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low f-stat is not due to multi-collinearity by itself , its just a completely wrong choice of the explanation set. If the combination of variables is not enough to explain the outcome , there is no point blaming collinearity for the problem , just do more research ad find which OTHER variables are responsible.

Collinearity ,serial correlation and cond. heteroskedasticity are problems that we have to be aware about , but its just good regression that pays the bills

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