partial_and_semipartial_correlation
Differences
This shows you the differences between two versions of the page.
Both sides previous revisionPrevious revisionNext revision | Previous revisionNext revisionBoth sides next revision | ||
partial_and_semipartial_correlation [2019/05/26 23:05] – [Semipartial cor] hkimscil | partial_and_semipartial_correlation [2019/10/13 21:25] – [regression gpa against clep] hkimscil | ||
---|---|---|---|
Line 7: | Line 7: | ||
* Separately regress Y and X1 against X2, that is, | * Separately regress Y and X1 against X2, that is, | ||
* regress Y against X2 AND | * regress Y against X2 AND | ||
- | * regression | + | * regress |
* Regress the Y residuals against the X1 residuals. | * Regress the Y residuals against the X1 residuals. | ||
In the below example, | In the below example, | ||
Line 82: | Line 82: | ||
> | > | ||
> </ | > </ | ||
+ | |||
+ | linear model | ||
+ | '' | ||
+ | '' | ||
+ | |||
+ | |||
{{lm.gpa.sat.png? | {{lm.gpa.sat.png? | ||
Line 88: | Line 94: | ||
[1] 0.7180529</ | [1] 0.7180529</ | ||
- | + | Collect | |
- | < | + | - sat, |
+ | - gpa, | ||
+ | - predicted value (y hat), | ||
+ | - residuals (error) | ||
+ | And see correlation among themselves. | ||
+ | < | ||
+ | > cor.gpa.sat <- as.data.frame(cbind(sat, | ||
> colnames(cor.gpa.sat) <- c(" | > colnames(cor.gpa.sat) <- c(" | ||
> round(cor.gpa.sat, | > round(cor.gpa.sat, | ||
Line 104: | Line 116: | ||
10 550 2.9 3.13544 -0.23544 | 10 550 2.9 3.13544 -0.23544 | ||
> | > | ||
- | > round(cor(cor.gpa.sat), | + | round(cor(cor.gpa.sat), |
sat | sat | ||
sat 1.000 0.718 1.000 0.000 | sat 1.000 0.718 1.000 0.000 | ||
Line 111: | Line 123: | ||
resid 0.000 0.696 0.000 1.000 | resid 0.000 0.696 0.000 1.000 | ||
> | > | ||
- | > </ | + | </ |
+ | Note that | ||
+ | * r (sat and gpa) = .718 (sqrt(r< | ||
+ | * r (sat and pred) = 1. In other words, predicted values (y hats) are the linear function of x (sat) values ('' | ||
+ | * r (sat and resid) = 0. residuals are orthogonal to the independent (sat) values. | ||
===== regression gpa against clep ===== | ===== regression gpa against clep ===== | ||
< | < | ||
Line 140: | Line 156: | ||
Residual standard error: 0.1637 on 8 degrees of freedom | Residual standard error: 0.1637 on 8 degrees of freedom | ||
Multiple R-squared: | Multiple R-squared: | ||
- | F-statistic: | + | F-statistic: |
+ | </ | ||
+ | |||
+ | '' | ||
+ | |||
< | < | ||
Line 146: | Line 167: | ||
res.lm.gpa.clep <- lm.gpa.clep$residuals | res.lm.gpa.clep <- lm.gpa.clep$residuals | ||
</ | </ | ||
+ | |||
{{lm.gpa.clep.png? | {{lm.gpa.clep.png? | ||
+ | |||
< | < | ||
# get cor between gpa, sat, pred, and resid from. lm.gpa.clep | # get cor between gpa, sat, pred, and resid from. lm.gpa.clep | ||
- | cor.gpa.clep <- as.data.frame(cbind(gpa, clep, lm.gpa.clep$fitted.values, | + | cor.gpa.clep <- as.data.frame(cbind(clep, gpa, lm.gpa.clep$fitted.values, |
- | colnames(cor.gpa.clep) <- c("gpa", "clep", " | + | colnames(cor.gpa.clep) <- c("clep", "gpa", " |
cor(cor.gpa.clep) | cor(cor.gpa.clep) | ||
</ | </ | ||
- | < | + | < |
- | gpa 1.0000 0.8763 0.8763 0.4818 | + | > round(cor(cor.gpa.clep),4) |
- | clep | + | clep gpa pred resid |
- | pred 0.8763 1.0000 1.0000 0.0000 | + | clep |
- | resid 0.4818 0.0000 0.0000 1.0000 | + | gpa |
- | > </ | + | pred 1.0000 |
+ | resid 0.0000 0.4818 0.0000 1.0000 | ||
+ | > | ||
+ | |||
+ | sat | ||
+ | sat | ||
+ | gpa | ||
+ | pred 1.0000 | ||
+ | resid 0.0000 0.6960 | ||
+ | > | ||
+ | </ | ||
Line 323: | Line 356: | ||
====== Semipartial cor ====== | ====== Semipartial cor ====== | ||
+ | See also [[: | ||
+ | |||
< | < | ||
> colnames(tests) <- c(" | > colnames(tests) <- c(" |
partial_and_semipartial_correlation.txt · Last modified: 2024/06/12 08:01 by hkimscil