The substituent parameter is now defined by field and resonance effects, F and R, which are dependent on the individual substituent.  Constants r and f account for the importance of each of the two effects.  These constants do not depend on the substituent but instead depend on the set of Hammett substituent parameters (σ, σ, σ, σ, etc.).
In order to find the weighted constants, r and f, for each set of substituent parameters, one would need to establish the fact that each new substituent parameter σ could be written as a linear combination of specific reaction substituent parameters, i.e.
where σ and σ are specific substituent parameters (i.e. σ, σ, etc.) and c and c are constants independent of the substituent (depend on the reaction conditions, i.e. temperature, solvent, and individual reaction being studied).  This can be expressed more generically as:
where i  is an intercept to keep from fixing the origin at (0,0). If this was not done, the equation would give exceedingly more weight to the unsubstituted compounds that one is trying to make a comparison to using this equation.
A linear least-squares analysis is used to determine the coefficients/constants a, b, and i (Swain and Lupton used a procedure called DOVE: Dual Obligate Vector Evaluation).
Constants were first based on three previous reactions (σ, σ, σ), which leads to more possible errors since the compiled data is only a minimal combination of a much larger pool.  Seeing possible error in this limited pool, the data pool was increased by assigning a scale to begin with. A zero-scale is used for hydrogen, because it is known to neither readily donate or accept electron density when attached to a carbon atom due to similar electronegativities. A value of 1 was assigned to NO, because previous research determined the effect of this substituent was predominantly due to resonance. Lastly, F was set equal to R for both components so that the field effects could be compared directly to the resonance effects. This then leads to:
:F = R = 0 for H (Hydrogen).
:F = R = 1 for NO (Nitrogen Dioxide).
Fig. 2 shows some relative F and R values that Swain and Lupton founded.