I am an executive being transferred from my home city on the west coast to one in the Midwest. I know nothing about the city I'm moving to, but I have to buy a house there. Realtors have told me all sorts of things about the area, but I don't trust them. Instead, I had data compiled on housing appraisals and pricing at sale, and the ratios of those two characteristics. It seems to me that the ratio of sale price to appraised price is a good indicator of how desirable a neighborhood is, but it's possible that there is skullduggery going on (crooked appraisers, for example), so I may be wrong in depending too much on this number. I need some guidance from your analysis to know.

I know I can't tell everything about a neighborhood from these numbers, but I'll use them as a starting point. I myself am not well versed in statistical analysis, so I'm hiring you to perform a basic analysis for me. Be assured that my brother-in-law is a stats teacher, so your analysis should be rigorous. But for me, you must write a report that, while it includes all your reasoning and calculations, still has parts that sum up your analysis and your recommendations in simple layman's terms. In the end, I will want your recommendations based on your analysis. I not only want your calculations, but your explanations.

My questions to you are:

• Out of all the neighborhoods, which one is the most desirable, based on the willingness of buyers to pay over and above the appraisal price? Can you see any other indicators of desirability? You can use one or more methods for figuring out which one is best, just make sure you show me exactly how you calculate each one. Using more than one may be best, just to check yourself, but that's up to you.
• Are there any neighborhoods with suspicious sales patterns that might reveal shady practices such as redlining (keeping out minorities by refusing to lend in certain places)? Are there any red flags you can see? Are there any irregularities that you think could signal the need for more investigation?
• If there is one neighborhood you would judge superior, what is the probability that I can bide my time for a while and wait for a listing with a favorable sales ratio? And what are the probabilities for various ratios? In other words, how much over and above appraisal should I expect to pay, based on how badly I want a house? What are the probabilities for the various ratios?
• What are your recommendations overall?