Exact simultaneous confidence intervals and bands for the regression line on a set Cx in simple linear regression have been known only when Cx is a finite set with one or two points or when Cx is a finite or infinite interval. Otherwise, conservative bands have been used. In this article we present a method for constructing exact confidence bands on an arbitrary finite union of intervals or points. Also, tables are provided for cases of finite Cx with three points and of Cx an interval.
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Esa Uusipaikka (1983) studied this question.
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