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Exact Confidence Bounds for Comparing Two Regression Lines with a Control Regression Line on a Fixed Interval
Author(s) -
Bhargava Parul,
Spurrier John D.
Publication year - 2004
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.200410072
Subject(s) - mathematics , statistics , design matrix , confidence interval , linear regression , coverage probability , segmented regression , simple linear regression , regression analysis , matrix (chemical analysis) , interval (graph theory) , line (geometry) , sample size determination , simple (philosophy) , proper linear model , polynomial regression , combinatorics , materials science , geometry , philosophy , epistemology , composite material
The problem of finding exact simultaneous confidence bounds for comparing simple linear regression lines for two treatments with a simple linear regression line for the control over a fixed interval is considered. The assumption that errors are iid normal random is considered. It is assumed 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 four t variables. The probability point depends on the size of an angle associated with the interval. We present probability points for various sample sizes and angles. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)