A number of new relations between the Kaplan-Yorke dimension, phase space contraction, transport coefficients and the maximal Lyapunov exponents are given for dissipative thermostatted systems, subject to a small but non-zero external field in a nonequilibrium stationary state. A condition for the extensivity of phase space dimension reduction is given. A new expression for the linear transport coefficients in terms of the Kaplan-Yorke dimension is derived. Alternatively, the Kaplan-Yorke dimension for a dissipative macroscopic system can be expressed in terms of the linear transport coefficients of the system. The agreement with computer simulations for an atomic fluid at small shear rates is very good.