HW8-Solutions

HW8-Solutions - STAT 101 Agresti Homework 8 Solutions...

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STAT 101 - Agresti Homework 8 Solutions 11/15/10 Chapter 9 9.13. 120 0.60 0.90 80 y x s b r s = = = ; a y bx = - = 500 – 0.90(480) = 68; ˆ y a bx = + = 68 + 0.90 x . 9.18. (a) (i) ˆ y = 30 + 0.60(100) = 90; (ii) ˆ y = 30 + 0.60(50) = 60. (b) ( 29 x y r b s s = = 0.60(10/10) = 0.60. (c) r = 1(10/10) = 1.0. (d) r = 0(10/10) = 0. 9.20. (a) ˆ y = –0.105 + 0.546 x ; for each \$1000 increase in GDP per person, the predicted annual oil consumption per person increases by 0.55 barrels. (b) r = 0.847; there is a moderately strong positive association between GDP per person and annual oil consumption per person. (c) ˆ y = –0.105 + 0.546(41) = 22.3; ˆ y y - = 26 – 22.3 = 3.7; the predicted annual oil consumption per person is 3.7 barrels higher than would be predicted by the regression line. 9.29. (a) 0 H : β = 0 and a H : ≠ 0, t = b / se = 0.294/0.0149 = 19.7, P < 0.001. There is extremely strong evidence that number of years of mother’s education has a positive effect on number of years of education. (b) b ± t 0.025 ( se ) = 0.294 ± 1.96(0.0149) = 0.265 to 0.323. We can be 95% confident that falls between 0.265 and 0.323. In the population, the mean number of years of education increases by between 0.27 and 0.32 for each additional year of the mother’s education. (c) Since r = 0.37 is less than 1, number of years of education is predicted to be fewer standard deviations from its mean than number of years of mother’s education is from its mean. 9.32. (a) P = 0.0015. There is strong evidence of an association between number of hours spent in the home on religious activity and political ideology, and the estimated slope shows that it is positive. In this case, more hours spent in the home on religious activity is associated with being more conservative. (b) While these results are statistically significant, the slope of 0.0064 is so close to 0 that it has no practical significance. For example, an increase in x of 10 hours a month corresponds to a predicted change on the political ideology scale of 0.064, which is extremely small because political ideology is on a scale from 1 to 7.

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9.38. A correlation matrix follows. Correlations Food Decor Service Cost Food Pearson Correlation 1 0.288(*) 0.616(**) 0.410(**) Sig. (2-tailed) 0.022 0.000 0.001 N 63 63 63 63 Decor Pearson Correlation 0.288(*) 1 0.677(**) 0.820(**) Sig. (2-tailed) 0.022 0.000 0.000 N 63 63 63 63 Service Pearson Correlation 0.616(**) 0.677(**) 1 0.718(**) Sig. (2-tailed) 0.000 0.000 0.000 N 63 63 63 63 Cost Pearson Correlation 0.410(**) 0.820(**) 0.718(**) 1 Sig. (2-tailed) 0.001 0.000 0.000 N 63 63 63 63 * Correlation is significant at the 0.05 level (2-tailed). ** Correlation is significant at the 0.01 level (2-tailed).
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HW8-Solutions - STAT 101 Agresti Homework 8 Solutions...

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