In　recent　years,　some　interested　data　can　be　recorded　only　if　the　values　fall　within　an　interval　range,　and　the　responses　are　often　subject　to　censoring.　Attempting　to　perform　effective　statistical　analysis　with　censored,　especially　heavy-tailed　and　asymmetric　data,　can　be　difficult.　In　this　paper,　we　develop　a　novel　linear　regression　model　based　on　the　proposed　skewed　generalized　t　distribution　for　censored　data.　The　likelihood-based　inference　and　diagnostic　analysis　are　established　using　the　Expectation/Conditional　Maximization　Either　algorithm　in　conjunction　with　smoothing　approximate　functions.　We　derive　relevant　measures　to　perform　global　influence　for　this　novel　model　and　develop　local　influence　analysis　based　on　the　conditional　expectation　of　the　complete-data　log-likelihood　function.　Some　useful　perturbation　schemes　are　discussed.　We　illustrate　the　finite　sample　performance　and　the　robustness　of　the　proposed　method　by　simulation　studies.　The　proposed　model　is　compared　with　other　procedures　based　on　a　real　dataset,　and　a　sensitivity　analysis　is　also　conducted.