Cellular behavior in response to stimulatory cues is governed by information encoded within a complex intracellular signaling network. An understanding of how phenotype is determined requires the distributed characterization of signaling processes (e.g., phosphorylation states and kinase activities) in parallel with measures of resulting cell function. We previously applied quantitative mass spectrometry methods to characterize the dynamics of tyrosine phosphorylation in human mammary epithelial cells with varying human epidermal growth factor receptor 2 (HER2) expression levels after treatment with epidermal growth factor (EGF) or heregulin (HRG). We sought to identify potential mechanisms by which changes in tyrosine phosphorylation govern changes in cell migration or proliferation, two behaviors that we measured in the same cell system. Here, we describe the use of a computational linear mapping technique, partial least squares regression (PLSR), to detail and characterize signaling mechanisms responsible for HER2-mediated effects on migration and proliferation. PLSR model analysis via principal component inner products identified phosphotyrosine signals most strongly associated with control of migration and proliferation, as HER2 expression or ligand treatment were individually varied. Inspection of these signals revealed both previously identified and novel pathways that correlate with cell behavior. Furthermore, we isolated elements of the signaling network that differentially give rise to migration and proliferation. Finally, model analysis identified nine especially informative phosphorylation sites on six proteins that recapitulated the predictive capability of the full model. A model based on these nine sites and trained solely on data from a low HER2-expressing cell line a priori predicted migration and proliferation in a HER2-overexpressing cell line. We identify the nine signals as a network gauge, meaning that when interrogated together and integrated according to the quantitative rules of the model, these signals capture information content in the network sufficiently to predict cell migration and proliferation under diverse ligand treatments and receptor expression levels. Examination of the network gauge in the context of previous literature indicates that endocytosis and activation of phosphoinositide 3-kinase (PI3K)-mediated pathways together represent particularly strong loci for the integration of the multiple pathways mediating HER2s control of mammary epithelial cell proliferation and migration. Thus, a PLSR modeling approach reveals critical signaling processes regulating HER2-mediated cell behavior.