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# 420Hw02 - STAT 420 Homework#2(due Friday September 7 by...

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STAT 420 Fall 2007 Homework #2 (due Friday, September 7, by 3:00 p.m.) 1. Sometimes it is known in advance that the least-squares regression line must go through the origin, i.e., the regression model is of the form Y i = β x i + ε i , i = 1, 2, … , n , where ε i ’s are i.i.d. N ( 0, σ 2 ) , and the equation of the regression line is y ˆ = ° ˆ x . In this case, finding the least-squares line reduces to finding the value ° ˆ that minimizes the expression ( ) [ ] ° = - = n i i i x y f 1 2 ° ° . Use the derivative of f with respect to β to derive the formula for the slope of the least-squares regression line in this case. 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 a)

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420Hw02 - STAT 420 Homework#2(due Friday September 7 by...

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