Bootstrapping Confidence Levels for Hypotheses about Quadratic (U-Shaped) Regression Models

TL;DR

This paper introduces a bootstrap-based method for calculating confidence levels in hypotheses about quadratic regression models, offering more detailed and flexible inference compared to traditional approaches.

Contribution

It presents a novel bootstrap approach for confidence levels in quadratic models, emphasizing interpretability and broad applicability.

Findings

Bootstrap provides clearer confidence levels for quadratic hypotheses.

Method is flexible and applicable to various models.

Enhanced utility with interpretable coefficients.

Abstract

Bootstrapping can produce confidence levels for hypotheses about quadratic regression models - such as whether the U-shape is inverted, and the location of optima. The method has several advantages over conventional methods: it provides more, and clearer, information, and is flexible - it could easily be applied to a wide variety of different types of models. The utility of the method can be enhanced by formulating models with interpretable coefficients, such as the location and value of the optimum. Keywords: Bootstrap resampling; Confidence level; Quadratic model; Regression, U-shape.