Question 774:

Asked on July 5, 2009

Tags: Linear Regression

1

Answer:

No answer provided yet.I'm not sure why you would want to restrict the coefficients to be all positive. When you conduct a regression analysis Minitab or whatever software you use will generate the best fitted least-squares model for the variables you included. 40 independent variables is a lot of course, so I'm assuming your sample size will be sufficiently large (>1000). It is often the case that an independent variable best predicts the dependent variable while taking into accounts its correlation with the other independent variables when it has a negative coefficient. So wanting the coefficients to be positive doesn't make much sense (or perhaps I'm misunderstanding your question). 

For example, I've often been interested in what factors affect customer loyalty. Customer loyalty can be measured on an 11 point scale 0 -10. We ask customers several questions such as how usable they think a product is, how satisfied they are with the price and service and installation. We then want to see which one of these aspects (usability, price, service, installation) affect customer loyalty. I often find that some of the variables have a negative coefficient. Since they are all measured on the same scales (higher is better) then these relationships don't make sense--who wants a higher price to be more loyal? or who wants worse service to be more loyal?  What is actually going on is that the strength of the relationship is so weak, that a large enough sample size gives you a significant correlation. The coefficient though is usually very close to 0 (e.g. -.01265). I then drop these from the regression equations.

Minitab has a function called step-wise or backwards selections which picks the best combination of variables. You should carefully select only meaningful variables to include as from chance alone you'll get some meaningless relationships.