### Abstract

A simultaneous confidence band provides a variety of inferences on the unknown components of a regression model. There are several recent papers using confidence bands for various inferential purposes; see for example, Sun et al. (1999), Spurrier (1999), Al-Saidy et al. (2003), Liu et al. (2004), Bhargava & Spurrier (2004), Piegorsch et al. (2005) and Liu et al. (2007). Construction of simultaneous confidence bands for a simple linear regression model has a rich history, going back to the work of Working & Hotelling (1929). The purpose of this article is to consolidate the disparate modern literature on simultaneous confidence bands in linear regression, and to provide expressions for the construction of exact 1 - α level simultaneous confidence bands for a simple linear regression model of either one-sided or two-sided form. We 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.

Original language | English (US) |
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Pages (from-to) | 39-57 |

Number of pages | 19 |

Journal | International Statistical Review |

Volume | 76 |

Issue number | 1 |

DOIs | |

State | Published - Apr 1 2008 |

### Keywords

- Bivariate normal
- Bivariate t
- Polar coordinators
- Simple linear regression
- Simultaneous inferences

### ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty