Linear regression is the workhorse of data analysis. It is the first step, and often the only step, in fitting a simple model to data. This brief book explains the essential mathematics required to understand and apply regression analysis. The tutorial style of writing, accompanied by over 30 diagrams, offers a visually intuitive account of linear regression, including a brief overview of nonlinear and Bayesian regression. Hands-on experience is provided in the form of numerical examples, included as Matlab code at the end of each chapter, and implemented online as Python and Matlab code. Supported by a comprehensive glossary and tutorial appendices, this book provides an ideal introduction to regression analysis.