  We use spectroscopic observations of a sample of 82 HII regions in 76 blue
compact galaxies to determine the primordial helium abundance Yp and the slope
dY/dZ from the Y-O/H linear regression. To improve the accuracy of the dY/dZ
measurement, we have included new spectrophotometric observations of 33 HII
regions which span a large metallicity range, with oxygen abundance 12+log(O/H)
varying between 7.43 and 8.30 (Zsun/30<Z<Zsun/4). For a subsample of 7 HII
regions, we derive the He mass fraction taking into account known systematic
effects, including collisional and fluorescent enhancements of HeI emission
lines, collisional excitation of hydrogen emission, underlying stellar HeI
absorption and the difference between the temperatures Te(HeII) in the He^+
zone and Te(OIII) derived from the collisionally excited [OIII] lines. We find
that the net result of all the systematic effects combined is small, changing
the He mass fraction by less than 0.6%. By extrapolating the Y vs. O/H linear
regression to O/H=0 for 7 HII regions of this subsample, we obtain
Yp=0.2421+/-0.0021 and dY/dO=5.7+/-1.8, which corresponds to dY/dZ=3.7+/-1.2,
assuming the oxygen mass fraction to be O=0.66Z. In the framework of the
standard Big Bang nucleosynthesis theory, this Yp corresponds to Omega_b h^2 =
0.012^+0.003_-0.002, where h is the Hubble constant in units of 100 km/s/Mpc.
This is smaller at the 2sigma level than the value obtained from recent
deuterium abundance and microwave background radiation measurements. The linear
regression slope dY/dO=4.3+/-0.7 (corresponding to dY/dZ=2.8+/-0.5) for the
whole sample of 82 HII regions is similar to that derived for the subsample of
7 HII regions, although it has a considerably smaller uncertainty.
