5 Matrix Algebra and Quadratic Forms
From here on, the model has \(k\) regressors and is written in matrix form. This section collects the matrix results and the distribution theory that the rest of the course uses. Most of it is the theory of quadratic forms \(X'AX\) in normal random vectors, which is what lies behind every \(\chi ^2\), \(t\) and \(F\) statistic in regression. At the end the theory is applied to the residuals of a regression, which delivers the two facts that Section 2.4 had to take on trust.
5.1 Matrix results
5.2 Random vectors
5.3 The multivariate normal distribution
5.4 Distributions of quadratic forms
5.5 Application: the residuals of a regression
5.6 Matrices in software
5.7 Practice Problems
5.2 Random vectors
5.3 The multivariate normal distribution
5.4 Distributions of quadratic forms
5.5 Application: the residuals of a regression
5.6 Matrices in software
5.7 Practice Problems
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