Testing Multiple Linear Regression Systems with Metamorphic Testing

TL;DR

This paper demonstrates that Metamorphic Testing effectively verifies multiple linear regression systems by identifying key mathematical properties and proposing 11 relations, improving testing reliability for regression-based applications.

Contribution

It introduces a set of 11 Metamorphic Relations specifically designed for testing linear regression systems, addressing the challenge of the absent test oracle.

Findings

Metamorphic Testing is effective for regression system verification.

Identified 11 intrinsic properties for testing linear regression.

Mutation analysis confirms the approach's effectiveness.

Abstract

Regression is one of the most commonly used statistical techniques. However, testing regression systems is a great challenge because of the absence of test oracle in general. In this paper, we show that Metamorphic Testing is an effective approach to test multiple linear regression systems. In doing so, we identify intrinsic mathematical properties of linear regression, and then propose 11 Metamorphic Relations to be used for testing. Their effectiveness is examined using mutation analysis with a range of different regression programs. We further look at how the testing could be adopted in a more effective way. Our work is applicable to examine the reliability of predictive systems based on regression that has been widely used in economics, engineering and science, as well as of the regression calculation manipulated by statistical users.