CAS Exam MAS-II Fall 2018, Question 35
Study guide: Exam MAS-II
A linear regression is modeled with the following structure:
\begin{align*}
Y_i &\sim \text{Poisson}(\lambda_i) \\
\ln(\lambda_i) &= \beta_0 + \beta_1 X_{1i} + \beta_2 X_{2i} \\
\beta_0 &\sim \text{Normal}(0,\ 5) \\
\beta_1 &\sim \text{Normal}(0,\ 2) \\
\beta_2 &\sim \text{Normal}(0,\ 2)
\end{align*}100 samples from four posterior distributions are placed in order from smallest to largest. Each posterior is independently ordered. The i^{\text{th}} row corresponds to the i^{\text{th}} smallest sample.
i |
\beta_0 |
\beta_1 |
\beta_2 |
\beta_1 + \beta_2 |
|---|---|---|---|---|
| 1 | -5.59 | -2.13 | -2.86 | -4.83 |
| 2 | -4.89 | -1.22 | -2.40 | -3.75 |
| 3 | -4.68 | -1.13 | -2.37 | -3.65 |
| 4 | -4.54 | -1.07 | -1.92 | -3.16 |
| 5 | -4.28 | -1.06 | -1.89 | -2.97 |
| ... | ... | ... | ... | ... |
| 96 | 5.08 | 1.23 | 1.64 | 3.15 |
| 97 | 5.38 | 1.30 | 1.66 | 3.19 |
| 98 | 5.79 | 1.37 | 1.86 | 3.26 |
| 99 | 5.80 | 1.39 | 2.12 | 3.36 |
| 100 | 6.32 | 1.63 | 2.14 | 3.67 |
You are told that the 98^{\text{th}} posterior interval for \beta_0 is [-4.89,\ 5.80].
Determine the upper bound of the 94^{\text{th}} posterior interval for \beta_1 + \beta_2.
- A) Less than or equal to 3.00
- B) Greater than 3.00 but less than or equal to 3.20
- C) Greater than 3.20 but less than or equal to 3.40
- D) Greater than 3.40 but less than or equal to 3.60
- E) Greater than 3.60
Answer this question and see the worked solution