Exercise - Design a data set with predefined correlations

The goal of this exercise is to get acquainted with the correlation coefficient. Try to design an artificial data set containing 20 "measurements" on 4 variables (v₁..v₄). The variables v₂ to v₄ should be correlated to variable v₁, showing the following approximate (+/- 0.1) correlation coefficients r_i,j:

Use the  DataLab  for all the work. When ready, you should come up with the following items, as well as answers to the following questions:
 

• The data set (20 objects, 4 variables) in ASC format.
• The cross-correlation matrix of your data set.
• What about the correlations between variables v₃, and v₄ ? Is it possible that these two variables are uncorrelated, although both of them show a high correlation to variable v₁?