R中的线性回归-约束和回归数的变化

Question

I want to do a linear regression with a varying number of regressors (sometimes 3, sometimes 15) and specific inequality constraints to some of the regressor coefficients: some shall be >= 0, others can also be negative.

I have done this with optim() and constrOptim() which both refer to another user-defined function that minimizes the residuals of the regression. My problem is that this will only give me coefficients and no additional data like residuals, $R^2$, etc.

Is there an easy way to use lm() , nl() or any other function that would account for the inequality constraints while being able to handle a varying number of regressors?

Answer 1

As a linear regression is somehow an orthogonal projection onto a vectorial space, it is not meaningfull to talk about linear regression with constrained coefficient.

In any case, once a model is fitted all the statistical quantities can always be calculated via the direct formula : if your output is y and your model predicts y_pred then R^2 = mean((y-y_pred)^2) etc.

Beware that confidence on the regression is not accurate anymore since it is based on some assumptions on the error term (iid normaly distributed)