# What area of statistics is this example?

Let's say that there are a series of physical objects each with properties (round, red, soft, etc.) and each property affects the value of the object. Certain combinations can affect the value as well (round and red are valuable when found together, but not separate).

Given a large list of objects and values, is there a way to ascertain the approximate contribution of value for each property and combination of properties? What is this called and where can I get more information? FWIW I am in the process of programming a module in Python.

Also, I tagged this as homework. It isn't, but I couldn't find any other general tags. Thanks

-

In economics, there's an approach called hedonic regression (link to real estate paper with a nice intro). It tries to decompose the market value of an item into its constituent attributes, usually using a regression of the price on various desirable and undesirable features. The red and round issue you raise would show up as the coefficients on red and round being small and insignificant, but the coefficient on their interaction being large and significant.

There reason to do this is that such attributes do not have an individual price, because they cannot be sold separately. One example is real estate valuation, where the price of the house may depend on its age, location, the numbers and size of rooms, scenic views, proximity to highways, good schools, jobs, and public transportation. You can't just go to a store and buy "1/4 mile to a Montessori kindergarten." This approach has also been used to study inflation (CPI), why certain jobs pay more, and why certain prostitutes earn more than others. The limitation of this approach is that you need heaps of data, and even then, multicollinearity will often give you funny estimates (urban and car emissions occur together, so it's hard to disentangle their contributions). Another issues is that parameters are hard to interpret. For a simple example, the coefficient on number of rooms will often have a negative sign when you include area in the model, but that merely means that if you're holding the size of the house constant, subdividing the rooms tends to make it less desirable.

-

This problem can be considered as feature selection. You basically have an outcome variable (the value as you call it) and its predictor variables (the properties). You want to know how good your features are in predicting the outcome.

You can look for feature selection algorithms. Here is a good one to start with, which you can try online: mRMR.

-