16.4 Exercises

EXERCISE 16.1   Compute the part-worths for the following table of rankings
  $X_2$
  1 2
1 1 2
$X_1$     2 4 3
3 6 5
.

EXERCISE 16.2   Consider again Example 16.5. Rewrite the design matrix $\data{X}$ and the parameter vector $\beta$ so that the overall mean effect $\mu$ is part of $\data{X}$ and $\beta$, i.e., find the matrix $\data{X}'$ and $\beta'$ such that $Y=\data{X}'\beta'$.

EXERCISE 16.3   Compute the design matrix for Example 16.5 for $n=3$ persons ranking the margarine with $X_1$ and $X_2$.

EXERCISE 16.4   Construct an analog for Table 16.8 for the car example.

EXERCISE 16.5   Compute the part-worths on the basis of the following tables of rankings observed on $n=3$ persons.
    $X_2$
  1 1 2
$X_1$ 2 4 3
  3 6 5
  $X_2$
  1 3
$X_1$ 4 2
  5 6
  $X_2$
  3 1
$X_1$ 5 2
  6 4

EXERCISE 16.6   Suppose that in the car example a person has ranked cars by the profile method on the following characteristics:
$X_1$ = motor
$X_2$ = safety
$X_3$ = doors
There are $k=18$ stimuli.
$X_1$ $X_2$ $X_3$ preference
1 1 1 1
1 1 2 3
1 1 3 2
1 2 1 5
1 2 2 4
1 2 3 6
$X_1$ $X_2$ $X_3$ preference
2 1 1 7
2 1 2 8
2 1 3 9
2 2 1 10
2 2 2 12
2 2 3 11
$X_1$ $X_2$ $X_3$ preference
3 1 1 13
3 1 2 15
3 1 3 14
3 2 1 16
3 2 2 17
3 2 3 18
Estimate and analyze the part-worths.