Distributed energy resources (DERs) are driving the need for detailed distribution circuit models which require accurate impedance estimates. Estimating the impedances can be time consuming and verifying the estimates is nearly impossible since the measurements available are noisy and limited to the edge nodes of the circuit. Therefore, electric distribution companies (EDCs) are interested in building models with data-driven methods to save time and improve accuracy. Previous work focused on building data-driven circuit models has not provided theoretical guarantees on the data quantity and quality, so their solutions may not be reliable enough for EDCs to adopt. Therefore, this work provides theoretical guarantees for recovering the impedances of a 3-node model which is designed to be a foundational building block that could eventually recover larger circuits. Our analysis bounds a proposed impedance estimator to the expected value which is extended to establish an upper limit of the data quantity required to meet an accuracy threshold. Unfortunately the proposed estimator, and other estimators examined in this paper, are biased. The estimators are studied empirically to begin to understand how the noise affects the bias. The outcomes suggest that using current instead of power measurements to estimate the impedance results in identical bounds and significantly less bias.