# Cannibalization of product sales

I am trying to determine the rate of cannibalization of product sales for A with product B. I am using ~ 2 years of daily sales data for product A and then ~8 months of data for product B. That is, product B launched 8 month ago. I am using the longer series for A to capture trend effects in the business (natural or industry rate of decline or growth). I also control for seasonality by using a weekday variable (= day of week 1-7) and a week number variable (1-52).

If I use the log-log regression to determine the elasticity of A to B, then I can use that to estimate cannibalization. By regressing the log (A) daily sales as the Y variable against the Log (X) i.e. products B's daily sales I get an equation in the terms of:

log (A)=Bo +B(log(X)) + error and this tells me the % change in A given a 1 % change in X. However, I want to express this in terms of dollars. Therefore, I have to transform the logs back into the original sales values (I do not use any smearing transformations).

Question: Is the equation below correct? If not please advise. Furthermore, is it proper to take the log coefficient of product B and do the following to estimate the % sales lost to B:

% cannibalization of year to date sales = [(EXP(B1)-1) x (year-to-date sales of B)] / (year-to-date sales of A); where B1 = coefficient from log-log regression Say the above equation gives me a % cannibalization of year to date sales of 87 %, how should I interpret it?

Thanks alot for helping me out

• What are you doing when B is not available, so log(X) is undefined? Also, I believe the coefficient B should be interpreted as the % change in A's sales for a 1% increase in sales of B. Commented Jan 28, 2013 at 19:19
• You are right, just edited that:)
– Tom
Commented Jan 29, 2013 at 9:19
• It's not good practice to destroy your post and repost just after. Better to update your question so that this thread remains self-contained. Thanks.
– chl
Commented Jan 31, 2013 at 22:47