The data of my research consists of 5 independent variables and 1 dependent variable. After running multiple linear regression in SPSS it is found that the beta coefficients of 2 independent variables are negative while 3 independent variables have positive beta coefficients.
The beta coefficients can be negative or positive, and have a t-value and significance of the t-value associated with each. The beta coefficient is the degree of change in the outcome variable for every 1-unit of change in the predictor variable. The t-test assesses whether the beta coefficient is significantly different from zero.
- If the beta coefficient is negative, the interpretation is that for every 1-unit increase in the predictor variable, the outcome variable will decrease by the beta coefficient value. For example, if the beta coefficient is -.80 and statistically significant, then for each 1-unit increase in the predictor variable, the outcome variable will decrease by .80 units.
- If the beta coefficient is positive, the interpretation is that for every 1-unit increase in the predictor variable, the outcome variable will increase by the beta coefficient value. For example, if the beta coefficient is .80 and statistically significant, then for each 1-unit increase in the predictor variable, the outcome variable will increase by .80 units.
I hope this will help you.
Hello Hina,
To the advice of Syed Abdul Rehman Bukhari , I'd like to add one thing. Do look at the zero-order correlations (ordinary Pearson correlations of each IV with the DV). When you have multiple IVs in a model, it can be the case that an estimated regression coefficient can be of opposite sign to that of the zero-order correlation. This is most often attributable to collinearity among the IVs. While the resultant linear combination is "optimal" (in terms of maximizing R-squared, or minimizing MSE), the assigned coefficients may no longer "make sense" in such situations.
Some tactics which can be helpful when excessive collinearity exists among your IVs include: (a) dropping IVs; (b) combining IVs (say, via factor analysis or PCA); (c) ridge regression.
Finally to address your question directly, the signs of the regression coefficients are what they are; for single IV models, the sign always reflects the direction of the (zero-order) relationship of IV & DV. For multiple IV models, not necessarily.
Good luck with your work.
I agree with both, Syed Abdul Rehman Bukhari and David Morse. The signs of the regressions coefficients are what they are and they only indicate the sort of relationship of one specific IV with the DV.
Collinearity should be one reason for an unexpected sign for a coefficient (researcher expected a positive sign but the result is a negative one, for instance).
This can be checked when you run the regression analysis by setting collinearity diagnostics in SPSS (Analyze / Regression / Linear / Statistics / Collinearity diagnostics.
When you do this, the SPSS output will provide values for Tolerance and VIF (Variance Inflation Factor), which indicate collinearity.
Literature is quite voluble regarding an acceptable parameter for VIF (I have seen from 3, which is OK for me, to 10, which is too loose in my opinion).
I have used < 3 as an acceptable VIF. More than this I tend to drop the IV once it is not helping the model.
Hope this can help.
Regards.
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