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### How can a regression be significant yet all predictors be non-significant? [duplicate]

My multiple regression analysis model has a statistically significant F value however all beta values are statistically non-significant. All the regression assumptions are met. No multicollinearity ...
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### Dealing with correlated regressors

In a multiple linear regression with highly correlated regressors, what is the best strategy to use? Is it a legitimate approach to add the product of all the correlated regressors?