R语言自学笔记：回归分析基础

最新推荐文章于 2025-11-09 11:45:06 发布

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最新推荐文章于 2025-11-09 11:45:06 发布 · 5.5k 阅读

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#r语言 #线性回归

本文介绍了R语言中的回归分析基础知识，包括线性回归的lm()函数及其评估，多元线性回归分析，以及多元非线性回归。文中详细探讨了glm()函数在非线性模型中的应用，还提到了使用earth和caret工具包进行机器学习回归分析，并展示了如何用nls和drm函数进行非线性最小二乘法拟合。同时，还讨论了如何评估自变量的重要性。

一. 线性回归

1. lm()函数返回的是对于输入变量的预测模型，返回的结果可以配合许多函数进行使用。

> lm.model <- lm(wt ~ mpg, data = mtcars)


> coefficients(lm.model) # 提取系数
(Intercept)         mpg 
   6.047255   -0.140862 

> confint(lm.model, level=0.95) # 得到线性模型相关系数的分布后，限定区间，得到边界点的值
                 2.5 %     97.5 %
(Intercept)  5.4168245  6.6776856
mpg         -0.1709569 -0.1107671


> fitted(lm.model) # 用建立的模型去预测wt
          Mazda RX4       Mazda RX4 Wag          Datsun 710      Hornet 4 Drive   Hornet Sportabout             Valiant          Duster 360 
           3.089154            3.089154            2.835602            3.032809            3.413136            3.497653            4.032929 
          Merc 240D            Merc 230            Merc 280           Merc 280C          Merc 450SE          Merc 450SL         Merc 450SLC 
           2.610223            2.835602            3.342705            3.539912            3.737119            3.610343            3.906153 
 Cadillac Fleetwood Lincoln Continental   Chrysler Imperial            Fiat 128         Honda Civic      Toyota Corolla       Toyota Corona 
           4.582291            4.582291            3.976584            1.483327            1.765051            1.272034            3.018723 
   Dodge Challenger         AMC Javelin          Camaro Z28    Pontiac Firebird           Fiat X1-9       Porsche 914-2        Lotus Europa 
           3.863894            3.906153            4.173791            3.342705            2.201723            2.384844            1.765051 
     Ford Pantera L        Ferrari Dino       Maserati Bora          Volvo 142E 
           3.821636            3.272274            3.934325            3.032809 



> residuals(lm.model) # 预测与实际之间的残差
          Mazda RX4       Mazda RX4 Wag          Datsun 710      Hornet 4 Drive   Hornet Sportabout             Valiant          Duster 360 
        -0.46915365         -0.21415365         -0.51560210          0.18219114          0.02686382         -0.03765336         -0.46292884 
          Merc 240D            Merc 230            Merc 280           Merc 280C          Merc 450SE          Merc 450SL         Merc 450SLC 
         0.57977705          0.31439790          0.09729481         -0.09991195          0.33288129          0.11965707         -0.12615307 
 Cadillac Fleetwood Lincoln Continental   Chrysler Imperial            Fiat 128         Honda Civic      Toyota Corolla       Toyota Corona 
         0.66770947          0.84170947          1.36841594          0.71667281         -0.15005113          0.56296577         -0.55372266 
   Dodge Challenger         AMC Javelin          Camaro Z28    Pontiac Firebird           Fiat X1-9       Porsche 914-2        Lotus Europa 
        -0.34389448         -0.47115307         -0.33379081          0.50229481         -0.26672324         -0.24484380         -0.25205113 
     Ford Pantera L        Ferrari Dino       Maserati Bora          Volvo 142E 
        -0.65163589         -0.50227421         -0.36432547         -0.25280886 



> anova(lm.model) # anova table
Analysis of Variance Table

Response: wt
          Df  Sum Sq Mean Sq F value    Pr(>F)    
mpg        1 22.3431 22.3431  91.375 1.294e-10 ***
Residuals 30  7.3356  0.2445                      
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1



> vcov(lm.model) # 协方差矩阵
             (Intercept)           mpg
(Intercept)  0.095289963 -0.0043626666
mpg         -0.004362667  0.0002171494



> influence(lm.model) # 相当与对分析的结果进行一个汇总
$hat
          Mazda RX4       Mazda RX4 Wag          Datsun 710      Hornet 4 Drive   Hornet Sportabout             Valiant          Duster 360 
         0.03198439          0.03198439          0.03776901          0.03277255          0.03296737          0.03476902          0.06102792 
          Merc 240D            Merc 230            Merc 280           Merc 280C          Merc 450SE          Merc 450SL         Merc 450SLC 
         0.04774195          0.03776901          0.03195442          0.03590963          0.04334604          0.03816586          0.05249086 
 Cadillac Fleetwood Lincoln Continental   Chrysler Imperial            Fiat 128         Honda Civic      Toyota Corolla       Toyota Corona 
         0.11464634          0.11464634          0.05705606          0.16580983          0.12563611          0.20060244          0.03301399 
   Dodge Challenger         AMC Javelin          Camaro Z28    Pontiac Firebird           Fiat X1-9       Porsche 914-2        Lotus Europa 
         0.04996488          0.05249086          0.07220085          0.03195442          0.07740711          0.06226177          0.12563611 
     Fo

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