How can I interpret the following situation: there are a, b, c and d as variables.
1. There are positive correlations among each couple containing a, b, and c.
2. a does not have a significant Person correlation with d.
3. a partial correlation (between a and d) turns significant and negative (which controlls for the effects of b and c)
How can I interpret this situation? Any basic reference for interpretation of partial correlations is appreciated.
Here is the mathematical expression of the Multiple Linear regression, which may give idea about the final picture.
a= 42.064 + 1.273Xb + 0.245Xc - 0.304Xd
I analyzed your regression results and I confirm that you have no problem with multicollinearity between the independent variables.
Usually I do not give any relevance to the zero-order correlations.
In order to interpret multiple regression I use the B or Beta coefficients (t-test and p-values) and also the part correlations. If you squaring the part correlations you quantify the effect size of each IV on the DV when the effects of other IV are controlled.
Part correlations are much more important than zero-order correlations. Is more or less the difference in managed a simple regression or a multiple regression when we really have several independent variables.
Firstly. When you say:
«a partial correlation (between a and c) turns significant and negative (which controlls for the effects of b and c)»
you want to say
«a partial correlation (between a and c) turns significant and negative (which controlls for the effects of b and d)???
What´s exactly the value of the partial correlation? As I see in the regression equation variable c have a positive effect on a!!!!
Firstly, I realize that I made a mistake in the question text in the 3rd step: The corrected version is as follows (also corrected in the question text):
"a partial correlation (between a and d) turns significant and negative (which controlls for the effects of b and c)"
The actual cefficients are as follows:
a-b: Pearson= .456, Partial= .441
a-c: Pearson= .232, Partial= .131
a-d: Pearson= .075, Partial= -.173
Two questions:
1) Pearson values you show are zero-order correlations, aren't they?
2) Did you analyze multicollinearity?
Probably you have an interaction effect between variable d and one of the others independent variables.
As you notify the regression equation represents a negative effect from variable d on variable a:
a= 42.064 + 1.273Xb + 0.245Xc - 0.304Xd
so the regression coefficient is coherent with partial correlation.
Thank you for your responses but, what I am also curious about is that how can I interpret this situation: a and d does not have a significant Pearson (zero-order) correlation, but they have a significantly negative partial correlation, which controlls for the effects of b and c. What may be the reason for that, should I say for instance, b and c may be suppressing the a-d relationship etc. ? Are these sufficient for interpretation or should I carry out some other analyses. I would be glad if you can guide to some references for interpreting this situation.
good-morning,
I'm wondering about tolerance (or VIF).
If you do not have a significant zero-order correlation between IV d and DV d, but when controlled the effects of other independent variables you obtain a significant effect, then you probably have multicollinearity.
Thank you for your answer, can you recommend a basic source (a book, a website, etc) which would help me handle these processes?
Do you know how to calculate the tolerance? What Software do you use?
I use SPSS 17 and I am pretty new to the issue, I do not know how to calculate tolerance nor investigate collinearity. There are some stastics books with SPSS applications yet there is not enough about collinearity and tolerance in them. Maybe I can only report the significant partial correlation and focus on the multiple regression equation for inferences.
But you should analyze multiple regressions assumptions and the absence of multicollinearity is one of them. So I suggest you redo the regression analysis and use that topic (please see the attached pdf).
If you want to send me the output of its regression
Than you very much for the useful material. I guess there is not a problem with collinerity according to the criteria you provided, or is there?
Tolerance-VIF
B ,778-1,286
C ,830-1,205
D ,773-1,294
(IV= A)
Good! You can attach the output? if you made a multiple regression (with all independent variables) the results for Tolerance and VIF do not refer only to IV = A.
I analyzed your regression results and I confirm that you have no problem with multicollinearity between the independent variables.
Usually I do not give any relevance to the zero-order correlations.
In order to interpret multiple regression I use the B or Beta coefficients (t-test and p-values) and also the part correlations. If you squaring the part correlations you quantify the effect size of each IV on the DV when the effects of other IV are controlled.
Part correlations are much more important than zero-order correlations. Is more or less the difference in managed a simple regression or a multiple regression when we really have several independent variables.
Dear Rolando Valdez thank you for your interest in helping. Dear Helena Carvalho, thank you very much for your concerned and satisfactory replies, which helped me very much. Which book or source I can use to provide reference for the facts you shared with me? Any suggestions would be appreciated. I cannot find thorough and satisfactory material in order to cite as reference when I need and of course for increasing my understanding.
Here is a good book. It has a interesting chapter about Multiple Regression:
Hair, J., Black, W. Babin, B. e Anderson, R. (2009). Multivariate Data Analysis, 7ª ed., Prentice-Hall International, Inc.
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