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# Chapter 7 Answers - Chapter 7 Hypothesis Tests and...

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Chapter 7 Hypothesis Tests and Confidence Intervals in Multiple Regression Solutions to Exercises Chapter 7 Exercises Answered 1.

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Regressor (1) (2) (3) College ( X 1 ) 5.46** (0.21) 5.48** (0.21) 5.44** (0.21) Female ( X 2 ) - 2.64** (0.20) - 2.62** (0.20) - 2.62** (0.20) Age ( X 3 ) 0.29** (0.04) 0.29** (0.04) Ntheast ( X 4 ) 0.69* (0.30) Midwest ( X 5 ) 0.60* (0.28) South ( X 6 ) - 0.27 (0.26)
Intercept 12.69** (0.14) 4.40** (1.05) 3.75** (1.06)

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(a)The t -statistic is 5.46/0.21 = 26.0 > 1.96, so the coefficient is statistically significant at the 5% level. The 95% confidence interval is 5.46 ± 1.96 × 0.21. (b) t -statistic is - 2.64/0.20 = - 13.2, and 13.2 1.96, so the coefficient is statistically significant at the 5% level. The 95% confidence interval is - 2.64 ± 1.96 × 0.20. 3. (a) Yes, age is an important determinant of earnings. Using a t -test, the t -statistic is 0.29 0.04 7.25, = with a p -value of 4.2 × 10 - 13 , implying that the coefficient on age is statistically significant at the 1% level. The 95% confidence interval is 0.29 ± 1.96 × 0.04. (b) Age × [0.29 ± 1.96 × 0.04] = 5 × [0.29 ± 1.96 × 0.04] = 1.45 ± 1.96 × 0.20 = \$1.06 to \$1.84 4. (a) The F -statistic testing the coefficients on the regional regressors are zero is 6.10. The 1% critical value (from the 3, F distribution) is 3.78. Because 6.10 > 3.78, the regional effects are significant at the 1% level. (b)The expected difference between Juanita and Molly is ( X 6,Juanita - X 6,Molly ) × β 6 = β 6 . Thus a 95% confidence interval is - 0.27 ± 1.96 × 0.26. (c)The expected difference between Juanita and Jennifer is ( X 5,Juanita - X 5,Jennifer ) × β 5 + ( X 6,Juanita - X 6,Jennifer ) × β 6 = - β 5 + β 6 . A 95% confidence interval could be contructed using the general methods discussed in Section 7.3. In this case, an easy way to do this is to omit Midwest from the regression and replace it with X 5 = West . In this new regression the coefficient on South
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