Linear regression with an observation distribution model

Despite the high complexity of real world, linear regression still plays an important role in estimating parameters to model a physical relationship between at least two variables. The precision estimated parameters, which can usually be considered as indicator solution quality, is conventionally obtained from inverse normal equations matrix for intensive computation required when number observations large. In addition, impacts distribution on parameter are rarely reported literature. this paper, we propose new methodology order predict prior actual data collection and performing regression. analysis readily performed given hypothesized distribution. has been verified with several simulated datasets. results show that empirical model-predicted precisions match very well, discrepancies up 6% 3.4% datasets, respectively. Simulations demonstrate these differences simply due finite sample size. simulation also demonstrates relative insensitivity method noise independent variables causes deviations function. proposed allows straightforward prediction based related their numerical limits geometry, greatly simplify design procedures various experimental setups commonly involved geodetic surveying such LiDAR collection.