9.2 What does Collinearity do to our regression?

The takeaway from our application is that collinearity can become a significant problem if the degree of correlation among the independent variables is large enough. What the application does not show is that collinearity also results in excessively large standard errors of the coefficient estimates. Intuitively, if the regression doesn’t know which variable is providing the (redundant) information, then it responds by placing little precision on the estimate - meaning excessively large standard deviations. The standard deviations are said to be positively biased - meaning that they are larger due to the presence of collinearity. Artificially large standard errors may impact the significance of estimates via confidence intervals and hypothesis tests.