Aggressive requirements for low power and high performance in VLSI designs have led to increased interest in approximate computation. Approximate hardware modules can achieve improved energy efficiency compared to accurate hardware modules. While a number of previous works have proposed hardware modules for approximate arithmetic, these works focus on solitary approximate arithmetic operations. To utilize the benefit of approximate hardware modules, CAD tools should be able to quickly and accurately estimate the output quality of composed approximate designs. A previous work  proposes an interval-based approach for evaluating the output quality of certain approximate arithmetic designs. However, their approach uses sampled error distributions to store the characterization data of hardware, and its accuracy is limited by the number of intervals used during characterization. In this work, we propose an approach for output quality estimation of approximate designs that is based on a lookup table technique that characterizes the statistical properties of approximate hardwares and a regression-based technique for composing statistics to formulate output quality. These two techniques improve the speed and accuracy for several error metrics over a set of multiply-accumulator testcases. Compared to the interval-based modeling approach of , our approach for estimating output quality of approximate designs is 3.75x more accurate for comparable runtime on the testcases and achieves 8.4x runtime reduction for the error composition flow. We also demonstrate that our approach is applicable to general testcases.