CAS Exam MAS-II Fall 2018, Question 23

A linear regression is fit with the model below:

 $\begin{align*} y_i &\sim \mathit{Normal}(\mu_i,\ \sigma) \\ \mu_i &= b_0 + b_1 x_{1i} + b_2 x_{2i} \\ b_0 &\sim \mathit{Normal}(10,\ 50) \\ b_1 &\sim \mathit{Normal}(2,\ 10) \\ b_2 &\sim \mathit{Normal}(2,\ 10) \\ \sigma &\sim \mathit{Uniform}(0,\ 10) \end{align*}$

It is known that $X_1$ and $X_2$ are both highly correlated with $Y$ .

Three posterior plots of $b_1$ and $b_2$ are provided below.

Determine the best interpretation regarding multicollinearity from these plots.

A) It is present in the data because $x_1$ and $x_2$ are highly positively correlated
B) It is present in the data because $x_1$ and $x_2$ are highly negatively correlated
C) It is present in the data because $b_1$ and $b_2$ are highly positively correlated
D) It is present in the data because $x_1$ and $x_2$ have low correlation with each other
E) It is not present in the data

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CAS Exam MAS-II Fall 2018, Question 23

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