Conservative sample size for multiple regression models

Abstract

A lower bound is given for the multiple correlation coefficient R. This lower bound is used to obtain conservative sample sizes for testing the hypothesis $H_0:R^2=0$ vs $H_1:R^2>0$ which is one method for obtaining the sample size for a Multiple Linear Regression Model. Results are given which can be used to determine how close the conservative sample sizes are to those obtained using the true value of R.

Keywords:

• Multiple linear regression models
• sample size
• multiple correlation coefficient