Multivariate Data There is a built-in data set  USArrests data in R software . 

?USArrests

We use this data set for Multivariate Data Analysis . 
But i have not understood why is this a multivariate data ?
As far i know , when there are more than one response variable and when the response variables are correlated , then the data is called multivariate data .

pairs(USArrests)


But in USArrests data :


*

*Which variables are response variables and which variables are explanatory variables ?

*How are those response variables correlated ? Where is the indication of collinearity in those response variables ?
 A: Data do not necessarily need to be correlated to be considered multivariate. It is up to you to define which variables are to be considered the response variables and which are to be considered independent variables.  Running a ?USArrests in R, one sees the following:
[,1]    Murder  numeric     Murder arrests (per 100,000)
[,2]    Assault     numeric     Assault arrests (per 100,000)
[,3]    UrbanPop    numeric     Percent urban population
[,4]    Rape    numeric     Rape arrests (per 100,000) 

If you were so inclined, you could consider all or any subset of these to be response variables.  You might event consider some to be predictors of others.  You will need to explore the correlation structure among these items.  See ?cor to get some hints on how you might do that in R.
What have you done so far?  It's generally not good practice to just post your questions without explaining what might be confusing you.  It seems you may need to obtain a better understanding of the basic definitions of statistical terms you used in your post.
A: In this small dataset, Murder, Assault and Rape can be considered outcome variables, while UrbanPop can be a predictor variable.  
Following plot shows correlation between different variables: 
library(corrgram)
corrgram(USArrests, order=TRUE, lower.panel=panel.shade, upper.panel=panel.ellipse, text.panel=panel.txt) 


Following shows correlation values: 
> library(Hmisc)
> rcorr(as.matrix(USArrests))
         Murder Assault UrbanPop Rape
Murder     1.00    0.80     0.07 0.56
Assault    0.80    1.00     0.26 0.67
UrbanPop   0.07    0.26     1.00 0.41
Rape       0.56    0.67     0.41 1.00

n= 50 


P
         Murder Assault UrbanPop Rape  
Murder          0.0000  0.6312   0.0000
Assault  0.0000         0.0695   0.0000
UrbanPop 0.6312 0.0695           0.0030
Rape     0.0000 0.0000  0.0030         

One can see high degree of correlation between Murder & Assault. Correlation with others is less strong, but still highly significant. 
