📄 中文摘要
线性回归的核心在于将数据点投影到一个最佳拟合的直线上。通过几何视角，线性回归可以被理解为在高维空间中寻找一个最小化误差的过程。该方法涉及到向量和投影的基本概念，利用这些概念可以更直观地理解线性回归的工作原理。通过图形化的方式，读者能够更清晰地看到数据点与回归线之间的关系，以及如何通过最小化距离来实现最佳拟合。这种几何直觉不仅有助于理解线性回归的数学背景，也为后续更复杂的回归分析奠定了基础。
线性回归实际上是一个投影问题，第一部分：几何直觉
📄 English Summary
Linear Regression Is Actually a Projection Problem, Part 1: The Geometric Intuition
The essence of linear regression lies in projecting data points onto a best-fit line. From a geometric perspective, linear regression can be understood as a process of finding a solution that minimizes error in high-dimensional space. This method involves fundamental concepts of vectors and projections, which allow for a more intuitive grasp of how linear regression operates. Through graphical representations, readers can clearly observe the relationship between data points and the regression line, as well as how minimizing distances leads to optimal fitting. This geometric intuition not only aids in understanding the mathematical foundations of linear regression but also lays the groundwork for more complex regression analyses in the future.