Bowden and Graybill construct uniform confidence bands under the familiar simple linear regression model, and use those bands to write joint confidence intervals forexpected YgivenX=Xofor allXoin a specified finite rangeXa≤Xo≤Xb. Their approach is extended here to provide joint confidence intervals forindividualobservations onYgivenX, and also forindividual XgivenY(the inverse interval estimation problem), in both cases using uniform confidence bands constructed forXa≤X≤Xb. We show that Bowden and Graybill's tables can be used in these applications, and give 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.