hw2 - (b Using an appropriate test(at the α = 0 05...

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Stat 704, Fall 2011: Homework 2 Due Tuesday Sept. 13 1. Regression through the origin We will consider a special case of simple linear regression where the intercept is assumed to be zero from the outset (this is often assumed in calibration of certain measuring devices). Let Y i = x i τ + ± i , where E ( ± i ) = 0 and var( ± i ) = σ 2 . (a) Define Q ( τ ) = n i =1 ( Y i - x i τ ) 2 . Show that the minimizer of Q ( τ ) is ˆ τ = n i =1 x i Y i n i =1 x 2 i . (b) Show E τ ) = τ . (c) Show var(ˆ τ ) = σ 2 n i =1 x 2 i . 2. A cereal company claims its boxes contain 445 grams of cereal. A random sample of 14 boxes produces the following measurements: 441.82 437.38 445.92 444.17 444.89 445.93 443.97 445.40 445.95 443.35 441.95 444.86 438.96 439.38 (a) Use a graph to determine whether the assumption of normality is reasonable.
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Unformatted text preview: (b) Using an appropriate test (at the α = 0 . 05 significance level), determine whether the center of the distribution of cereal weights is 445 grams. Use R or SAS and report the p-value of your test. Do the following problems from the textbook: • Thought & pencil/paper problems, chapter 1: 1.2, 1.5, 1.8, 1.11, 1.16, 1.18, 1.30, 1.33. • Thought & pencil/paper problems, chapter 2: 2.10, 2.12. • Grade point average (use SAS): 1.19, 1.23(b), 2.4(a,b,c), 2.13(a,b,c), 2.23. • Plastic hardness (use SAS): 1.22, 1.26(b), 2.7(a,b), 2.16(a,b), 2.26. • Property assessments (use SAS): 2.42(a,b,c), 2.46. 1...
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