The application of linear regression to data analysis is traditionally a tedious calculation delegated to a computer. This article presents a physical model to facilitate an intuitive way of thinking about the slope of a fit. In this simple model, data points are envisioned as beads applying torques on a massless, rigid, horizontal rod. To illustrate how this model can help colleagues directly address special questions about fits, the model is applied to two situations in which there are repeated measurements of data. This rod-and-bead model also arrives at the coefficient of determination formula in a very straightforward way and makes the recollection of the least-squared slope formula and coefficient of determination much easier.

中文翻译：

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直观线性回归的物理模型

将线性回归应用于数据分析传统上是委托给计算机的繁琐计算。本文提出了一个物理模型，以方便直观地思考拟合斜率。在这个简单的模型中，数据点被设想为在无质量、刚性、水平杆上施加扭矩的珠子。为了说明该模型如何帮助同事直接解决有关拟合的特殊问题，该模型应用于重复测量数据的两种情况。这种杆珠模型还以非常直接的方式得出了决定系数公式，并且使最小二乘斜率公式和决定系数的回忆变得更加容易。