R Programming 9: Correlation and Covariance in R

Correlation:
Correlation is a statistical technique that can show whether and how strongly pairs of variables are related

Ex:
Height and Weight are related.taller people tend to be heavier than shorter people.

Types of Correlation:
1) Pearson
2) Product-Moment correlation.

The main result of a correlation is called the correlation coefficient.it ranges from -1.0 to +1.0. The closed r is to +1 or -1, the more closely the two variables are related.

If r is close to 0, it means there is no relationship between the variables. If r is positive, it means that as one variable gets larger the other gets larger. If r is negative it means that as one gets larger, the other gets smaller (often called an "inverse" correlation).

R Command:

> cor(speed,dist)
[1] 0.8068949

> cor(speed,dist,method="spearman")

[1] 0.8303568
> cor(speed,dist,method="kendall")
[1] 0.6689901

> cor.test(speed,dist,method="pearson")
 Pearson's product-moment correlation
data:  speed and dist
t = 9.464, df = 48, p-value = 1.49e-12
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 0.6816422 0.8862036
sample estimates:
      cor 
0.8068949 
 cor.test(speed,dist,method="spearman",exact=F)
 Spearman's rank correlation rho
data:  speed and dist
S = 3532.819, p-value = 8.825e-14
alternative hypothesis: true rho is not equal to 0
sample estimates:
      rho 
0.8303568 
> cor.test(speed,dist,method="pearson",alt="greater",conf.level=0.99)
 Pearson's product-moment correlation
data:  speed and dist
t = 9.464, df = 48, p-value = 7.45e-13
alternative hypothesis: true correlation is greater than 0
99 percent confidence interval:
 0.6519786 1.0000000
sample estimates:
      cor 
0.8068949 

Covariance:

Covariance indicates how two variables are related. A positive covariance means the variables are positively related, while a negative covariance means the variables are inversely related.