CAS Exam MAS-I Fall 2019, Question 37
Study guide: Exam MAS-I
For a set of data with 40 observations, 2 predictors (X_1 and X_2), and one response (Y), the residual sum of squares has been calculated for several different estimates of a linear model with an intercept. Only integer values from 1 to 3 were considered for estimates of \beta_0 (the intercept), \beta_1 and \beta_2.
The grid below shows the residual sum of squares for every combination of the parameter estimates, after standardization:
\hat{\beta}_0 = 1
\hat{\beta}_1 |
\hat{\beta}_2 = 1 |
\hat{\beta}_2 = 2 |
\hat{\beta}_2 = 3 |
|---|---|---|---|
| 1 | 3,924 | 1,977 | 1,250 |
| 2 | 1,858 | 1,141 | 711 |
| 3 | 1,386 | 822 | 369 |
\hat{\beta}_0 = 2
\hat{\beta}_1 |
\hat{\beta}_2 = 1 |
\hat{\beta}_2 = 2 |
\hat{\beta}_2 = 3 |
|---|---|---|---|
| 1 | 3,949 | 1,822 | 1,174 |
| 2 | 1,907 | 1,187 | 717 |
| 3 | 1,363 | 711 | 349 |
\hat{\beta}_0 = 3
\hat{\beta}_1 |
\hat{\beta}_2 = 1 |
\hat{\beta}_2 = 2 |
\hat{\beta}_2 = 3 |
|---|---|---|---|
| 1 | 3,784 | 1,671 | 1,107 |
| 2 | 1,827 | 1,128 | 668 |
| 3 | 1,294 | 700 | 344 |
Let \hat{\beta}_i^R be the estimate of \beta_i using a ridge regression with budget parameter s = 5. Assume the intercept is not subject to the budget parameters.
Calculate the value of \hat{\beta}_0^R + \hat{\beta}_1^R + \hat{\beta}_2^R.
- A) Less than 6
- B) 6
- C) 7
- D) 8
- E) Greater than 8
Answer this question and see the worked solution