V2EX linear model

Linear Model

Definition / 定义

linear model(线性模型):一种用自变量的线性组合来解释或预测因变量的统计/机器学习模型。常见形式如
\( y = \beta_0 + \beta_1 x_1 + \cdots + \beta_p x_p + \varepsilon \)。
(也可泛指满足“对参数线性”的模型;在不同语境中含义略有扩展。)

Pronunciation / 发音

/lnir mdl/(美式常见)

Examples / 例句

We used a linear model to predict house prices.
我们用线性模型来预测房价。

After checking the residuals, the team found the linear model violated the equal-variance assumption and considered a transformation.
检查残差后,团队发现线性模型不满足方差齐性假设,于是考虑对数据做变换。

Etymology / 词源

linear 来自拉丁语 linearis(“线的、成直线的”),源于 linea(“线、绳”);model 来自拉丁语 modulus(“尺度、模板”)。合在一起强调:用“直线式/线性关系”的结构来刻画数据与变量之间的关系。

Related Words / 相关词

Literary Works / 文学作品

  • Linear Models(McCullagh & Nelder)
  • Applied Linear Statistical Models(Kutner, Nachtsheim, Neter 等)
  • The Elements of Statistical Learning(Hastie, Tibshirani, Friedman)
  • An Introduction to Statistical Learning(James, Witten, Hastie, Tibshirani)
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