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Simple Linear Regression

In: Fundamentals of Statistical Inference

Author

Listed:
  • Konstantin M. Zuev

    (California Institute of Technology, Department of Computing and Mathematical Sciences)

Abstract

Suppose we are interested in studying and learning about a certain phenomenon that can be schematically represented as a system that takes an “input” X and generates or associates with X a “response” Y . Let D = {(X1, Y1), . . . , (Xn, Yn)} be the data, a collection of inputs and the corresponding responses, obtained by experiment or observation of the phenomenon. Regression analysis is the study of dependence between X and Y . The primary goal of regression analysis is to construct a stochastic model for predicting response Y from a new input X based on the observed data D. Regression analysis originated in the early XIX century in the works of Adrien-Marie Legendre and Carl Gauss, who used astronomical observations for studying the orbits of planets and comets around the Sun. The theory of regression and its methods were further developed, and applications were extended to other domains by Francis Galton, Karl Pearson, and Ronald Fisher. Regression analysis is still an active area of modern research and its methods play a central role in machine learning, information and data sciences. In this chapter, we will study the simplest version of the model, namely, the simple linear regression model.

Suggested Citation

  • Konstantin M. Zuev, 2026. "Simple Linear Regression," International Series in Operations Research & Management Science, in: Fundamentals of Statistical Inference, chapter 11, pages 263-305, Springer.
    • Handle: RePEc:spr:isochp:978-3-032-03848-7_11
    DOI: 10.1007/978-3-032-03848-7_11
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