What happens when there is a linear regression of the kind
y ~ x1 + x2 + x3 + x4
What determines which variables will be granted the explained variance rather than the others given a correlation matrix (not assuming independence)?
In case this really is unpredictable, why do we insist on using regression rather than simply looking at the correlation matrix: at least then you know you are not accounting for effects of other variables when looking at the correlation coefficient, while using regression you'd be oblivious to which variable gets the explained variance (and how correctly or wrong this is!).