title: “correlation” author: “jagadish” date: “November 9, 2015” output: html_document
library("MASS")
data(cats)
str(cats)## 'data.frame': 144 obs. of 3 variables:
## $ Sex: Factor w/ 2 levels "F","M": 1 1 1 1 1 1 1 1 1 1 ...
## $ Bwt: num 2 2 2 2.1 2.1 2.1 2.1 2.1 2.1 2.1 ...
## $ Hwt: num 7 7.4 9.5 7.2 7.3 7.6 8.1 8.2 8.3 8.5 ...summary(cats)## Sex Bwt Hwt
## F:47 Min. :2.000 Min. : 6.30
## M:97 1st Qu.:2.300 1st Qu.: 8.95
## Median :2.700 Median :10.10
## Mean :2.724 Mean :10.63
## 3rd Qu.:3.025 3rd Qu.:12.12
## Max. :3.900 Max. :20.50with(cats,plot(Bwt,Hwt))
title(main="Heart Weight (g) vs. Body Weight (kg)\nof Domestic Cats")
with(cats, plot(Hwt ~ Bwt))
with(cats, cor(Bwt, Hwt))## [1] 0.8041274with(cats, cor(Bwt, Hwt))^2## [1] 0.6466209with(cats, cor.test(Bwt, Hwt))##
## Pearson's product-moment correlation
##
## data: Bwt and Hwt
## t = 16.119, df = 142, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.7375682 0.8552122
## sample estimates:
## cor
## 0.8041274with(cats, cor.test(Bwt, Hwt, alternative="greater", conf.level=.8))##
## Pearson's product-moment correlation
##
## data: Bwt and Hwt
## t = 16.119, df = 142, p-value < 2.2e-16
## alternative hypothesis: true correlation is greater than 0
## 80 percent confidence interval:
## 0.7776141 1.0000000
## sample estimates:
## cor
## 0.8041274with(cats, cor.test(~ Bwt + Hwt)) ##
## Pearson's product-moment correlation
##
## data: Bwt and Hwt
## t = 16.119, df = 142, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.7375682 0.8552122
## sample estimates:
## cor
## 0.8041274with(cats, cor.test(~ Bwt + Hwt, subset=(Sex=="F")))##
## Pearson's product-moment correlation
##
## data: Bwt and Hwt
## t = 4.2152, df = 45, p-value = 0.0001186
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.2890452 0.7106399
## sample estimates:
## cor
## 0.5320497with(cats, plot(Bwt, Hwt, type="n", xlab="Body Weight in kg", ylab="Heart Weight in g", main="Heart Weight vs. Body Weight of Cats"))
with(cats,points(Bwt[Sex=="F"],Hwt[Sex=="F"],pch=16,col="red"))
with(cats,points(Bwt[Sex=="M"],Hwt[Sex=="M"],pch=17,col="blue"))
rm(cats)
data(cement)
str(cement)## 'data.frame': 13 obs. of 5 variables:
## $ x1: int 7 1 11 11 7 11 3 1 2 21 ...
## $ x2: int 26 29 56 31 52 55 71 31 54 47 ...
## $ x3: int 6 15 8 8 6 9 17 22 18 4 ...
## $ x4: int 60 52 20 47 33 22 6 44 22 26 ...
## $ y : num 78.5 74.3 104.3 87.6 95.9 ...cor(cement)## x1 x2 x3 x4 y
## x1 1.0000000 0.2285795 -0.8241338 -0.2454451 0.7307175
## x2 0.2285795 1.0000000 -0.1392424 -0.9729550 0.8162526
## x3 -0.8241338 -0.1392424 1.0000000 0.0295370 -0.5346707
## x4 -0.2454451 -0.9729550 0.0295370 1.0000000 -0.8213050
## y 0.7307175 0.8162526 -0.5346707 -0.8213050 1.0000000cov(cement)## x1 x2 x3 x4 y
## x1 34.60256 20.92308 -31.051282 -24.166667 64.66346
## x2 20.92308 242.14103 -13.878205 -253.416667 191.07949
## x3 -31.05128 -13.87821 41.025641 3.166667 -51.51923
## x4 -24.16667 -253.41667 3.166667 280.166667 -206.80833
## y 64.66346 191.07949 -51.519231 -206.808333 226.31359cov.matr = cov(cement)
cov2cor(cov.matr)## x1 x2 x3 x4 y
## x1 1.0000000 0.2285795 -0.8241338 -0.2454451 0.7307175
## x2 0.2285795 1.0000000 -0.1392424 -0.9729550 0.8162526
## x3 -0.8241338 -0.1392424 1.0000000 0.0295370 -0.5346707
## x4 -0.2454451 -0.9729550 0.0295370 1.0000000 -0.8213050
## y 0.7307175 0.8162526 -0.5346707 -0.8213050 1.0000000pairs(cement)