The A Priori Procedure (APP) for estimating regression coefficients in linear models

Abstract

Regression coefficients are crucial in the sciences, as researchers use them to determine which independent variables best explain the dependent variable. However, researchers obtain regression coefficients from data samples and wish to generalize to populations; without reason to believe that sample regression coefficients are good estimates of corresponding population regression coefficients, their usefulness would be curtailed. In turn, larger sample sizes provide better estimates than do smaller ones. There is much recent literature on the a priori procedure (APP) that was designed for the general purpose of determining the sample sizes needed to obtain sample statistics that are good estimates of corresponding population parameters. We provide an extension of the APP to regression coefficients, which works for standardized or unstandardized regression coefficients. A simulation study and real data example support the mathematical derivations. Also, we include a free and user-friendly computer program to aid researchers in making the calculations.

The a priori procedure (APP) for estimating median under skew normal settings with applications in economics and finance

“…There have been additional advances too (e.g. Cao et al, 2021Cao et al, , 2022Chen et al, 2021;Tong et al, 2022;Trafimow et al, 2020;Wang et al, 2021Wei et al, 2020;Wilson et al, 2022). However, as the APP literature continues to expand, there is a simple issue that somehow has escaped investigation.…”