Overparameterized Multiple Linear Regression as Hyper-Curve Fitting

arXiv:2404.07849v1 Announce Type: cross
Abstract: The paper shows that the application of the fixed-effect multiple linear regression model to an overparameterized dataset is equivalent to fitting the data with a hyper-curve parameterized by a single scalar parameter. This equivalence allows for a predictor-focused approach, where each predictor is described by a function of the chosen parameter. It is proven that a linear model will produce exact predictions even in the presence of nonlinear dependencies that violate the model assumptions. Parameterization …

abstract application arxiv cs.lg data dataset function linear linear regression multiple paper regression shows stat.ml type