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420Hw06 - STAT 420 Homework#6(due Friday October 12 by 3:00...

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STAT 420 Fall 2007 Homework #6 (due Friday, October 12, by 3:00 p.m.) 1. Recall Problems #1 and #2 from Homework 2: 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 R = Y Y ˆ ˆ T = ° 2 y ˆ = Σ 2 ° ˆ x 2 . Set up the ANOVA table. Does β appears to be different from zero? State the null and the alternative hypotheses, report the value of the test statistic, the critical value, and the decision. Use a 5% level of significance.
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