Chapter 3: Problem 22
Readers may have encountered the multiple regression model in a previous course in statistics. We can briefly write it as follows. Suppose we have a vector of \(n\) observations \(\mathbf{Y}\) which has the distribution \(N_{n}\left(\mathbf{X} \boldsymbol{\beta}, \sigma^{2} \mathbf{I}\right)\), where \(\mathbf{X}\) is an \(n \times p\) matrix of known values, which has full column rank \(p\), and \(\beta\) is a \(p \times 1\) vector of unknown parameters. The least squares estimator of \(\boldsymbol{\beta}\) is $$ \widehat{\boldsymbol{\beta}}=\left(\mathbf{X}^{\prime} \mathbf{X}\right)^{-1} \mathbf{X}^{\prime} \mathbf{Y} $$
Short Answer
Step by step solution
Key Concepts
These are the key concepts you need to understand to accurately answer the question.