  Hydrogen-rich Type II-Plateau supernovae exhibit correlations between the
plateau luminosity $L_{\rm pl}$, the nickel mass $M_{\rm Ni}$, the explosion
energy $E_{\rm exp}$, and the ejecta mass $M_{\rm ej}$. Using our global,
self-consistent, multi-band model of nearby well-observed supernovae, we find
that the covariances of these quantities are strong and that the confidence
ellipsoids are oriented in the direction of the correlations, which reduces
their significance. By proper treatment of the covariance matrix of the model,
we discover a significant intrinsic width to the correlations between $L_{\rm
pl}$, $E_{\rm exp}$, and $M_{\rm Ni}$, where the uncertainties due to the
distance and the extinction dominate. For fixed $E_{\rm exp}$, the spread in
$M_{\rm Ni}$ is about 0.25 dex, which we attribute to the differences in the
progenitor internal structure. We argue that the effects of incomplete
$\gamma$-ray trapping are not important in our sample. Similarly, the physics
of the Type II-Plateau supernova light curves leads to inherently degenerate
estimates of $E_{\rm exp}$ and $M_{\rm ej}$, which makes their observed
correlation weak. Ignoring the covariances of supernova parameters or the
intrinsic width of the correlations causes significant biases in the slopes of
the fitted relations. Our results imply that Type II-Plateau supernova
explosions are not described by a single physical parameter or a simple
one-dimensional trajectory through the parameter space, but instead reflect the
diversity of the core and surface properties of their progenitors. We discuss
the implications for the physics of the explosion mechanism and possible future
observational constraints.
