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I'm considering the regression model $y_i = \beta_0 + \beta_1x_{1i} + \beta_2x_{2i} + \varepsilon_i$ where the $\varepsilon_i$ are iid and $\mathcal N(0,\sigma^2)$

A study question asks to show the relationship between the variance of the least square estimates of $\beta_i$ and ${\rm VIF}_i$ for $i = 1,2$.

Would it be enough to say that the actual variance of the regression coefficient in the model is equal to the least square estimate's variance multiplied by the variance inflation factor or am I leaving something out?

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