Least Squares Method Part 1: background and derivation, with examples

In this lecture, we look at the least squares method, a fundamental technique in data analysis used for finding the line or curve of best fit for a given dataset. We start by reviewing key linear algebra concepts such as matrix multiplication, dot product, matrix transpose, and matrix inverse--skip this slide if you are solid on these ideas.

These concepts lay the groundwork for applying the least squares method to both perfect and imperfect data sets. We derive the least squares formula using linear algebra and extend its application from linear to polynomial models. The lecture includes practical MATLAB implementations, showing how to compute coefficients for linear and quadratic fits efficiently.

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