CAS Exam MAS-I Spring 2018, Question 37
Study guide: Exam MAS-I
You fit a linear model using the following two-level categorical variables:
X_1 = \begin{cases} 1 & \text{if Account} \\ 0 & \text{if Monoline} \end{cases} \qquad X_2 = \begin{cases} 1 & \text{if Multi-Car} \\ 0 & \text{if Single Car} \end{cases}
with the equation:
E(Y) = \beta_0 + \beta_1 X_1 + \beta_2 X_2 + \beta_3 X_1 X_2
This model produced the following parameter estimates:
\hat\beta_0 = -0.10, \quad \hat\beta_1 = -0.25, \quad \hat\beta_2 = 0.58, \quad \hat\beta_3 = -0.20.
Another actuary modeled the same underlying data, but coded the variables differently as such:
Z_1 = \begin{cases} 0 & \text{if Account} \\ 1 & \text{if Monoline} \end{cases} \qquad Z_2 = \begin{cases} 0 & \text{if Multi-Car} \\ 1 & \text{if Single Car} \end{cases}
with the equation:
E(Y) = \alpha_0 + \alpha_1 Z_1 + \alpha_2 Z_2 + \alpha_3 Z_1 Z_2
Afterwards you made a comparison of the individual parameter estimates in the two models.
Calculate how many pairs of coefficient estimates (\hat\alpha_i, \hat\beta_i) switched signs, and how many pairs of estimates stayed identically the same, when results of the two models are compared.
- A) 1 sign change, 0 identical estimates
- B) 1 sign change, 1 identical estimate
- C) 2 sign changes, 0 identical estimates
- D) 2 sign changes, 1 identical estimate
- E) The answer is not given by (A), (B), (C), or (D)
Answer this question and see the worked solution