I'd like to fit integer coefficients, e.g. summing to 10, to a regression equation. The absolute values of the coefficients (i.e. predicted y) aren't important, I just want to retain the appropriate relative values. The use case is for an easily interpretable scoring system.

For example, this regression yields the following coefficients (ignoring the intercept):

set.seed(0)
y <- rnorm(100)
x <- matrix(rnorm(300), ncol=3)
m <- lm(y ~ x)
(coef <- m$coefficients[-1])
#          x1          x2          x3 
#  0.12100965  0.05506511  0.14708549 

Rounding with the below code yields a rounding error (sums to 11):

round(10 * coef / sum(coef))
# x1 x2 x3 
#  4  2  5 

A method like this also doesn't guarantee maximally similar weights to the regression equation.

This was asked here without satisfactory answers, and might be addressed in this paywalled research paper.

Edit: looks like http://stackoverflow.com/questions/792460/how-to-round-floats-to-integers-while-preserving-their-sum may be able to help minimize the roundoff error. If my question is further specified as minimizing the error of a predicted (scaled) y, I'm unsure whether this is an equivalent optimization.

I'd like to fit integer coefficients, e.g. summing to 10, to a regression equation. The absolute values of the coefficients (i.e. predicted y) aren't important, I just want to retain the appropriate relative values. The use case is for an easily interpretable scoring system.

For example, this regression yields the following coefficients (ignoring the intercept):

set.seed(0)
y <- rnorm(100)
x <- matrix(rnorm(300), ncol=3)
m <- lm(y ~ x)
(coef <- m$coefficients[-1])
#          x1          x2          x3 
#  0.12100965  0.05506511  0.14708549 

Rounding with the below code yields a rounding error (sums to 11):

round(10 * coef / sum(coef))
# x1 x2 x3 
#  4  2  5 

A method like this also doesn't guarantee maximally similar weights to the regression equation.

This was asked here without satisfactory answers, and might be addressed in this paywalled research paper.

Edit: looks like https://stackoverflow.com/questions/792460/how-to-round-floats-to-integers-while-preserving-their-sum may be able to help minimize the roundoff error. If my question is further specified as minimizing the error of a predicted (scaled) y, I'm unsure whether this is an equivalent optimization.