In　this　paper,　we　firstly　introduce　the　definition　of　d2　for　sets.　Then　we　give　the　best　mean　square　approximation　of　multivalued　random　variables　in　the　sense　of　d2　metric,　which　is　the　basis　of　estimator＇s　existence　for　multivalued　linear　models　in　the　sense　of　d2.　Lastly,　we　give　two　kinds　of　cases　of　linear　models　for　interval　valued　data.　©　2024　Yokohama　Publications.　All　rights　reserved.