CAS Exam MAS-II Fall 2019, Question 22
Study guide: Exam MAS-II
Your coworker built a linear model predicting a random variable Y:
\begin{align*}
Y_i &\sim \text{Normal}(\mu_i, \sigma) \\
\mu_i &= \alpha + \beta_{x_1}\log(x_{1i}) + \beta_{x_{2i}}x_2 \\
\alpha &\sim \text{Normal}(100, 100) \\
\beta_{x_1} &\sim \text{Normal}(0, 5) \\
\beta_{x_{2i}} &\sim \text{Normal}(0, 5) \\
\sigma &\sim \text{Uniform}(0, 100)
\end{align*}You are given additional detail about pre-processing performed on the predictor variables:
- All variables are continuous numeric
x_{1i}is strictly positive- Variable
x_{2i}has been standardized to have mean 0 and standard deviation 1
Your coworker gives you the following three statements:
I. \alpha = average outcome
II. \beta_{x_1} = change in outcome for each 1 log change of x_{1i}
III. \beta_{x_2} = change in outcome for each 1 standard deviation change of x_{2i}
Determine which of the above statements are false.
- A) I only
- B) II only
- C) III only
- D) I, II and III
- E) The answer is not given by (A), (B), (C), or (D)
Answer this question and see the worked solution