In the spectral prediction technology of the primary ink of halftone prints manuscript, the representative vector number obtained by principal component analysis will be greater than the actual number of primary inks used in the reflectance space. The space is not suitable for spectral prediction, and the based vectors obtained by PCA will appear negative. There is no physical meaning. Aiming at the above problems, a subtractive linear experimental space model and space conversion model were created. And the factors influencing the linearity degree of the space n value were explored. Through experiments and optimization algorithms, the methods for determining the best n value were found innovatively. Then the prediction experiments of the primary ink of halftone prints manuscript were carried out in the space. The experimental results showed that, under different n values, the n value corresponding to the minimum square value of the f norm was effective for determining the best n value to establishing the linear empirical space. Finally, the n value was determined to be 3.5. In the space, the number of representative base vectors obtained by the method of number prediction was exactly equal to 4, which was the actual primary ink number. In spectral prediction, in addition to K color, other CMY color compared to the actual primary ink spectrum, the fitting degree of GFC was greater than 99.9%. That was to establish a new method for the optimization of n proposed in this paper. The value of color space was an effective linear empirical linear space which can be used as a halftone color ink number prediction and spectral prediction. That is to say, the space created by the new method is an effective linear space that can be used to predict the number of primary ink and the spectrum of halftone prints manuscript.