A Geometric View on Inner Transformation between the Variables of a Linear Regression Model

In the teaching and researching of linear regression analysis, it is interesting enlightening to explore how dependent variable vector can be inner-transformed into coefficient estimator from a visible geometrical view. As an example, roadmap such inner transformation presented based on simple multiple model in this work. By applying matrix algorithms like singular value decomposition (SVD) Moore-Penrose generalized inverse, lands right space independent metamorphosed through three-step transformation. This work explores relationship between as well presents new approach for rotating.