Marcos Sanches writes:
I am hoping you could give me some light on how to handle a variable in a regression model. My model tries to predict choice in a market place using as independent variable the size of the package and the price of the product (among others), since this product can come in different sizes and prices. My issue is whether I should model price and size as they are (two variables) or as a price per gram (dividing price by size). I would like to understand more about this issue (you can reference your books since I have all of them), what would be the difference between these two strategies themselves and perhaps also bring a third strategy which would be to model the interaction between price and size.
My reply: If you write the model on the log scale (as you probably should), then you can include size and price per gram as two linear predictors, and this will take care of everything. You can also try interactions. We discuss this in chapters 3 and 4 of ARM.
If "size" is measured in grams and "price" is measured as "dollars per gram", won't this lead to the "size" and "price" being unnecessarily correlated? But leaving "price" as "dollars" is not very useful for comparison purposes. How would you resolve this problem?
log(price/gram) = log(price) – log(gram) so I think that's why Andrew is recommending logarithms.