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?