulation has n + 2 variables and 2n constraints, while the second
one has 2n + 2 variables and n constraints. Both are very practical for
n less than a few hundred, using readily available LP software.

R.G. Vickson
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draccarlawpet
science forum beginner


Joined: 09 Jan 2006
Posts: 41

PostPosted: Tue Jun 27, 2006 7:12 pm    Post subject: Re: Regression equation using absolute errors Reply with quote
I'm interested in a 1-variable model which minimizes the absolute
errors, and not the squared errors.

Does an equation exist?
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C6L1V@shaw.ca
science forum Guru


Joined: 23 May 2005
Posts: 628

PostPosted: Tue Jun 27, 2006 7:40 pm    Post subject: Re: Regression equation using absolute errors Reply with quote
draccarlawpet wrote:
Quote:
I'm interested in a 1-variable model which minimizes the absolute
errors, and not the squared errors.

Does an equation exist?

My previous reply told you exactly how to do it. And NO, there is no
formula or equation, as my reply clearly stated in the first sentence.

R.G. Vickson
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