Multiple Regression under constraints

Hi,

I am looking at doing a linear multiple regression on one dependent variable and 15 independent varaibles. My first issue is that I would like to be sure there is no multicollinearity in between the IV. Is there a function to take care of that? I guess some forward, backward, stepwise could partially take care of that. My second issue is that I would like to have constraints on the beta coefficient. For example I would like beta1>0.5 and beta2<1... Would you have any suggestion regarding the function to use.

Thanks in advance

Answer 1

[Richard Willey]

Lets start with the regression side of the problem:

Given that you want to place constraints on your coefficients, you're going to need to use Optimzation Toolbox. The constraints that you're describing a pretty simple, so you should be able to use lsqcurvefit.

http://www.mathworks.com/help/toolbox/optim/ug/lsqcurvefit.html

With more complicated constraints, you'd probably want to use quadprog instead.

Let's move onto the multicollinearity question:

I'd start by using something simple like a scatterplot matrix to visualize the data, and follow up by calculating some simple summary statistics.

If you determine that multicollinearity is a problem, your best best will be to wrap the sequentialfs function from Statistics Toolbox around lsqcurvefit.

Answer 2

[Sophy]

Hi Guys, I would like to use Linear regression with constraints on equality of some of features' coefficients. Anyone know how to define this? For example I have 6 features and features No 1 and 5 need to have equal coefficients also features 2 and 4 should have the same coefficients in the linear regression model. I really appreciate if anyone can help me. Thanks,