It is known that when the predictor variables are highly correlated with each other (e.g, correlation coefficient is 0.9) the regression coefficients are unstable as they have high standard errors. I have two questions in this context:

  • Interpretation of parameter estimates being 'unstable'

    An intuitive understanding of instability would be that the regression estimates would fluctuate a lot if we were to re-estimate the model using different data sets all of which come from the same data generating process.

    Is the above understanding an accurate interpretation of parameter instability?

  • Instability of predictions

    Multicollinearity is an issue when it comes to interpreting the coefficients and it seems that if parameter estimates are unstable then the predictions might also be unstable.

    Is there a study/paper/blog post that discusses the above issue?



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