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Statistics Homework Solutions 186

# Statistics Homework Solutions 186 - 186 CHAPTER 7 32838847...

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Unformatted text preview: 186 CHAPTER 7 32838847 8. Â¡ Â¥ Â¨ 337 133439. 0 098x. Â¨ Â¡ 337 133 Î²1 x Â¡ Â¢ Â¨ Â¤ Â¦Â¥ Â¡ Â¥ Â¡ Â¤ Â¡ Â¡ Â¤ Â¤ Â¡ Â¡ The least-squares line is y y Â¡ 0 098006 and Î²0 Â¨ x yi y xi x 2 Â¡ Â¤Â¥ xi n âˆ‘i 1 1 Â¡ âˆ‘n i Î²1 y Â¡ x yi Â¡Â¥ xi 1 Â¨ âˆ‘n i Â¡ 3000 (b) Residual 2000 1000 0 âˆ’1000 2 76 576108, âˆ‘n i Â¨ Â¡ Â¥ Â¤ Â¨ 1 vi v 2 78 642836, 62 773323. Â¨ Â¡ Â¨ 0 465835. 0 820 ln x. Â¨ Â¢ 0 466 Â¡ Â¨ Â¥ Â¡ Â¡ Â¡ Â¨ Â¤Â¥ Â¡ Â¤ Â¦Â¥ Â¡ Â¥ Â¤ Â¡ Â¤ Â¡ Â¡ Â¤ Â¡ Â¡ Â¡ The least-squares line is ln y Î²1 u Â¡ v Â¡ 0 819751 and Î²0 Â¨ Â¡ Â¡ u vi v ui u 2 Â¡ Â¡Â¥ ui n âˆ‘i 1 1 u âˆ‘n i v ui Â¤ Î²1 u vi 1 Â¥ ui 5 089504, âˆ‘n i Â¡ 6 776864, v âˆ‘n 1 i ln yi . Â¨ ln xi and let vi Â¡ u 2000 Â¡ (c) Let ui 1000 1500 Fitted Value Â¡ 500 Â¡ âˆ’2000 0 3 (d) 2 Residual 1 0 âˆ’1 âˆ’2 6 8 ln yi . Â¡ ln 3000, and v Î²1 ln 3000 Â¢ Â¡ ln x Â¤ Â¡ Â¡ 3000, so u 6 09739080. Â¡Â¥ Î²0 Â¡ Â¡ x Â¨ ln xi and let vi Â¡ (e) Let ui 4 Fitted Value Â¡ 2 Â¡ âˆ’3 0 1 17317089. 2 Â¡ Â¥ y 513 116667, Â¨ Â¤ Â¡ yi Â¨ Â¤ 1  Â¥  Â¡ Â¥ Â¤ 12. 37500, âˆ‘n i Â¨ Â¡ Â¡ Â¤ Â¨ 4370, n 2 , or 38 75 5103 01 . Â¥ Â¡Â¥ y x Â¡ Â¡ Â¡ x yi xi Â¤Â¥ Â¡ xi 1 2 080 1 17317089 , or (3.657195, 8.537586). Â¨ Â¡ Â¤ Â¡ âˆ‘n 1 i 86 48333, âˆ‘n i e 8 537586 Â¨ Â¢ 225, y ln y is 6 09739080 Â¤ Â¢ 13. (a) x 3 657195 Â¨ Â¡ Â¤ Therefore a 95% prediction interval for v A 95% prediction interval for y is e 2 080. Â¥ 025 Â¤ There are 21 degrees of freedom. t21 Â¡ 2 Â¨ u ui 2 Â¥ u Â¡ u âˆ‘n 1 i Â¡ 1 n Â¥ 1 Â¡ s Â¨ spred ...
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