Overparameterized Multiple Linear Regression as Hyper-Curve Fitting: Insights into Predictive Power and Regularization

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, enabling the identification and removal of noisy or improper predictors to improve the predictive power of the linear model.