How to solve linear regression using a QR matrix decomposition.
Linear regression and the matrix reformulation with the normal equations.
In this tutorial, you discovered the matrix formulation of linear regression and how to solve it using direct and matrix factorization methods.
The Linear Algebra View of Least-Squares Regression.
Singular-value decomposition on Wikipedia.
Linear least squares (mathematics) on Wikipedia.
Section 15.4 General Linear Least Squares, Numerical Recipes: The Art of Scientific Computing, Third Edition, 2007.
Section 2.9 The Moore-Penrose Pseudoinverse, Deep Learning, 2016.
Chapter 12, Singular-Value and Jordan Decompositions, Linear Algebra and Matrix Analysis for Statistics, 2014.
Chapter 5, Orthogonalization and Least Squares, Matrix Computations, 2012.
Lecture 11, Least Squares Problems, Numerical Linear Algebra, 1997.
Section 4.3 Least Squares Approximations, Introduction to Linear Algebra, Fifth Edition, 2016.
No Bullshit Guide To Linear Algebra, 2017.
Section 7.7 Least squares approximate solutions.
This section provides more resources on the topic if you are looking to go deeper. If you explore any of these extensions, I’d love to know.
Load a tabular dataset and test each linear regression method and compare the results.
Test each linear regression on your own small contrived dataset.
Implement linear regression using the built-in lstsq() NumPy function.
This section lists some ideas for extending the tutorial that you may wish to explore. Scatter Plot of SVD Solution to the Linear Regression Problem Extensions
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