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I have high collinearity between one of the covariates (credit score variable with values ranging from 600 to 800) and the intercept term, when regressing a continuous dependent variable on some behavioral attributes. I checked multiple multicollinearity metrics and the story is the same. Correlation coefficeint is 0.952, condition index is 80 with proportion of variation of intercept & FICO being 0.98 and 0.97 respectively. The VIF is also very high. Credit score does have a very flat relationship with the dependent variable but that probably would not have any implication here. Can someone please explain why this might be happening? And if this happens with an independent variable that has a more significant relationship with the dependent variable, should I consider dropping the intercept term from my model?

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Dropping the intercept from your model is in general a bad idea unless you know for sure that when your predictors all have value zero your outcome must be zero. Instead you might try subtracting some suitable constant from your credit score variable. In the absence of other information I would suggest starting with 700. The coefficient for credit score should be unaffected by this although it will change the intercept. Since the intercept is seldom of scientific interest that usually does not matter.

The formula for the covariance between estimates of intercept and slope and some intuitive explanation are available here Correlation between OLS estimators for intercept and slope so I will not explain further.

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  • $\begingroup$ Thanks! I am still a bit confused how intercept (a constant term) could be collinear with credit score (which is a continuous variable). Can you please share if you've any insights on that? $\endgroup$ – Nagesh Rathi Apr 24 at 13:52
  • $\begingroup$ I have added a link to another Q&A on the site which explains further. $\endgroup$ – mdewey Apr 24 at 14:56
  • $\begingroup$ Thanks once again. The links suggested in your answer explain correlation between intercept and slope parameters. What I have here is correlation between intercept and an independent variable. Do you have any suggestions on how this could arise and what are the implications of it (for e.g. multicollinearity between two independent variables would lead to unstable estimates of their coefficients but would we have a similar problem here given the correlation is not with another independent variable but with intercept)? $\endgroup$ – Nagesh Rathi May 1 at 15:28
  • $\begingroup$ I am afraid I do not see the distinction you are making there. $\endgroup$ – mdewey May 2 at 11:00
  • $\begingroup$ Assuming $Y = \alpha + \beta*X_1 + \gamma*X_2$ is a regression equation, one could talk about correlation between $X_1$ and $X_2$ i.e the variables OR $\beta$ and $\gamma$ i.e. their slopes. I am trying to make the same distinction in my comment above. Question is- when I have a high condition index for intercept and another variable, is it due to correlation between $\alpha$ and $X_1$ OR $\alpha$ and $\beta$? $\endgroup$ – Nagesh Rathi Jul 5 at 19:27

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