Dears,
I have different variables in multiple regression. Two variables are highly correlated.
To solve the collinearity issue, I dropped one of them from the multiple regression model.
The multiple regression results show that the remaining variable is significant, can I say that the dropped variable is also significant.
Thanks
Akram
First, no, you cannot say it is significant. That would be silly (are seriously asking this?).
On the what to do, I have a different take than David Eugene Booth and Blaine Tomkins . I should stress, we are all giving good advice, just for different purposes. If you was to say X1 and X2 are both related to Y, correlate each with Y. It depends what you are interested in. Given you are proposing hypotheses to test, state these hypotheses.
Why not compute the partial correlation to see how strong the association between the first predictor and criterion is while controlling for the second predictor? I think this would be more informative regarding the relationship among these variables than dropping a predictor would be.
I would agree with Blaine Tomkins if this is an explanatory model. If it is a predictive model, I would recommend an adaptive lasso variable selection because the resulting model will be an optimal prediction equation given the predictor set you started with. Lasso, in general, is resistant to multicollinearity.. you might look at this paper with references. Best, David Booth
Preprint Boosting and Lassoing Cancer Risk Factors: New Prostate Canc...
First, no, you cannot say it is significant. That would be silly (are seriously asking this?).
On the what to do, I have a different take than David Eugene Booth and Blaine Tomkins . I should stress, we are all giving good advice, just for different purposes. If you was to say X1 and X2 are both related to Y, correlate each with Y. It depends what you are interested in. Given you are proposing hypotheses to test, state these hypotheses.
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