# [R] Constraining linear regression model

Peter Flom peterflomconsulting at mindspring.com
Sat May 23 14:42:48 CEST 2009

```Jean-Paul Kibambe Lubamba <jean-paul.kibambe at uclouvain.be> wrote
>
>I have two questions:
>
>I am computing a linear regression model with 0 as Intercept.
>
>Well, I would like the sum of my predicted values be equal to a constant
>and therefore analyze if my coefficients are significatively different
>using or not this constraint.
>
>Does anyone know how I can constrain my model in a such way?
>
>Here is the code:
>
>lm <-lm(pop ~ ag + sav + mf -1, data=data)
>pred <- predict(lm)
>sum(pred)
>
>So I want to constrain my sum (pred) to be equal to C, with C=sum(pop)
>
>
>
>My second question is: is it possible to make the same constraint BUT with
>C as a vector of values?
>
>Let's say If I have 5 observations in 'data', with 'pop' as the first
>column. I want to compute the same model as above with a 'vector' of
>constraints. In that case, C=xi (with i from 1 to 3)
>
>x1 = sum (data[c(2,4), 1])
>x2 = sum(data [c(1,3), 1])
>x3 = data[5,1]
>
>
>Thanks in advance -- Any help is welcome!
>

This sounds very odd.  OLS linear regress *does* constrain the predicted values - the constraint is to minimize the sum of squared error.  There are variations of regression that use different constraints, like sums of absolute errors and so on .... but why constrain the sum of predicted values to a constant?

Peter

Peter L. Flom, PhD
Statistical Consultant
www DOT peterflomconsulting DOT com

```