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2003 | OriginalPaper | Chapter

The Linear Regression Model

Author : Jürgen Groß

Published in: Linear Regression

Publisher: Springer Berlin Heidelberg

Included in: Professional Book Archive

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In this chapter, we consider point estimation of the parameters ß ∈ ℝP and σ2 ∈ (0, ∞) in the linear regression model $$y = X\beta + \varepsilon , \varepsilon \sim (0,{{\sigma }^{2}}{{I}_{n}}) $$ We will focus our attention to the ordinary least squares estimator$$ \hat \beta = (X'X)^{ - 1} X'y $$ and the least squares variance estimator$$ \hat \sigma ^2 = \frac{1} {{n - p}}(y - X\hat \beta )'(yy - X\hat \beta ) $$ both estimators being unbiased for ß and σ2, respectively.

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