Geodesic
Two-sided Tolerance Intervals in a Simple Linear Regression
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 52 (2013) no. 2, pp. 31-41.

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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, see Lee and Mathew (2002), but the numerical computation of the limits of the multiple-use confidence intervals is needed. We modified the Lieberman–Miller method (1963) 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.
Classification : 62F25, 62J05
Keywords: multiple-use confidence interval; simultaneous two-sided tolerance interval 
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Chvosteková, Martina. Two-sided Tolerance Intervals in a Simple Linear Regression. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 52 (2013) no. 2, pp. 31-41. http://geodesic.mathdoc.fr/item/AUPO_2013__52_2_a2/