We conducted a long-slit spectrophotometry analysis to obtain the chemical abundances of seven metal-poor HII regions in three galaxies: UM 160, UM 420, and TOL 0513-393. The data have been taken with the Focal Reducer Low Dispersion Spectrograph 1 (FORS1) at the 8.2-m Very Large Telescope. We derived the physical conditions and the chemical abundances of N, O, Ne, S, Ar, and Cl. We also performed a detailed analysis that involves abundance determinations using the $t^2$ formalism. Based on HeI recombination line intensity ratios, together with the Helio14 code, we derived the abundance of He. In addition, for a value $\Delta Y/\Delta Z_O =3.3\pm 0.7$, we have estimated that the primordial helium abundance by mass is $Y_{\rm P}=0.2448\pm0.0033$. This value agrees with values derived from Standard Big Bang Nucleosynthesis and with other recent determinations of $Y_{\rm P}$.

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