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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.

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Look in this. Simple regression coef. corresponds to simple correlation coef. Multiple regression coef. - to partial correlation coef. –  ttnphns Dec 15 '12 at 13:35
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1 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).

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There is no no multicollinearity in my data, what will be the solution if the next two reasons are causing? –  Kamran Dec 18 '12 at 7:27
    
For the 2nd reason - there is no solution. If the parameter estimates are close to 0 they can easily switch. For the 3rd reason - you have identified a mediating variable. There's lots of material both here, elsewhere on the web and in books and articles on mediation. I recommend the works of MacKinnon on this subject. –  Peter Flom Dec 18 '12 at 10:52
    
What should I do, whether to include or exclude this problematic variable from my research? What are the reasons of small effect size and how can I increase effect size? –  Kamran Dec 18 '12 at 11:50
    
Small effect size - well, it could just be a small effect - that is, your theory is wrong. If you can increase precision of measurement, that can affect effect size. But is it a small effect or is it a mediator? –  Peter Flom Dec 18 '12 at 11:54
    
A small effect. In a correlation table the pearson correlation between ROA and Debt to Asset ratio is .107 with sig. value of 0.165. But in a coefficient table the unstandardized coefficient of -.022 with sig. value of .425. –  Kamran Dec 18 '12 at 12:14
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