Testing for Signal-to-Noise Ratio in Linear Regression: A Test for Big Data Era

Abstract

This paper proposes a test for the signal-to-noise ratio applicable to a range of significance tests and model diagnostics in a linear regression. It is particularly useful under a large or massive sample size, where a conventional test frequently rejects an economically negligible deviation from the null hypothesis. The test is conducted in the context of the traditional $F$-test, with its critical values increasing with sample size. It maintains desirable size properties under a large or massive sample size, when the null hypothesis is violated by a practically negligible margin.