Single image super-resolution (SISR) deals with a fundamental problem of upsampling a low-resolution (LR) image to its high-resolution (HR) version. Last few years have witnessed impressive progress propelled by deep learning methods. However, one critical challenge faced by existing methods is to strike a sweet spot of deep model complexity and resulting SISR quality. This paper addresses this pain point by proposing a linearly-assembled pixel-adaptive regression network (LAPAR), which casts the direct LR to HR mapping learning into a linear coefficient regression task over a dictionary of multiple predefined filter bases. Such a parametric representation renders our model highly lightweight and easy to optimize while achieving state-of-the-art results on SISR benchmarks. Moreover, based on the same idea, LAPAR is extended to tackle other restoration tasks, e.g., image denoising and JPEG image deblocking, and again, yields strong performance.