I have checked the relationships of dimensions of independent variable with the dependent variable in a simple linear regression on SPSS, but when I performed multiple linear regression on SPSS of the same dimension collectively then some dimensions have changed signs of regression coefficients against simple linear regression. what is the reason for this change in relationship?
e.g., in a simple linear regression analysis debt to assets ratio showed positive relationship with ROA (Return on Assets) but when I add more variables then debt to asset ratio shows negative relationship with ROA.
Best Answer
One possible reason is colliearity. Have you checked for this? I believe there is a check-box in the SPSS menus for "condition indexes" or something similar (I am not an SPSS user, but I remember seeing this when I helped someone else). If a set of IVs is approximately collinear, it can do odd things to the parameter estimates.
Another possible reason is that the signs change, but the effect is always small (close to 0 on one side or the other). Is this the case in your situation?
If neither of those is the case, then it could be that there is a mediation relationship. For example, if you gather data on fires and the damage caused and so on, then run a regression with "damage" as the DV and "number of firemen" as the IV, you will find a strong positive relationship (more firemen, more damage). If you add in "size of fire" the sign will flip (for a given size of fire, more firemen = less damage).