Best solution & OLS

Best-fit models as projections onto model subspaces

This chapter develops ordinary least squares through concrete examples of fitting lines, parabolas, planes and paraboloids. It shows how a regression model defines a subspace in the data space, how the best solution is obtained by projection and how changing the model changes the geometry of the fit.

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Chapter contents

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Topic	Pages
OLS example 1: fitting a line	1–4
OLS example 2: fitting a parabola with 2 parameters	5–8
Two models for same dataset	9–11
Higher-dimensional set	12–13
Summary: models with one input variable	14–16
Model with 2 input variables	17
Non-linear model with 2 input variables	18–21
Summary: models with > 1 input variable	22–23
Two ways to change a regression model	24–26

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