Least squares approximation is a mathematical technique used to find the best-fit line or curve for a set of data points by minimizing the sum of the squares of the differences between the observed values and the values predicted by the model. This method is closely related to concepts of orthogonality and projections, where the least squares solution represents the projection of data onto a subspace spanned by basis functions. By leveraging these principles, it allows for effective modeling and analysis of linear relationships in various contexts.
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