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Variable selection algorithm for Sliced Inverse Regression using penaltyfunction is proposed. We noted SIR models can be expressed as generalizedeigenvalue decompositions and incorporated penalty functions on them. Wefound from small simulation that the HARD penalty function seems to bethe best in preserving original directions compared with other well-knownpenalty functions. Also it turned out to be eective in forcing coecientestimates zero for irrelevant predictors in regression analysis. Results fromillustrative examples of simulated and real data sets will be provided.