This　paper　introduces　a　new　type　of　statistical　model:　the　interval-valued　linear　model,　which　describes　the　linear　relationship　between　an　interval-valued　output　random　variable　and　real-valued　input　variables.　Firstly,　we　discuss　the　notions　of　variance　and　covariance　of　set-valued　and　interval-valued　random　variables.　Then,　we　give　the　definition　of　the　interval-valued　linear　model　and　its　least　square　estimation,　as　well　as　some　properties　of　the　least　square　estimation.　Thirdly,　we　show　that,　whereas　the　best　linear　unbiased　estimation　does　not　exist,　the　best　binary　linear　unbiased　estimator　exists　and　it　is　just　the　least　square　estimator.　Finally,　we　present　simulation　experiments　and　an　application　example　regarding　temperature　of　cities　affected　by　their　latitude,　which　illustrates　the　application　of　our　model.　©　2013　Proceedings　of　the　8th　International　Symposium　on　Imprecise　Probability.