Given a dataset with a dependent variable (Y), and three independent variables/features {X1,X2,X3}, where collinearity exists, and if we fit it using linear regression, is there any relationship between the parameter estimates?
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Are you interested in a particular relationship? If so, what kind? It is a well known result that correlated predictors result in covariance in the sampling distirbution of the coefficients. – Demetri Pananos Jan 24 '22 at 15:37
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Do you mean the parameter estimates (or coefficients) are correlated？Can you point me to some source to look at it @DemetriPananos – william007 Jan 24 '22 at 15:41
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Hey William, are you comfortable looking at a variance-covariance matrix? This is the clearest way to see correlation between parameter estimates, in my opinion. – John Madden Jan 24 '22 at 16:29
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Where *collinearity* exists, yes: there will exist linear relations among parameter estimates. I would suppose, though, that you might be trying to ask about *multicollinearity,* which is a different phenomenon. As far as correlation of parameter estimates goes, please search our site: you can find formulas for their variance-covariance matrix and many worked examples of its calculation and application. – whuber Jan 24 '22 at 17:02