. 2016 Oct 19;11(10):e0165015. doi: 10.1371/journal.pone.0165015

Table 1. Regression models considered for GC normalization.

We explored several regression models, from simple linear models using only one input variable (genome GC content) to more complex by progressively increasing the number of terms and using two input variables (read GC content and genome GC content). While this strategy helped us find models with lower RMSE, it eventually led to overfitting and a significant increase in RMSE (the forth-degree polynomial model). However, using non-linear regression with a Gaussian exponential term significantly improved RMSE (last model). Complete results of model testing with estimates of abundance of each bacterium in the validation sets are provided in S2 Table. R output with statistics for the tested models is included in S2 File.

Model of normalized coverage	Unique solution found	Residual standard error	Degrees of freedom	RMSE (Experiment 1, 250 ng bacterial DNA), %	RMSE (Experiment 2, 20 ng bacterial DNA), %
θ₁ + θ₂ log(GC_G)	Yes	0.6519	340	8.35	8.51
θ₁ + θ₂GC_G + θ₃GC_G²	Yes	0.6515	339	8.09	8.26
θ₁ + θ₂GC_R + θ₃GC_R² + θ₄ log(GC_G)	Yes	0.4414	338	8.41	8.69
θ₁ + θ₂GC_R + θ₃GC_R² + θ₄GC_R³ + θ₅ log(GC_G)	Yes	0.373	337	6.24	6.53
θ₁ + θ₂GC_R + θ₃GC_R² + θ₄GC_R³ + θ₅GC_R⁴ + θ₆ log(GC_G)	Yes	0.3441	336	11.7	11.92
$θ_{1} e^{- 0.5 {(\frac{G C_{R} - θ_{2}}{θ_{3}})}^{2}} + θ_{4} + θ_{5} \log (C G_{G})$	No	NA	NA	NA	NA
$θ_{1} e^{- 0.5 {(\frac{G C_{R} - θ_{2}}{θ_{3}})}^{2}} + θ_{4} + θ_{5} G C_{R} + θ_{6} G C_{R}^{2}$	No	NA	NA	NA	NA
$θ_{1} e^{- 0.5 {(\frac{G C_{R} - θ_{2}}{θ_{3}})}^{2}} + θ_{4} + θ_{5} G C_{R} + θ_{6} G C_{R}^{2} + θ_{7} \log (G C_{G})$	No	NA	NA	NA	NA
$θ_{1} e^{- 0.5 {(\frac{G C_{R} - θ_{2}}{θ_{3}})}^{2}} + θ_{4} + θ_{5} G C_{R} + θ_{6} G C_{R}^{2} + θ_{7} G C_{R}^{3} + θ_{8} \log (G C_{G})$	Yes	0.3283	334	2.87	2.91