  Based on the highly improved staggered quark action, we perform lattice
simulations of $N_f=8$ QCD and confirm our previous observation of a
flavor-singlet scalar meson (denoted as $\sigma$) as light as the pion and
various "walking signals" through low-lying spectra, with higher statistics,
smaller fermion masses $m_f$, and larger volumes. We measure $M_\pi$, $F_\pi$,
$M_\rho$, $M_{a_0}$, $M_{a_1}$, $M_{b_1}$, $M_N$, $M_\sigma$, $F_\sigma$,
$\langle \bar{\psi} \psi\rangle$ (both directly and through the GMOR relation),
and the string tension. The data are consistent with the spontaneously broken
phase of the chiral symmetry, in agreement with the previous results: ratios of
the quantities to $M_\pi$ monotonically increase in the smaller $m_f$ region
towards the chiral limit similarly to $N_f=4$ QCD, in sharp contrast to
$N_f=12$ QCD where the ratios become flattened. The hyperscaling relation holds
with roughly a universal value of the anomalous dimension, $\gamma_m \simeq 1$,
with a notable exception of $M_\pi$ with $\gamma_m \simeq 0.6$ as in the
previous results. This is a salient feature ("walking signal") of $N_f=8$,
unlike either $N_f=4$ which has no hyperscaling relation at all, or $N_f=12$
QCD which exhibits universal hyperscaling. We further confirm the previous
observation of the light $\sigma$ with mass comparable to the pion in the
studied $m_f$ region. In a chiral limit extrapolation of the $\sigma$ mass
using the dilaton chiral perturbation theory and also using the simple linear
fit, we find the value consistent with the 125 GeV Higgs boson within errors.
Our results suggest that the theory could be a good candidate for walking
technicolor model, having anomalous dimension $\gamma_m \simeq 1$ and a light
flavor-singlet scalar meson as a technidilaton, which can be identified with
the 125 GeV composite Higgs in $N_f=8$ one-family model.
