Construction engineers increasingly use 3D laser scanners on job sites to capture detailed as-built geometries for construction monitoring, while their data collection time and quality can vary significantly. Various data collection parameters influence the quality of data and time for data collection. These parameters include internal (e.g., the laser signal strength, spatial resolution of the used scanner) and external parameters (e.g., color, object dimension, distance, and lighting condition). Correlations among these parameters, data collection time, and as-built modeling errors, contain principles of efficient and effective laser scan planning. Limited quantitative studies of these correlations result in ad-hoc laser scan planning, missing geometric information, and unnecessarily long data collection time. This paper presents a series of controlled experiments and seven statistical methods for quantitatively modeling the correlations between 3D as-built modeling errors and various parameters mentioned above. The major findings include: 1) internal correlations among data collection parameters need to be resolved for precise as-built error prediction; 2) all tested statistical methods are based on linear regression, while non-Gaussian distribution of the as-built modeling errors and nonlinear correlations in the experimental results distort the parametric error models. Future research will explore nonlinear or non-parametric methods for obtaining more reliable error models for proactively guiding engineers to conduct laser scanning in the field.