# How to take care of the percentage/rate of an absolute number as independent variable?

I am working on a mixed model, where suppose I have several stores of different sizes. The number of products manufactured in each store is different, say one store can manufacture 100 and other can do 10000 products as well. I have one independent variable as "total number of defects in a store". I am assuming that larger the products manufactured at a store, more will be the defects at that store.

Now if I take only the "absolute total number of defects" at a store, I am losing on the info about the total size of the stores. Can I use "percentage = (total defects at the store/total size of the store)" as my independent variable instead of "total defects at the store". Will that solve my issue? Or do I need to include interaction? Will the model become complicated in this scenerio?

• Can you use size of the stores as an independent variable? This should help you avoid using percentages. – Arun Jose Oct 13 '14 at 11:48
• Also, you mentioned that number of defects is the independent variable. I would assume this would be your dependent variable instead? – Arun Jose Oct 13 '14 at 11:49
• Sorry for my extreme late reply! To your first answer, do you mean to use both the number of defects and size of store as independent variables? – Anjali Oct 21 '14 at 10:07
• Assuming that I want to use both of them at the independent variable side, what is the best possible way to do that? Is it to use percentages/rate (using one as numberator and other as denominator) or using both as two separate independent variable? – Anjali Oct 21 '14 at 10:10
• It is very unclear what your final objective is. Are you trying to predict number of errors? Calculating a percentage can be done even after predicting number of errors – Arun Jose Oct 21 '14 at 10:30