# Regression with averages and collinearity

I am stuck with the definition of a regression model regarding the inclusion of a constant averaged by the dependent variable.

I have a dataset M=(id, x1,x2,x3,x4) where:

id: is the id of the product
x1: is a continuous variable denoting price (0 to 999 USD)
x2: is a categorical variable denoting whether the product belongs to category A
x3: is a categorical variable denoting whether the product belongs to category B
x4: is a discrete variable having the customer rating with values V=(1,2,3,4,5)


Through a transformation for each product id I generate the averages for x4 as AVG(x4)_{i} where i={1,2,3,4,5}. Now my dataset becomes

M=(id, x1, x2, x3, AVG(x4)_{1}, AVG(x4)_{2}, AVG(x4)_{3}, AVG(x4)_{4}, AVG(x4)_{5})


I want to regress AVG(x4)_{i} on x1, x2, x3, however because x1 from theory has a direct interaction with the dependent variable, I want to regress the model:

AVG(x4)_{i} = b1*x1+b2*x2+b3*x3+b4*(AVG(x4)_{i}*x1)+C+e


for each value of i.

• Is that definition of the model correct?
• Should b4 dropped due to collinearity?
• I don't understand. If ID is just an ID, then you don't want to transform it. And what are you averaging X4 over? That is, what is the denominator? X4 seems to have one value for each ID. – Peter Flom Aug 24 '12 at 14:03