For Exercises 10.1 and 10.2, see page 488; for 10.3 and 10.4, see page 490; for 10.5, see pages 493–494; for 10.6 to 10.8, see pages 498–499; for 10.9 and 10.10, see page 500; and for 10.11 and 10.12, see page 502.

Question 10.12

10.12 Two regressions.

CASE 10.1 We have regressed the log income of entrepreneurs on their years of education, with the results appearing in Figures 10.5 and 10.6. Use software to regress years of education on log income for the same data.

  1. What is the equation of the least-squares line for predicting years of education from log income? Is it a different line than the regression line from Figure 10.4? To answer this, plot two points for each equation and draw a line connecting them.
  2. Verify that the two lines cross at the mean values of the two variables. That is, substitute the mean years of education into the line from Figure 10.5, and show that the predicted log income equals the mean of the log incomes of the 100 subjects. Then substitute the mean log income into your new line, and show that the predicted years of education equals the mean years of education for the entrepreneurs.
  3. Verify that the two regressions give the same value of the statistic for testing the hypothesis of zero population slope. You could use either regression to test the hypothesis of zero population correlation.

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