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A Further Problem of Interval Estimation of an Unknown Regressor in Model I of Linear Regression
Author(s) -
Hess J.,
Horn M.
Publication year - 1982
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.4710240321
Subject(s) - confidence interval , value (mathematics) , mathematics , linear regression , interval (graph theory) , statistics , combinatorics , regression analysis , regression
For the model y = α + β x + ϵ (model I) of linear regression we dealt with in K UHNERT and H ORN (1980) the determination of a confidence interval for that x 0 where the expectation E y reaches a given value y 0 . Here we start with realizations of random variables y * i( i = 1,…, m ) being independent of x which are given in addition to the realizations of‐ y . Now y 0 denotes the unknown value of \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \sum \limits_{i = 1}^m $\end{document} ci E y * iand x 0 the x ‐value where the expectation E y reaches that value y 0 . For this x 0 we give a confidence interval. Applications stem from dose response assays.