Green L−σ relation for our 102 HII galaxies with SDSS [OIII]5007 luminosities and Gauss-Hermite velocity dispersions. The black solid and dashed lines represent direct (L vs. σ) and inverse (σ vs. L) standard Least Squares (LSQ) fits to the data. The orange line shows a maximum-likelihood (ML) fit that takes the observational errors into account as described in Appendix B. The relevant parameters of the three fits are listed in Table D.1. The 30 galaxies from the BT11 sample are not plotted because we lack [OIII]5007 luminosities.