Equivalence testing for linear regression

We introduce equivalence testing procedures for linear regression analyses. Such tests can be very useful for confirming the lack of a meaningful association between a continuous outcome and a continuous or binary predictor. Specifically, we propose an equivalence test for unstandardized regression coefficients and an equivalence test for semipartial correlation coefficients. We review how to define valid hypotheses, how to calculate $p$-values, and how these tests compare to an alternative Bayesian approach with applications to various examples in the literature.