The introduction of differential privacy to the 2020 Census using the TopDown Algorithm (TDA) to protect respondent confidentiality has led to increasing interest in the quantification of the usability of the final privacy-protected population counts. Wright and Irimata (2021) introduced an empirical measure for evaluating reliability of redistricting plans using 2010 Census data, with block groups as a proxy for districts; however, this approach relied upon the official Census counts released in 2010, and thus cannot directly be used in evaluating the reliability of geographic units in the 2020 data products. The present work investigates the use of statistical modeling to produce estimates of variability using publicly available data sources as predictors, with a focus on models that are easy to digest. Three different models, with varying levels of complexity are introduced and evaluated using data from the 2010 Census and are used to produce estimates of reliability for the 2020 Census counts. The model fitting exercise showed that the linear regression model with interactions and the BART model were the preferred approaches. Using these two models, we found that block groups larger than 300 to 349 persons tend to be reliable when using predictions from the linear regression model with interactions, and that block groups larger than 350 to 399 persons tend to be reliable when using predictions from the BART model.