Multicollinearity problem might affect the signs (positive or negative) or/and the significant levels of regression coefficients (Betas).
In order to check this issue, can one compare correlation coefficients of dependent and independent variables with related coefficients (betas) of multiple regression of the said variables?
To explain this question, assume that we have Y, X1, and X2. where Y is the dependent variable and X1 and X2 are the independent variables.
Assume that the correlation metrics shows a positive correlation between Y and X1 on one hand, but the multiple regression between Y, X1, and X2 shows X1 with a negative coefficient (beta), not positive as in correlation metrics. Can I say that multicollinearity affects the regression since the sign is changed from positive (in case of correlation metrics) to negative (in case of multiple regression)?
Keep in mind that Gujarati: Basic Econometrics, Fourth Edition says, in page 231, that "The terms r1 2.3 and r12 (and similar comparisons) need not have the same sign."
Thanks
The tolerance value as well as the VIF(Variance Inflation Factor) value tell you if your data are subject to multicollinearity or not.
I agree with you that VIF can detect multicollinearity. But, I asked about using correlation and regression coefficient signs to detect multicollinearity
Yes you can,usually the correction matrix give more accurate results than the VIF. So u can depending upon it
Sorry, but no you cannot if you are interested in multiple linear regression. see:
https://www.amazon.com/s?k=Kutner+Applied+linear+statistical+models&i=stripbooks&ref=nb_sb_noss_2
for full details. Correlation gives only special case help.
Best, David Booth
If the regression give positive relationship between IV and DV but the correction give a negative sign between the same relationship, this indicate that there is multicollinearity problem.
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