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Dmitrij Celov
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I think the field you are interesting in is related to conjoint analysis. Sawtooth, to my knowledge, are the leaders in this type of analysis, though SPSS and R also provide the tools and libraries to perform the conjoint analysis.

This part of the applied statistics consider the questions related to how a particular group of costumers actually choose the product valuing different features of the latter, but jointly. The design of a questionnaire can be concentrated upon individual preferences of a particular person, or you would probably like to generalize the preferences of a certain group of people.

To apply this analysis in practice you have to know what cars, apartments, computers, cell phone plans where actually bought or chosen, or at least the sample of respondents you study would buy or choose, if not facing the budget constraint directly. However, if you just collect the advertisements from newspapers or Internet the actual choices are hidden, because you do not observe them. To put it another way, you do not know in advance the qualitative answer to the question if there was a person with high enough reservation price and/or money in the pocket to like this suggested set of attributes (notice that price is the attribute as well) at all. Knowing the latter, you could build some kind of multinomial logit model, where the price would be the impact variable.

So to add more details, I think, we all need more details on:

  1. What do you actually observe: the set of attributes only (price IS the attribute, for example, I would like to rent the cheapest car with the best other attributes available, why not?) or some additional data not presented in your context part
  2. What you believe could be your dependent variable (the probability of purchase to my mind is the most suitable here)
  3. Do you need the model for forecasting needs or just to understand what attributes are the most influential

And a bit more on the topic...

There are, to my mind, several still open related questions:

  1. Decision making involves steps: do I need a car, what features I value most, how much I willing to pay for the features (answering the last question you indeed perform something like simple regression model)
  2. What prices do you observe? Those that are set by sellers, by buyers or the actual transaction. Without knowing the latter, suppose you observe 100 units of

V6, red, automatic, 140hp, 2010, $300

that where not purchased and 1

V6, blue, manual, 140hp, 2005, $100

that actually was? So what your conclusions based on regression analysis would be than?

Dmitrij Celov
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