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Explore multi-dimensional linear regression and polynomial regression techniques in this 81-minute university lecture from the University of Utah's Foundations of Data Analysis course. Learn how to extend simple linear regression to multiple dimensions by transforming input vectors x_i to augmented vectors (1, x_i) = ~x_i, and discover the optimal least-squares solution using the closed-form formula alpha^* = (~X^T ~X)^{-1} ~X^T y. Master polynomial regression by further extending the feature space to include higher-order terms (1, x_i, x_i^2, ..., x_i^p) while applying the same mathematical framework and closed-form solution for parameter estimation.
