CAS Exam MAS-I Spring 2018, Question 36
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 no intercept. Only integer values from 1 to 5 were considered for estimates of \beta_1 and \beta_2.
The grid below shows the residual sum of squares for every combination of the parameter estimates, after standardization (rows are \hat\beta_1, columns are \hat\beta_2):
\hat\beta_1 \backslash \hat\beta_2 |
1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| 1 | 2,855.0 | 870.3 | 464.4 | 357.2 | 548.6 |
| 2 | 1,059.1 | 488.4 | 216.3 | 242.8 | 567.9 |
| 3 | 657.0 | 220.0 | 81.6 | 241.9 | 700.8 |
| 4 | 368.4 | 65.1 | 60.5 | 354.5 | 947.1 |
| 5 | 193.2 | 23.7 | 152.8 | 580.6 | 1,307.0 |
Let:
\hat\beta_1^L= Estimate of\beta_1using a lasso with budget parameters = 5\hat\beta_2^L= Estimate of\beta_2using a lasso with budget parameters = 5
Calculate the ratio \hat\beta_1^L / \hat\beta_2^L.
- A) Less than 0.5
- B) At least 0.5, but less than 1.0
- C) At least 1.0, but less than 1.5
- D) At least 1.5, but less than 2.0
- E) At least 2.0
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