📉 残差计算器（线性回归）Residual Calculator (Linear Regression)

使用说明与常见问题How-to & FAQ

「残差计算器（线性回归）」是什么？What is the Residual Calculator (Linear Regression) tool?

输入成对的 (x, y) 数据，拟合最小二乘直线 ŷ = a + bx，列出每个点的预测值和残差 y − ŷ，并给出残差平方和、残差标准误和最大残差。Enter paired (x, y) data to fit the least-squares line ŷ = a + bx and list each point's predicted value and residual y − ŷ, with the residual sum of squares, residual standard error and the largest residual.

如何使用「残差计算器（线性回归）」？How do I use the Residual Calculator (Linear Regression) tool?

在「残差计算器（线性回归）」中，填写上方字段等参数，结果会随输入实时计算并显示在下方。In the Residual Calculator (Linear Regression): Fill in the fields above; results are recalculated instantly as you type.

残差是什么？What is a residual?

残差 = 实际值 y − 回归直线的预测值 ŷ。正残差表示点在直线上方。最小二乘直线的残差之和为 0。Residual = observed y − predicted ŷ from the regression line; a positive residual means the point is above the line. Least-squares residuals add up to 0.

残差有什么用？What are residuals for?

看残差能判断直线模型是否合适：残差应随机分布在 0 两侧；如果呈弯曲或喇叭形规律，说明关系不是线性的或方差不恒定。They show whether a straight line fits: residuals should scatter randomly around 0. A curved or funnel pattern means the relationship is not linear or the variance is not constant.

残差标准误怎么算？How is the residual standard error found?

s = √(SSE ÷ (n − 2))，除以 n − 2 是因为估计了截距和斜率两个参数。s = √(SSE ÷ (n − 2)); n − 2 because two parameters (intercept and slope) were estimated.

计算精度如何？How precise are the results?

「残差计算器（线性回归）」使用 JavaScript 双精度浮点数（约 15–16 位有效数字）；极大或极小的数值可能存在精度误差。The Residual Calculator (Linear Regression) uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.

「残差计算器（线性回归）」免费吗？需要注册吗？Is the Residual Calculator (Linear Regression) free? Do I need an account?

「残差计算器（线性回归）」完全免费，无需注册或安装，打开网页即可使用，手机和电脑都能用；输入的内容只在你的浏览器本地处理。The Residual Calculator (Linear Regression) is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.