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ieor_hw4_sol

# ieor_hw4_sol - IEOR 165 Engineering Statistics Quality...

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IEOR 165: Engineering Statistics, Quality Control and Forecasting, Spring 2008 Homework 4 Solution Chapter 9 Question 1 (b) Noting ¯ x = 11 . 625, ¯ Y = 16 . 4875 B = n i =1 ( x i - ¯ x ) Y i n i =1 x 2 i - n ¯ x 2 = 1 . 206 A = ¯ Y - B ¯ x = 2 . 464 Thus the estimated regression line is Y = 2 . 464 + 1 . 206 x . Question 3 (b) Noting ¯ x = 2 . 6667, ¯ Y = . 0385 B = n i =1 ( x i - ¯ x ) Y i n i =1 x 2 i - n ¯ x 2 = . 0117 A = ¯ Y - B ¯ x = . 0072 Thus the estimated regression line is Y = . 0072 + . 0117 x (c) The estimated response at x = 3 . 2 is . 0446. Question 7 Noting ¯ x = 35 . 65, ¯ Y = 525 . 7 B = n i =1 ( x i - ¯ x ) Y i n i =1 x 2 i - n ¯ x 2 = - 1 . 213 A = ¯ Y - B ¯ x = 568 . 94 Thus the estimated regression line is Y = 586 . 94 - 1 . 213 x . The estimated means for the next 5 states are 471.9, 555.6, 558.03, 564.09, 558.03 respectively. Question 11 Noting ¯ x = 82 . 1429, ¯ Y = 50 . 3929 B = n i =1 ( x i - ¯ x ) Y i n i =1 x 2 i - n ¯ x 2 = . 0481 A = ¯ Y - B ¯ x = 46 . 44 1

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Thus the estimated regression line is y = 46 . 44 + . 0481 x . Further, S xx = 28601, SS R = 101 . 256 v = v u u t ( n - 2) S xx SS R | B | = 2 . 8 The p -value when testing β = 0 is P {| T 12 | > 2 . 8 } = . 032 .
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