Geometry and Least Squares

This lecture explores the geometry of least squares from two perspectives: row geometry, focusing on observations, and column geometry, focusing on variables. The row geometry involves scatterplot interpretation, while the column geometry deals with the column space of the explanatory variables. The lecture delves into the interpretations of least squares estimators, hyperplanes, projections, residuals, and the hat matrix. It also covers the dual space perspective, the column vectors of X, the MLE estimates of B, and the unique vectors of coordinates with respect to the X-column basis.