2008
DOI: 10.1111/j.1751-5823.2007.00027.x
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Construction of Exact Simultaneous Confidence Bands for a Simple Linear Regression Model

Abstract: SummaryWe center attention on the three most recognized shapes: hyperbolic, two-segment, and three-segment (which is also referred to as a trapezoidal shape and includes a constant-width band as a special case). Some of these expressions have already appeared in the statistics literature, and some are newly derived in this article. The derivations typically involve a standard bivariate t random vector and its polar coordinate transformation.

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Cited by 36 publications
(20 citation statements)
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References 53 publications
(90 reference statements)
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“…Analysts often plot T s around the meta‐regression line, which helps to capture the meaning of the meta‐regression and to see how well it explains variability in T s (Borman and Grigg, ; Lau et al ., ). Relatively rare to date are meta‐regression plots including confidence bands around the regression line to highlight at what levels of a moderator estimates exceed the null value or some benchmark criterion of clinical significance (Hayter et al ., ; Liu et al ., ). There also are few tools presently available to display patterns from meta‐regressions with multiple moderator factors.…”
Section: A Bivariate Example Moving the Constantmentioning
confidence: 97%
“…Analysts often plot T s around the meta‐regression line, which helps to capture the meaning of the meta‐regression and to see how well it explains variability in T s (Borman and Grigg, ; Lau et al ., ). Relatively rare to date are meta‐regression plots including confidence bands around the regression line to highlight at what levels of a moderator estimates exceed the null value or some benchmark criterion of clinical significance (Hayter et al ., ; Liu et al ., ). There also are few tools presently available to display patterns from meta‐regressions with multiple moderator factors.…”
Section: A Bivariate Example Moving the Constantmentioning
confidence: 97%
“…These pointwise confidence intervals are calculated at a value x using the well-known result . Simultaneous confidence intervals that have 95% probability of simultaneously including all true y values are somewhat wider [17].…”
Section: Consistency Checksmentioning
confidence: 99%
“…Liu, Lin, and Piegorsch (2008) review theory and methodology associated with simultaneous confidence bands for linear regression. Scheffé's (1953Scheffé's ( , 1959 familiar method for comparing all contrasts readily extends to the multiple regression context.…”
Section: Introductionmentioning
confidence: 99%