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I have two variables, the price of hay and insurance usage. Stata gives their correlation coefficient as 0.1227. This tells me that they are not highly correlated. When I have each variable in a regression separately they are each highly significant, yet together the significance is destroyed.

Next, when the errors of a regression of inventory on hay are run on insurance, insurance is highly significant. When the errors of a regression of inventory on insurance are run on hay, hay is not significant.

I'm assuming insurance is correlated with some variable but hay seems to be fine. Is there any recourse besides just getting rid of the insurance variable?

Thank you in advance.

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  • $\begingroup$ There isn't enough information here. What other variables do you have? What exactly have you done with everything? Can you tell us more about your situation, your goals, & your data? $\endgroup$ Commented May 6, 2013 at 15:59
  • $\begingroup$ Possible instrumental variable here? $\endgroup$ Commented May 6, 2013 at 22:28

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You are likely to be over-emphasising here significance as a yes-no matter. P = 0.05, or whatever, does not demarcate valid choices from invalid choices. Also, "multicollinearity" is too strong a word just for relationships among predictors.

There is no infallible solution that can be suggested remotely without seeing your data and learning more about your goals. You need to be digging deeper into what is going on, e.g.

o look at a scatter plot matrix (in Stata use graph matrix)

o check for marked outliers, skewness or nonlinearity as complicating factors

o consider the best functional form for inventory as a function of hay and insurance and whatever else (for example, if inventory is necessarily positive or zero, check out Poisson or some other GLM)

http://blog.stata.com/2011/08/22/use-poisson-rather-than-regress-tell-a-friend/ not only discusses this generally, it points to Stata code.

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