ps6sol_F08

ps6sol_F08 - The Hong Kong University of Science and...

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Unformatted text preview: The Hong Kong University of Science and Technology IS O M 111 - Business S tatistics Problem Sheet 6 Solutions 1. (a) = 1.7483 = - 8.0068 ∴ = - 8.0068 + 1.7483 x 1 ˆ β ˆ β y ˆ When there is a 1% increase in the market return, the average return on Dalton Company’s stock tends to increase by 1.7483 %. (b) H : β 1 = 1 H a : β 1 > 1 Test statistic t = 2.5963; and t α , n – 2 = t 0.05, 8 = 1.86 Since t > t 0.05, 8 , reject H at 0.05 level of significance. We have sufficient evidence that Dalton’s Company’s Stock is sensitive to the market. (c) A 90% P. I. for y given x = 10.5 is (6.6151, 14.0856) (d) r = 0.9063 ⇒ R 2 = 0.8214 or 82.14% (e) A 98% C. I. for E( y | x = 14) is (13.2046, 19.7342) 2. (a) = - 364.6 1 ˆ β On average, the Calorie content decreases by 364.6 when there is an unit increase in the Price per ounce. (b) H : β 1 = 0 H a : β 1 ≠ 0 Test statistic t = - 3.603; and t 0.025, 7 = 2.365 Since | t | > t 0.025, 7 , reject H at 0.05 level of significance. The price is a good predictor of the calorie content. (c) R 2 = 0.6498 = 64.98% That means 64.98% of the variability of the calorie content can be explained by the price. 3. (a) = 0.564347826 = 7.086956522 1 ˆ β ˆ β (b) 35.30434783 (c) A 95% P. I. is (2.039713895, 45.99506871) 4. (a) y = 0.22072 + 0.47114 x ˆ (b) No. It is not meaningful to interpret (reasons should be given) . (c) For a unit increase in the test score ( x ), the grade point average ( y ) is expected to increase by 0.47114 points. (d) A 95% C. I. for β 1 is 0.47114 ± 2.069(0.0932) = (0.27823, 0.66405) The interval (0.27823, 0.66405) has 95% chance to cover the true slope parameter β 1 . Page 1 of 6 Assignment 6 Suggested Solutions (e) H : β 1 = 0.5 H a : β 1 ≠ 0.5 By (d), 0.5 is included in the 95% C. I. We do not reject Ho at 0.05 level of significance. (f) 95% P. I. is (1.9783, 4.3995) (g) 95% C. I. is (2.32196, 2.83088) (h) r = 0.7253 ⇒ x and y have quite high positive linear relationship. 5. (a) = 0.9258 = 73.3856 r = 0.9496 1 ˆ β ˆ β (b) For x = 65 ⇒ = 133.562 For x = 165 ⇒ = 226.142 y ˆ y ˆ The first one is more reliable because the x-value for the first estimate is inside the range (23 to 100) of the data set, while the second one is outside the range. 6. (a) = 3.235 = 12.353 ⇒ = 12.353 + 3.235 x 1 ˆ β ˆ β y ˆ (b) r = 0.9272 H : ρ = 0 H a : ρ > 0 Test statistic t = 4.9491, and t α , n – 2 = t 0.05, 4 = 2.132 Since t > t 0.05, 4 , reject H at 0.05 level of significance. The ρ is positive. (c) For G, x = 8 ⇒ = 38.2353 For H, x = 15 ⇒ = 60.8824 y ˆ y ˆ The estimation for district G is more reliable because the x-value (8) for the estimate is inside the range (4 to 11) of the data set, while the second one (15) is outside the range....
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ps6sol_F08 - The Hong Kong University of Science and...

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