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--- suppressor_in_multiple_regression [2025/11/09 12:02] – hkimscil
+++ suppressor_in_multiple_regression [2025/11/11 01:09] (current) – hkimscil
@@ Line 470: / Line 470: @@
 >
 </code>
-====== Headline ======
+====== 도식화 ======
-{{pasted:20251109-205717.png?600}}
+{{pasted:20251109-205717.png?400}}
 <code>
 lm.y.x2 <- lm(y ~ x2)
 summary(lm.y.x2)$r.squared = 0
 lm.y.x1 <- lm(y ~ x1)
-summary(lm.y.x1)$r.squared = a
+summary(lm.y.x1)$r.squared = a, p > .05 (may be not significant)
+# 그러나 아래처럼 x2가 포함됨으로써
+# x1 내의 x2와 관련된 부분이 제거되어
+# 분석됨으로 significant하게 됨
 lm.y.x1x2 <- lm(y ~ x1 +  x2)
 summary(lm.y.x1)$r.squared = a
+</code>
+<code>
+> cor(cs.dat)
+                Sales  CompPrice      Price
+Sales      1.00000000 0.06407873 -0.4449507
+CompPrice  0.06407873 1.00000000  0.5848478
+Price     -0.44495073 0.58484777  1.0000000
+> lm.y.x1 <- lm(Sales~Price, data = cs.dat)
+> lm.y.x2 <- lm(Sales~CompPrice, data = cs.dat)
+> lm.y.x1x2 <- lm(Sales~Price+CompPrice, data = cs.dat)
+> summary(lm.y.x1)$r.squared
+[1] 0.1979812
+> summary(lm.y.x1x2)$r.squared
+[1] 0.3578332
+> summary(lm.y.x1x2)$r.squared - summary(lm.y.x1)$r.squared
+[1] 0.159852   # x2 고유의 설명력? b, c, d 중 d 파트
+>
+> summary(lm.y.x2)$r.squared
+[1] 0.004106084   # 그러나 c, d 파트가 위의 결과보다 더 작음
+> lm.x1.x2 <- lm(Price~CompPrice, data = cs.dat)
+> res.x1x2 <- lm.x1.x2$residuals
+> lm.y.onlyx1<- lm(Sales~res.x1x2)
+> summary(lm.y.onlyx1)$r.squared
+[1] 0.3537271
+> summary(lm.y.x1x2)$r.squared
+[1] 0.3578332
+>
+> summary(lm.y.x1x2)$r.squared - summary(lm.y.onlyx1)$r.squared
+[1] 0.004106084
+>
+>
+> summary(lm.y.x1)$r.squared
+[1] 0.1979812
+>
+> summary(lm.y.x1)$r.squared
+[1] 0.1979812
+> pcor.test(Sales, Price, CompPrice)
+    estimate     p.value statistic   n gp  Method
+-0.5959744 9.95161e-40 -14.78787 400  1 pearson
+> pcor.test(Sales, Price, CompPrice)$estimate^2
+[1] 0.3551855
+> summary(lm.y.x2)$r.squared
+[1] 0.004106084
+>
 </code>