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Boston housing data provided by GeoDa center is a well-known dataset. GeoDa Center provides this data in shapefile format. A metadata file included in the download indicates that the data use projection UTM 19N. However the shapefile does not have a projection defined (no accompanying .prj file), and I am unable to load it correctly.

I would like to overlap the Boston data with the census tract data available at Census Bureau using ArcMap.

How can I do this?

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The shapefile distributed by GeoDa Center does not have a PRJ file, so normally you would have to define the projection in order to line it up with other spatial data. But it appears that while the shapefile distributed by GeoDa Center does in fact use the UTM 19N zone, for some reason the units are in kilometers, where UTM coordinates are usually expressed in meters. If you already used ArcGIS to define the shapefile's projection as, for example, NAD 1983 UTM Zone 19N (not immediately clear that NAD 1983 is the datum, but often a good guess for United States data), all of your points will be way off because ArcGIS will interpret the coordinates as meters where the underlying data are actually in kilometers.

Your best bet is to make use of the boston.txt file that is also included in the ZIP archive you downloaded from GeoDa Center to create your own shapefile from the coordinates. This file has the coordinates in both lat-long and UTM 19N, but since the UTM coordinates are in kilometers, you would need to divide all the values by 1000 to import it correctly into ArcGIS using any of the predefined UTM coordinate systems. It will be easier to just use the lat-long coordinates.

Steps to do so are as follows:

  1. Strip the first line from boston.txt (containing the text 506,23), so that header which was on line 2 is promoted to line 1.
  2. In ArcGIS go to File→Add Data→Add XY Data.
  3. Select the boston.txt file and set X Field = LON and Y Field = LAT. Note that since the file has fields named x and y, the dialog will sensibly default to assuming that the X Field is x and the Y Field is y, but these are the coordinates in UTM kilometers, which we don't want to use.
  4. Under "Coordinate System of Input Coordinates" click the Edit button, and set the coordinate system to Geographic Coordinate Systems→North America→NAD 1983.
  5. Right-click the boston.txt Events layer that appeared in the Table of Contents. Choose Data→Export Data. Name it and export it to the desired format (shapefile, file geodatabase, …).

If you follow the above procedures, the data align tolerably with 2010 vintage Census Bureau shapefiles, which also use the NAD 1983 lat-long coordinate system. Note that using NAD 1983 for the housing data is just a guess. WGS 1984 will produce virtually indistinguishable results (see http://mappingcenter.esri.com/index.cfm?fa=ask.answers&q=740). But if you need to do larger scale mapping, and find that the points don't seem to align with streets or other features of another layer you are using, you may have to do some research to determine the correct datum. This last part taken from a comment by @ChrisW.

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