Re: "How does the local crime rate impact housing rate," I'm unclear as to what the hypothesis is regarding housing density. Especially since housing density can be traced to a number of factors, like whether a given block or neighborhood contains lots of parking lots. You might find high crime and low occupancy, just because an area contains lots of dark parking lots. But does that imply a causative relationship there? I'm worried that you might find spurious correlations.
Re: "how does selected demographics characteristics differ at the zip code level," this feels like it needs more specificity.
If it were me, if I were looking at crime over time, I would want to know how it correlates with economic inequality, that is, the gap in income between rich and poor, and other factors such as green space, lighting, number of sidewalk trees, predominant type of housing, and so on. You can find a more specific angle, I think, that's new and fresh.
Maybe do some reading about crime rates and their correlations? If you do lots of background research, you'll get an idea for the kinds of things that are possible, and where your work might be a new contribution.
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