Abstract.:　A　new　metric,　called　variation　of　conditional　mean　(VCM),　is　proposed　to　measure　the　dependence　of　conditional　mean　of　a　response　variable　on　a　predictor　variable.　The　VCM　has　several　appealing　merits.　It　equals　zero　if　and　only　if　the　conditional　mean　of　the　response　is　independent　of　the　predictor;　it　can　be　used　for　both　real　vector-valued　variables　and　functional　data.　An　estimator　of　the　VCM　is　given　through　kernel　smoothing,　and　a　test　for　the　conditional　mean　independence　based　on　the　estimated　VCM　is　constructed.　The　limit　distributions　of　the　test　statistic　under　the　null　hypothesis　and　alternative　hypothesis　are　deduced,　respectively.　We　further　use　VCM　as　a　marginal　utility　to　do　high-dimensional　feature　screening　to　screen　out　variables　that　do　not　contribute　to　the　conditional　mean　of　the　response　given　the　predictors　and　prove　the　validity　of　the　sure　screening　property.　Furthermore,　we　find　the　cross　variation　of　conditional　mean　(CVCM),　a　variant　of　the　VCM,　has　a　faster　convergence　rate　than　the　VCM　under　conditional　mean　independence.　Numerical　comparison　shows　that　the　VCM　and　CVCM　performs　well　in　both　conditional　independence　testing　and　feature　screening.　We　also　illustrate　their　applications　to　real　data　sets.　©　2024　Taylor　&　Francis　Group,　LLC.