  We present a new multivariate regression model for analysis and parameter
estimation of gravitational waves observed from well but not perfectly modeled
sources such as core-collapse supernovae. Our approach is based on a principal
component decomposition of simulated waveform catalogs. Instead of
reconstructing waveforms by direct linear combination of physically meaningless
principal components, we solve via least squares for the relationship that
encodes the connection between chosen physical parameters and the principal
component basis. Although our approach is linear, the waveforms' parameter
dependence may be non-linear. For the case of gravitational waves from rotating
core collapse, we show, using statistical hypothesis testing, that our method
is capable of identifying the most important physical parameters that govern
waveform morphology in the presence of simulated detector noise. We also
demonstrate our method's ability to predict waveforms from a principal
component basis given a set of physical progenitor parameters.
