PSet 25: Matrices and Linear Regression

(videos: up to and including Linear Regression)

1. Invert this matrix using Gauss-Jordan elimination:

2. Given the following data, perform linear regression. Give me the weight vector $w$. Feel free to use tools to multiply and invert matrices, but show each step.

   Recall the weight vector $w$ equation:

   $\textbf{w}=(X^TX)^{-1}X^T\textbf{y}$

   Here is the input $X$ and their values $y$:

   $$X = \begin{pmatrix} 1 & 5\\ 1&10\\ 1&15\\ 1&20\\ \end{pmatrix}, \textbf{y}=\begin{pmatrix} 12.06\\ 18.472\\ 26.378\\ 34.724\\ \end{pmatrix}$$

   (2)