No commercially available AVMs let the user know the equations used in calculating values, as the equations are proprietary. Sometimes you can find out which variables are most important. A few let you see adjustments that were made on their appraiser emulation models, where adjustments are made on a grid, like on an appraisal report. Some AVMs allow user input, such as changing a square footage or inputting a time adjustment, and others don't allow any input. The main reason for not allowing user input is to eliminate the human element from valuation.
Good data is the key Public records is the primary data source for all commercially available AVMs.
This data is typically purchased by the AVM vendor. Some vendors collect part of their data, particularly if they work only a few states. Public records data is used for both the subject and the comps. Freddie and Fannie use their extensive appraisal database for their AVMs. Freddie's AVM is marketed through Dataquick also.