Question 11.87

11.87 Compare regression coefficients.

Again refer to Exercise 11.85.

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  1. In Example 10.5 (page 497), parameter estimates for the model that included just EDUC were obtained. Compare those parameter estimates with the ones obtained from the full model that also includes age and locus of control. Describe any changes.
  2. Consider a 36-year-old entrepreneur with 12 years of education and a locus of control of −0.25. Compare the predicted log incomes based on the full model and the model that includes only education level.
  3. In Example 10.12 (pages 521–522), we computed for the model that included only education level. It was 0.0573. Use and to test whether age and locus of control together are helpful predictors, given EDUC is already in the model.

11.87

(a) For the model with EDUC: . For the model with all three: . With just Education, the intercept was larger and the effect size of each year of education was larger, 0.1126, on LogIncome. Once we account for both Locus of control and Age, the intercept isn’t quite as large, and the effect size of each year of education goes down to 0.08542. (b) For the full model: . For the EDUC model: . The predictions don’t seem too different unless we undo the log transformation; the predicted incomes are $17,940.21 and $14,849.18, which seems like a substantial difference. (c) are 2 and . Locus of control and Age are helpful predictors in explaining LogIncome when Education is already in the model.