Life in a city is very expensive: Not only do you pay more for your home, you also pay more for the things you enjoy about living here. Our museums, sporting events, restaurants, and entertainment are all more expensive than similar (if not fully comparable) experiences elsewhere. Don’t even get me going on the taxes.
Why do we pay so much? One explanation is the “network effect” of housing. The theory says that the more people live in an area, the more valuable that area is because people exude positive externalities—our very presence causes other people pleasure.
That’s not as narcissistic as it sounds. In a dense city like Chicago, we are much more likely to be able to establish business contacts, find others who share our interests, make interesting friendships, and find customers for our small businesses. The simple fact of having a lot of people around enhances our lives—and we pay for it.
If that’s true for cities and rural counties, then it ought to be true for neighborhoods within our city—and in fact it does hold true. I looked at every neighborhood’s population density and its housing values and found there is a strong correlation. The charts here show the relationship. Neighborhoods with more people have, on average, higher home values than those that are less dense.
(I got the idea to test this question from reading Tim Harford’s “The Logic of Life,” an excellent book that has several chapters on urban economics.)

It’s important to point out though that density can also save money (and energy and resources). This is exactly why people started forming cities thousands of years ago. And transportation is a great example — people in dense areas with more than one transportation option enjoy significant savings, often enough to outweigh the increased cost of housing. See CNT’s research on this: http://htaindex.cnt.org/
Interesting data for #32 & 32 which are part of South Loop and Near South, with median values already strong, what inceramental value is going to be had for increasing by say 5,000 people per mile, and will it impact the bell curve for these locals. I would assume location has more to do with these numbers (close to lake, downtown, etc) more than ammeneties or restaurants which still lag a bit.
Would be interesting to overlay this data with more info on housing stock and foreclosure information.