[질문] 다중회귀분석에서 summary 와 anova 의 결과 차이...

[국제미아]

> out=lm(bwt~age+lwt+factor(race)+smoke+ptl+ht+ui, data=birthwt)

> summary(out)

Call:
lm(formula = bwt ~ age + lwt + factor(race) + smoke + ptl + ht +
    ui, data = birthwt)

Residuals:
    Min      1Q  Median      3Q     Max
-1838.7  -454.5    57.6   465.1  1711.0

Coefficients:
              Estimate Std. Error t value Pr(>|t|)   
(Intercept)   2934.132    311.450   9.421  < 2e-16 ***
age             -4.093      9.440  -0.434 0.665091   
lwt              4.301      1.722   2.497 0.013416 * 
factor(race)2 -488.196    149.604  -3.263 0.001318 **
factor(race)3 -353.334    114.319  -3.091 0.002314 **
smoke         -351.314    106.180  -3.309 0.001132 **
ptl            -47.423    101.663  -0.466 0.641443   
ht            -586.836    200.841  -2.922 0.003925 **
ui            -514.937    138.483  -3.718 0.000268 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 648.7 on 180 degrees of freedom
Multiple R-squared:  0.2424,    Adjusted R-squared:  0.2087
F-statistic: 7.197 on 8 and 180 DF,  p-value: 2.908e-08

> anova(out)
Analysis of Variance Table

Response: bwt
              Df   Sum Sq Mean Sq F value    Pr(>F)   
age            1   815483  815483  1.9380 0.1656022   
lwt            1  2967339 2967339  7.0519 0.0086284 **
factor(race)   2  4750632 2375316  5.6450 0.0041901 **
smoke          1  6291918 6291918 14.9529 0.0001538 ***
ptl            1   732501  732501  1.7408 0.1887130   
ht             1  2852764 2852764  6.7796 0.0099900 **
ui             1  5817995 5817995 13.8266 0.0002676 ***
Residuals    180 75741025  420783                     
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’

intercept가 없어서 그런가... 물론 둘 다 age 와 ptl 두 변수가 p-value가 높긴 한데

수치상으로 두 그룹이 매치가 안 됩니다...

다중회귀분석에서 summary와 anova는 각각 다른 의미의 p-value를 표시해주나요?

그리고 summary 에서는 factor(race) 를 왜 2,3 으로 쪼갠건가요?

더미변수로 바꾼 것 같긴 한데 그럼 anova는 왜 그냥 한꺼번에 했을까요...

혼자서 나름 연구한답시고 summary에서는 factor(race)2,3 를 더미변수로 쪼개서 해서 결과가 조금 다른 것 뿐인가 하고

factor 변수를 빼고 한 번 비교를 해 봤는데

> summary(lm(bwt~lwt+smoke+ht+ui, data=birthwt))

Call:
lm(formula = bwt ~ lwt + smoke + ht + ui, data = birthwt)

Residuals:
     Min       1Q   Median       3Q      Max
-1665.02  -452.62    11.16   473.64  1858.65

Coefficients:
            Estimate Std. Error t value Pr(>|t|)   
(Intercept) 2577.096    226.794  11.363  < 2e-16 ***
lwt            4.506      1.660   2.714 0.007270 **
smoke       -242.113    100.127  -2.418 0.016579 * 
ht          -649.098    206.327  -3.146 0.001931 **
ui          -549.878    139.424  -3.944 0.000114 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 669.9 on 184 degrees of freedom
Multiple R-squared:  0.1741,    Adjusted R-squared:  0.1561
F-statistic: 9.695 on 4 and 184 DF,  p-value: 3.886e-07

> anova(lm(bwt~lwt+smoke+ht+ui, data=birthwt))
Analysis of Variance Table

Response: bwt
           Df   Sum Sq Mean Sq F value    Pr(>F)   
lwt         1  3448639 3448639  7.6852 0.0061402 **
smoke       1  3326720 3326720  7.4135 0.0070964 **
ht          1  3646795 3646795  8.1268 0.0048597 **
ui          1  6979875 6979875 15.5545 0.0001139 ***
Residuals 184 82567628  448737                     
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1

그래도 여전히 조금 차이가 있는 것 같고...

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