This report summarizes the work of the Census Undercount Adjustment for Small Area Group pertaining to the use of regression methodology to implement an adjustment of census counts down to the small area level. While this report concentrates on the investigation and findings based on the use of various regression models it is important to bear in mind that a regression model formed at one level of aggregation does not necessarily apply to another level of aggregation. For example, while a model formed at the state level may perform quite well for states, use of this model at a county level (or other small area) may involve the use of explanatory variables with levels outside the range at which the model was built--this extra extrapolation can result in misleading results. Other reasons why a model formed at the state level may not be applicable to lower levels of aggregation include the possibility that different explanatory variables may be more appropriate at a county or block level as well as the possibility that values for the explanatory variables formed at the state level are not very reliable at the county level. In the work presented here the assumption has been made that after a regression model has been formed at a given level of geography such as state, synthetic estimation would play a role in adjusting down to lower levels of geography such as the block. Synthetic estimation is described in a separate report.