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# cannibalization of product

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

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Comment by Jeffrey Ng on February 4, 2013 at 7:35am

sound alright except that I wish to ask if the Bo big? Also, i am not sure if you can explain well with the coefficient B1, which portray the log-log relationship...does it work for simple regression without log? if it still works within a tolerable level, I will go for the simple model for the sake of explanation to the management. Unless your management is a quant or experienced with model, otherwise the first priority is to  get the management trust any model before you refine to use log-log.

Comment by Tom on February 4, 2013 at 2:20am

I need to log it because it makes the interpretation easy...and also because the box-cox transformation indicates that log is the appropriate transformation

Comment by Jeffrey Ng on February 2, 2013 at 12:26am

why do you have to log everything? I am just asking from an end user point of view

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