Exact confidence bounds comparing two regression lines with a control regression line

摘要

There have been several recent papers discussing multiple comparisons of treatments based on two-sided comparisons of simple linear regression models for an unrestricted predictor variable. In this dissertation, I first present one-sided simultaneous confidence bounds for comparing simple linear regression lines for two treatments with a simple linear regression line for the control for the cases of an unrestricted and a restricted predictor variable. Then I present results for two-sided simultaneous confidence bounds for comparing simple linear regression lines for two treatments with a simple linear regression line for the control for a restricted predictor variable. The assumptions that normal errors are iid and the mean predictor variable for all treatments is zero have been made. I had to also assume that the design matrices for the two treatments are equal and the design matrix for the control has the same number of copies of each distinct row of the design matrix for the treatments. The method is based on a pivotal quantity that can be expressed as a function of 4-dimensional multivariate-t variables. It was found that by rotating the axis the probability point is dependent only on the angle associated with the arc. I present tables of probability points for various sample sizes, various angles and levels of significance.