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I'm currently working on an assignment related to house prices in the UK. I have a list of prices that depend on the size of the property (small, medium, large) and the property location in terms of how close the property is to urban areas (Yes = close to Urban areas | No = far away).

The data that I have is from two extremes, so all the properties are either close to urban areas or far away. As you can assume, the prices are high for large properties that are close to urban areas. In contrast, the prices are low for small properties that are far from urban areas.

However, the data is quite overlapping and a small house in urban area might have the same price (or close) to a large property outside the urban zone.

Now, my task is to determine whether the property is located in urban areas just by using house prices (the only available feature). But to do so I need to determine the size of the property as this has a significant affect on the price as well.

In reality, I would like to test my algorithm(s) on a range of property prices even those that are somewhere in between that is, not far to urban areas but no so close either. Can someone share their ideas on how one would tackle such a problem using only the house prices as my features? Thanks in advance for your input!

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Could you plot something like heatmap or 3D plot (x=size,y=location,z=prices) ? I would try something like a simple decision tree to fit your data.

Using only the houses prices as feature, I would first plot prices versus location. If there are two distinct clusters slightly overlaping, maybe fixing just one threshold is good enough.

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