420Hw04 - STAT 420 Homework #4 (due Friday, February 15, by...

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STAT 420 Spring 2008 Homework #4 (due Friday, February 15, by 4:00 p.m.) 1. Recall Problems #5 and #6 from Homework 1: It has been proposed that the brightness measured in some unit of color or a commercial product is proportional to the time it is in a certain chemical reaction during the production process, or Y i = β x i + ε i , i = 1, 2, … , n , where ε i ’s are i.i.d. N ( 0, σ 2 ), where Y i measures brightness, x i measures time, and β is a parameter. The following data on x and Y are available: x 1.0 1.2 1.4 1.6 1.8 2.0 Y 3.4 7.0 6.0 9.0 8.0 11.0 x y y ˆ = 5 x e = y y ˆ 1.0 3.4 5 1.6 1.2 7.0 6 1.0 1.4 6.0 7 1.0 1.6 9.0 8 1.0 1.8 8.0 9 1.0 Then ˆ = = = n i i n i i i x y x 1 2 1 = 5. 2.0 11.0 10 1.0 Without β 0 in the model, SSTotal = Y T Y = Σ y 2 . Without β 0 in the model, dfTotal = n . RSS = Σ e 2 . Without β 0 in the model, SS Reg = Y Y ˆ ˆ T = 2 y ˆ = Σ 2 ˆ x 2 . Set up the ANOVA table. Does
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420Hw04 - STAT 420 Homework #4 (due Friday, February 15, by...

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