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--- partial_and_semipartial_correlation [2024/10/16 08:03] – [e.g. Using ppcor.test with 4 var] hkimscil
+++ partial_and_semipartial_correlation [2024/10/17 10:28] (current) – [e.g. Using ppcor.test with 4 var] hkimscil
@@ Line 441: / Line 441: @@
 # install.packages("ppcor")
 library(ppcor)
+reg.g.sh <- lm(GREV ~ SATV + HSGPA)
+res.g.sh <- resid(reg.g.sh)
+reg.g.fh <- lm(GREV ~ FGPA + HSGPA)
+res.g.fh <- resid(reg.g.fh)
+reg.g.sf <- lm(GREV ~ SATV + FGPA)
+res.g.sf <- resid(reg.g.sf)
 reg.f.sh <- lm(FGPA ~ SATV + HSGPA)   # second regression
@@ Line 460: / Line 469: @@
 summary(reg.2)
 summary(reg.3)
+reg.1a <- lm(res.g.sh~res.f)
+reg.2a <- lm(res.g.fh~res.s)
+reg.3a <- lm(res.g.sf~res.h)
 reg.1$coefficient[2]
 reg.2$coefficient[2]
 reg.3$coefficient[2]
+reg.1a$coefficient[2]
+reg.2a$coefficient[2]
+reg.3a$coefficient[2]
 spr.y.f <- spcor.test(GREV, FGPA, scholar[,c("SATV", "HSGPA")])
@@ Line 576: / Line 593: @@
 > attach(scholar)
 The following objects are masked from scholar (pos = 3):
-    FGPA, GREV, HSGPA, SATV
-The following objects are masked from scholar (pos = 4):
-    FGPA, GREV, HSGPA, SATV
-The following objects are masked from scholar (pos = 5):
-    FGPA, GREV, HSGPA, SATV
-The following objects are masked from scholar (pos = 6):
-    FGPA, GREV, HSGPA, SATV
-The following objects are masked from scholar (pos = 7):
-    FGPA, GREV, HSGPA, SATV
-The following objects are masked from scholar (pos = 8):
-    FGPA, GREV, HSGPA, SATV
-The following objects are masked from scholar (pos = 9):
-    FGPA, GREV, HSGPA, SATV
-The following objects are masked from ivs.orthogonal (pos = 10):
-    FGPA, HSGPA, SATV
-The following objects are masked from ivs.orthogonal (pos = 11):
-    FGPA, HSGPA, SATV
-The following objects are masked from ivs.orthogonal (pos = 12):
-    FGPA, HSGPA, SATV
-The following objects are masked from scholar (pos = 13):
-    FGPA, GREV, HSGPA, SATV
-The following objects are masked from scholar (pos = 14):
-    FGPA, GREV, HSGPA, SATV
-The following objects are masked from scholar (pos = 15):
-    FGPA, GREV, HSGPA, SATV
-The following objects are masked from scholar (pos = 16):
-    FGPA, GREV, HSGPA, SATV
-The following objects are masked from scholar (pos = 17):
-    FGPA, GREV, HSGPA, SATV
-The following objects are masked from scholar (pos = 18):
-    FGPA, GREV, HSGPA, SATV
-The following objects are masked from scholar (pos = 19):
-    FGPA, GREV, HSGPA, SATV
-The following objects are masked from scholar (pos = 22):
-    FGPA, GREV, HSGPA, SATV
-The following objects are masked from scholar (pos = 23):
     FGPA, GREV, HSGPA, SATV
@@ Line 821: / Line 766: @@
 multiple regression 분석을 보면 독립변인의 coefficient 값은 각각
-  * HSGPA         -25.475
+  * HSGPA         8.3214
-  * FGPA          17.679
+  * FGPA          1.3994
-  * SATV           0.131
+  * SATV          0.8143
 이 기울기에 대해서 t-test를 각각 하여 HSGPA와 FGPA의 설명력이 significant 한지를 확인하였다. 그리고 이 때의 R<sup>2</sup> 값은
-  * 0.672 (67.2%) 이었다.
+  * 0.799 이었다.
 그런데 이 coefficient값은 독립변인 각각의 고유의 설명력을 가지고 (spcor.test(GREV, x1, 나머지제어)로 얻은 부분) 종속변인에 대해서 regression을 하여 얻은 coefficient값과 같음을 알 수 있다. 즉, <fc #ff0000>multiple regression의 독립변인의 b coefficient 값들은 고유의 설명부분을 (spr) 추출해서 y에 (GREV) regression한 결과와 같음을</fc> 알 수 있다.
-<code>
+또한 세 독립변인이 공통적으로 설명하는 부분은
-> reg.1$coefficient[2]
+  * 0.39
-res.f
+임을 알 수 있다.
-.68
-> reg.2$coefficient[2]
- res.s
-.1305
-> reg.3$coefficient[2]
-res.h
-.97
->
-</code>
 ====== e.g., 독립변인 들이 서로 독립적일 때의 각각의 설명력 ======
 In this example, the two IVs are orthogonal to each other (not correlated with each other). Hence, regress res.y.x2 against x1 would not result in any problem.