Re: SPSS and Regression

Y=Beta+B1X1+B2G1+B3G2+B4(G1*X1)+B5(G2*X1)+E

My result shows a significant overall model and a significant
interaction G1*X1 with a -t value and p=0.006.

Is this an appropriate interpretation: Since G1 represents group1
(because grp2 and control=0) does this mean that as Y increases, G1
decreases for group 1 only? If so, what is happening in the control
group? How can I know?
Yes, your interpretation is correct (IMHO).
As you have used dummy coding, B1 is telling you what's going on in the
control group. If you had used effect coding ((1,0,-1),(0,1,-1)), then
B1 would be the overall effect.
.