Testing of intercept when slope is under suspicion

Abstract

In simple regression analyses, the inference on the intercept depends on the knowledge of the slope. This paper studies the problem of testing the intercept of a simple regression model when slope is under suspicion. Depending on the situation the slope may be unknown or unspecified, known or specified, and uncertain if the suspected value is unsure. The three different scenarios on the slope lead to three different tests of the intercept. Here we define the unrestricted test (UT), restricted test (RT) and pre-test test (PTT) for the intercept parameter depending on the level of knowledge on the slope. The test statistics, their sampling distributions, and power functions of the tests are derived and compared when the error variance is assumed to be known.