We give the detailed calculation of various correlation functions of t
he system described by the Edwards-Wilkinson (EW) equation with long-r
ange noise correlation of the power-law form for arbitrary substrate d
imensionality. The obtained information can be employed for comparison
with experimental data directly, permitting extraction of various phe
nomenological parameters. Furthermore, we explicitly evaluate the larg
e-distance asymptotic form of the equal-time correlation function. The
result shows that it goes as a power-law form of distance, instead of
the exponential decaying form as the case with white noise. This dist
inct behavior can be used to experimentally distinguish whether the ro
ughening of a system is caused by white noise or correlated noise.