A novel approach to reaction set reduction is presented which utilizes variable selection (VS) techniques from the statistics literature to identify a family of reduced reactions sets. By taking advantage of the structure of elementary reactions sets and the nature of macroscopic reactor balances, a linear regression model of the complete reaction set is developed from a sampling of data points along the reactor concentration and reaction-rate profiles. Utilizing a modification of the Leaps and Bounds algorithm (Furnival and Wilson, 1974, Techometrics, 16(4), 499-511), the best reduced linear models for each parameter subset size are identified, and these solutions are used as approximations of the global solutions of the reaction set reduction problem that would be found by complete enumeration of all reduced reaction sets. With the use of weighted least squares, the procedure can be directed to preferentially select reduced reaction sets that accurately represent the full reaction set kinetics for specific species while downplaying the importance of other species. The proposed VS procedure offers significant computational savings over complete enumeration by avoiding the repeated integration of differential equations for reduced reaction sets. The VS procedure is tested on an 18 reaction 10 species reaction set for a batch reactor, and results compare favorably with those found using complete enumeration.