AbstractRegression modeling has been based on analyzing error terms between the predicted output and the target output without addressing the variance of the predicted output and the impact of individual input parameters on the variance. This research critically reviews established methods for variance analysis on commonly applied multiple linear regressions (MLR). An MLR model with high accuracy (the mean of the prediction close to the target value) but low precision (too high of a variance of the prediction) would be deemed insufficient in the context of cost estimating applications. An analytical method to account for the impact of the uncertainty associated with each input parameter on the uncertainty of the final output has yet to be formalized. This research integrates the error propagation theory with MLR modeling in an attempt to quantify the variance of the MLR predicted output in estimating labor cost for prefabricated products. A metric based on the resulting variance analysis (i.e., the ratio of the standard deviation over the mean) is found effective to gauge the precision of the MLR model. The research has advanced regression modeling methods with respect to MLR variance analysis and contributed to the estimating practice for prefabricated products such as structural steel fabrication, precast concrete, industrial modules, and building modules.