Multiple Linear Regression

Konstantin M. Zuev ()
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Konstantin M. Zuev: California Institute of Technology, Department of Computing and Mathematical Sciences

Chapter 12 in Fundamentals of Statistical Inference, 2026, pp 307-363 from Springer

Abstract: Abstract The behavior of complex systems often depends on many different factors. For example, the level of blood cholesterol depends on age, diet, physical exercise, and various genetic factors. A stock price tomorrow may depend on its price over the last several days, the company’s performance measures, and overall economic and financial factors. For most real systems, it is impossible to account for all factors that affect its behavior. That is why we try to identify the most important factors, or simply factors that are available for measurements, and build a stochastic model of the system with the hope that it will mimic the behavior of the real system adequately, at least to some extent. In this final chapter, we will discuss the multiple linear regression model, which is an extension of the simple linear regression model for the case, where system’s response Y depends not just on a single input X, but on a vector X = (X(1), . . . ,X(p)) of p different inputs.

Keywords: multiple linear regression; ordinary least squares; Gauss-Markov theorem; ranking predictors; multivariate multiple linear regression (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1007/978-3-032-03848-7_12

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