Quantitative ultrasound parameters such as backscatter and attenuation coefficients can be used to characterize tissues along with B-mode image ultrasound. However, these coefficients must be accurately found, and can be hard to measure. Simultaneous estimation of both backscatter coefficient and the total attenuation reduces the necessity of rely on previous studies to accurate know the attenuation of each separate tissue. Furthermore, the total attenuation up to the region of analysis can be also found on heterogeneous media, such as gynecological tissues. A technique for this estimation, the least square fitting (LSF) method, has been proposed to simultaneously estimate the total attenuation coefficient slope α, the magnitude b and frequency dependence n of the backscatter coefficient. The aim of the present study is to analyze the precision and accuracy of the LSF method. Simulated data, physical calibrated phantoms and six healthy thyroids cases have been used to this purpose. The estimation bias was used to quantify the accuracy of the method with the simulated and physical phantom data, whereas the coefficient of variation (CV) was used to quantify the precision of the method with simulated, physical phantom and in vivo data. The analysis was performed with regions of 12λ axially and varying lateral size. In both simulations and physical phantom experiments, the CV ranged between 0.003 and 1.29 for all estimated variables. With the in vivo data, the maximum CV values were 4.25 for b, 2.15 for n and 0.86 for the ACS. This increase may be partially explained by the reduced number of effective lines per region (3-6 lines) for the in vivo data when compared to the simulated and physical phantom data (down to 20-30 lines) The bias of n and the total attenuation was less of 10% for the simulated and physical phantoms, but increased to 50-100 % for b, The results suggest that for regions of analysis with clinically relevant sizes the precision of the method is compromised but accurate estimates of α and n may be obtained.