In this study, we investigate whether a nonlinear intensity component can be beneficial for multispectral (MS) pansharpening based on component-substitution (CS). In classical CS methods, the intensity component is a linear combination of the spectral components and lies on a hyperplane in the vector space that contains the MS pixel values. Starting from the hyperspherical color space (HCS) fusion technique, we devise a novel method, in which the intensity component lies on a hyper-ellipsoidal surface instead of on a hyperspherical surface. The proposed method is insensitive to the format of the data, either floating-point spectral radiance values or fixed-point packed digital numbers (DNs), thanks to the use of a multivariate linear regression between the squares of the interpolated MS bands and the squared lowpass filtered Pan. The regression of squared MS, instead of the Euclidean radius used by HCS, makes the intensity component no longer lie on a hypersphere in the vector space of the MS samples, but on a hyperellipsoid. Furthermore, before the fusion is accomplished, the interpolated MS bands are corrected for atmospheric haze, in order to build a multiplicative injection model with approximately de-hazed components. Experiments on GeoEye-1 and WorldView-3 images show consistent advantages over the baseline HCS and a performance slightly superior to those of some of the most advanced methods.