Trout, J. Richard; Swallow, William H. (1979, ASQC and the American Statistical Association) Rutgers University, New Brunswick, NJ
Bowden and Graybill construct uniform confidence bands under the familiar simple linear regression model, and use those bands to write joint confidence intervals for expected Y given X = Xo for all Xo in a specified finite range Xa < or = Xo X or = Xb. Their approach is extended here to provide joint confidence intervals for individual observations on Y given X, and also for individual x given Y (the inverse interval estimation problem), in both cases using uniform confidence bands constructed for Xa < or = X < or = Xb. We show that Bowden and Graybill's tables can be used in these applications, and given supplementary tables to cover additional cases which more commonly arise in these new contexts. Asymptotic results are also given, allowing the user to generate additional "table" values.The relative efficiencies of the uniform and Scheffe procedures for inverse interval estimation of individual X given Y are extensively compared. It seems that one need not pay a price in efficiency for the convenience of the uniform procedure.