Linear　regression　models　for　interval-valued　data　have　been　widely　studied.　Most　literatures　are　to　split　an　interval　into　two　real　numbers,　i.e.,　the　left-　and　right-endpoints　or　the　center　and　radius　of　this　interval,　and　fit　two　separate　real-valued　or　two　dimension　linear　regression　models.　This　paper　is　focused　on　the　bias-corrected　and　heteroscedasticity-adjusted　modeling　by　imposing　order　constraint　to　the　endpoints　of　the　response　interval　and　weighted　linear　least　squares　with　estimated　covariance　matrix,　based　on　a　generalized　linear　model　for　interval-valued　data.　A　three　step　estimation　method　is　proposed.　Theoretical　conclusions　and　numerical　evaluations　show　that　the　proposed　estimator　has　higher　efficiency　than　previous　estimators.