What is the relationship between Multicollinearity and Standard error?

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Can somebody give a clear explanation for the relationship between Multicollinearity and Standard error? I heard if multicollinearity exists, then the standard error goes up, but I don't understand this sentence. How does multicollinearity make the standard error go up?

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Multicollinearity does not bias regression results; it just produces large standard deviations for the parameters related to the independent variables.