The process of single-point incremental forming (SPIF) is a relatively new technology that is primarily used in the production of prototypes and small quantities of products. However, the process has several limitations with respect to the quality characteristics of its products. This study examined the effects of four process parameters—namely, tool diameter, feed rate, step size, and sheet thickness—on the characteristics of the final product. A total of 15 product responses were measured and/or calculated during the experiments. The responses fell under three different categories; surface profile accuracy, strain/stress/thinning, and forming forces. In previous published work, responses were studied separately for each category. The aim of this paper was to determine the relationships between responses using a principal component analysis (PCA). PCA is a well-known multivariate analysis technique used to reduce the dimensionality of data. As a result of the PCA, the product’s characteristic dimensions were reduced from 15 while 71% of the total variance of data was preserved. The results showed that only 8 responses were enough to characterize the final product, rather than 15. A relationship was detected between the side wall accuracy and forming forces and between strain, circularity, and surface roughness. These findings could not be detected with single-variable analyses.