The line of best fit

M. Edge
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Abstract

One way to visualize a set of data on two variables is to plot them on a pair of axes. A line that “best fits” the data can then be drawn as a summary. This chapter considers how to define a line of “best” fit—there is no sole best choice. The most commonly chosen line to summarize the data is the “least-squares” line—the line that minimizes the sum of the squared vertical distances between the points and the line. One reason for the least-squares line’s popularity is convenience, but, as will be seen later, it is also related to some key ideas in statistical estimation. The derivations of expressions for the intercept and slope of the least-squares line are discussed.
最合适的线
可视化关于两个变量的一组数据的一种方法是将它们绘制在一对坐标轴上。然后可以画一条“最适合”数据的线作为总结。本章考虑如何定义“最佳”匹配线——没有唯一的最佳选择。最常选择的汇总数据的线是“最小二乘”线——这条线使点与线之间垂直距离的平方和最小。最小二乘线受欢迎的一个原因是方便,但是,正如稍后将看到的,它也与统计估计中的一些关键思想有关。讨论了最小二乘直线的截距和斜率表达式的推导。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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