Multiple regression is introduced with a case study of a company that retails a wide range of mobile phones. The company has 10 stores and has records of sales from these stores. The company also knows the average number of pedestrians passing by each shore during opening hours and its floor area. The objective is to choose between two prospective new stores which are available for purchase. Only the pedestrian statistics and floor area are known for these two stores, so a regression of sales on pedestrians and area is fitted and used to inform the decision. This case study is used to illustrate the matrix formulation of the multiple regression model, the fitting of the model, and the use of the model for making predictions. Model building, including quadratic terms and indicator variables is then demonstrated through examples and the fit between data and models is assessed. The use of the multiple regression model for the analysis of time series, including lagged terms, is covered. The concluding sections cover the fitting of models by non-linear least squares, and in particular logistic and Poisson regression models. The use of software functions, and the interpretation of their output is emphasised throughout the chapter. The experiment ‘Company efficiency, resources and teamwork” in Appendix E is designed for groups of six, or so, participants. They are asked to make a subjective assessment of a company, for which they have worked, in terms of efficiency, resources and teamwork. on a six point scale. They then fit a regression of efficiency on resources and teamwork and interpret the results. The chapter ends with: a summary of: notation used; the main results, MATLAB and R syntax; and exercises.