Two-sided tolerance intervals in a simple linear regression. (English) Zbl 1302.62155

Summary: Numerical results for a simple linear regression indicate that the non-simultaneous two-sided tolerance intervals nearly satisfy the condition of multiple-use confidence intervals, but the numerical computation of the limits of the multiple-use confidence intervals is needed. We modified the Lieberman-Miller method [G. J. Lieberman and R. G. Miller, Biometrika 50, 155–168 (1963; Zbl 0124.35501)] for computing the simultaneous two-sided tolerance intervals in a simple linear regression with independent normally distributed errors. The suggested tolerance intervals are the narrowest of all the known simultaneous two-sided tolerance intervals. The computation of the multiple-use confidence intervals based on the new simultaneous two-sided tolerance intervals is simple and fast.


62J05 Linear regression; mixed models
62F25 Parametric tolerance and confidence regions


Zbl 0124.35501
Full Text: Link


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