Discrimination Intervals for Percentiles in Regression

Abstract

In simple linear regression the 100pth percentile of the distribution of Y for a given value of X is β₀ + β₁ X + Z_p σ, where Z_p is the 100pth percentile of the standard normal distribution. The problem considered is to estimate the value of X for which this percentile is equal to some specified value, Y_p . Both point and interval estimates are considered. A procedure for obtaining exact confidence intervals is derived, and in addition, two approximate and two conservative procedures for obtaining intervals are presented and compared. An example is given to illustrate these procedures and an application to covariance analysis is given.