01-16-2012 08:50 AM
I need to perform one regression to predict sale amounts of two types ofcars in one city. Now my data include the sale amounts of two types of cars (product1,product2) and
other ‘dependent’variables x1, x2,x3, x4 (the population of the city, average income,and so on) in 2010.
It seems inappropriate to perform regression on product1and product2 respectively, because the other car will not be chosen if theclient chooses one car. Any suggestion about the regression?
01-18-2012 03:42 PM
Different approaches might be applicable - depending on the scenario you are facing - for example, your assumption that the sales patterns are highly correlated needs to be tested. For example: my choice of cars might not be between the 2 models you are referring to - but between similar models from different vendors.
Having said this, here are some examples which come to my mind (by no means exclusive): market mix modelling approaches (see for example http://www.people.hbs.edu/dbell/market%20share%20theorem.pdf), maybe discrete choice models are more appropriate (see for example: https://files.nyu.edu/mrg217/public/unordered_multiresponse.pdf).
A time series modeling based approach might be to consider modeling the sales amounts of cars (P1 and P2) in an hierarchical fashion - which means that you would aggregate the total sales and model all 3 series independently. Then you could adjust the individual forecasts by the total forecasting using a top-down reconciliation approach.
01-18-2012 05:04 PM
If your two product types encompass most of the market then it might be a good idea to model Total car sales (product1+product2) and Car type preference (product1-product2) separately instead of each product type, as a function of your predictors (X1, X2, ...)
Mind you, with a single year's data, you will miss any effect that affects all cities at the same time, such as gas prices, interest rates or consumer optimism.