How to graphically reveal data structures? I have a dataframe with 8 columns (variables, X1 to X8) . Each column represents a different model parameter. Each row of the dataframe represents a modelling scenario.
All the modelling scenarios result in some desired output (i.e. Y1). In other words, different model parameters can result in Y1.
I was wondering - are there ways in R to graphically reveal the data structure of my dataframe?
Ideally, I would like some way to quantify: if the value of variable X1 is 1000, what are the likely values of variables X2 to X8? 
I was thinking that perhaps some kind of tree diagram might be useful.
Hope I am making sense.
 A: Although your data represent particular things - estimates of parameters under different scenarios - the net result is the same as though you have any ordinary set of eight-dimensional (nine if you count Y1) data.  So all the ordinary multidimensional visualisation techniques apply.
Normally I would start with a scatterplot matrix - there are implementations in base graphics, lattice or ggplot2 according to your preference.
A: I would suggest you to use matrix scatter plots such as
Scatterplot Matrices in R
or
Plot matrix in MatLab
Here is sample code for R:
library(car)
scatterplotMatrix(x = mtcars)

It will help you to understand the one-to-one dependencies in data and possibly find the prediction you are looking for (if they really exist). E.g., if some Xs are perfectly correlated you will see the points lying in strait line.
A: If you want a tree with conditions, check out rpart. It fits a CART/Regression tree to your data. Simply run
fit = rpart(Y1~X1+X2+X3+X4+X5+X6+X7+X8, data=d)
plot(fit, uniform=TRUE)
text(fit, use.n=TRUE, all=TRUE, cex=.8)

Which leads to a tree like this:

