5.2. Refer to the example in Section 1.3.3. Generate 100 observations from the given latent variable model, which has E(y*) — 20 + 0.60.x - 40.0z.

(a) Plot the data and fit the model using OLS.

(b) Categorize y* into y using five categories, as in that example. Now using y as the response, fit the same model as well as the extended model allowing interaction, using OLS with the scores (1, 2, 3, 4, 5). In the interaction model, compare the slopes for the two levels of z.

(c) Fit the ordinal probit model to y. Show how results compare to those for the model for y*, and show that there is actually no need for an interaction term.