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--- partial_and_semipartial_correlation [2019/05/23 10:27] – [regression gpa against sat] hkimscil
+++ partial_and_semipartial_correlation [2019/05/26 23:04] – [Semipartial cor] hkimscil
@@ Line 323: / Line 323: @@
 ====== Semipartial cor ======
+<code>> tests <- read.csv("http://commres.net/wiki/_media/r/tests_cor.csv")
+> colnames(tests) <- c("ser", "sat", "clep", "gpa")
+> tests <- subset(tests, select=c("sat", "clep", "gpa"))
+> attach(tests)
+> cors <- cor(tests)
+> round(cors,3)
+       sat  clep   gpa
+sat  1.000 0.875 0.718
+clep 0.875 1.000 0.876
+gpa  0.718 0.876 1.000
+> lm.sat.clep <- lm(sat ~ clep, data = tests)
+> summary(lm.sat.clep)
+Call:
+lm(formula = sat ~ clep, data = tests)
+Residuals:
+     Min       1Q   Median       3Q      Max
+-101.860  -19.292    1.136   28.306   54.132
+Coefficients:
+            Estimate Std. Error t value Pr(>|t|)
+(Intercept)  -19.421    114.638  -0.169  0.86967
+clep          17.665      3.464   5.100  0.00093 ***
+---
+Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
+Residual standard error: 48.2 on 8 degrees of freedom
+Multiple R-squared:  0.7648,	Adjusted R-squared:  0.7353
+F-statistic: 26.01 on 1 and 8 DF,  p-value: 0.0009303
+> res.lm.sat.clep <- lm.sat.clep$residuals
+>
+> install.packages("ppcor")
+> library(ppcor)
+Loading required package: MASS
+> # regression test for semipartial correlation (holding clep constant)
+> spcor.gpa.sat.clep <- lm(gpa ~ res.lm.sat.clep)
+> summary(spcor.gpa.sat.clep)
+Call:
+lm(formula = gpa ~ res.lm.sat.clep)
+Residuals:
+    Min      1Q  Median      3Q     Max
+-0.3756 -0.2694 -0.0092  0.2514  0.4686
+Coefficients:
+                  Estimate Std. Error t value Pr(>|t|)
+(Intercept)      3.1600000  0.1069377  29.550 1.86e-09 ***
+res.lm.sat.clep -0.0007015  0.0024806  -0.283    0.785
+---
+Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
+Residual standard error: 0.3382 on 8 degrees of freedom
+Multiple R-squared:  0.009898,	Adjusted R-squared:  -0.1139
+F-statistic: 0.07997 on 1 and 8 DF,  p-value: 0.7845
+</code>
+From the above: Multiple R-squared: 0.009898
+From the below: spcor.gpa.sat.clep$estimate^2: 0.009897835
 <code>> spcor.gpa.sat.clep <- spcor.test(gpa,sat,clep)
 > spcor.gpa.sat.clep
@@ Line 330: / Line 393: @@
 [1] 0.009897835
 > </code>
 ====== e.g., ======