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?
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.