Projection Matrices and Least Squares
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Lesson Description:
Projection Matrices and Least Squares -- Lecture 16. Review of projection matrices, orthogonality, and a discussion of least squares matrices and computation of best straight line.
Gilbert Strang, 18.06 Linear Algebra, Spring 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed November 22, 2008). License: Creative Commons BY-NC-SA.
More info at: http://ocw.mit.edu/terms
Additional Resources:
- Least Squares Java Applet - Java applet to play around with to investigate Least Squares lines / equations.
- Least Squares Java Applet 2 - Another interactive Least Squares java applet to play around with.
Questions answered by this video:
- How do you find a least squares matrix?
- What is a best fit line?
- What is a best straight line?
- How do you find the best fit line for a data set?
- What is x hat?
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Staff Review
This video talks a lot more about projections and orthogonal spaces as a lead-in to finding a least-squares matrix for a data set. By minimizing the error of a straight line through data points, it is explained how to do linear regression to find the best fit line. A great explanation of what is going on, why it works, and how to find the best straight line.
