18 SM_Ch16 - Chapter 16 16.1 a The slope coefficient tells...

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Chapter 16 16.1 a The slope coefficient tells us that for additional inch of father’s height the son’s height increases on average by .516. The y-intercept is meaningless. b On average the son will be shorter than his father. c On average the son will be taller than his father. 16.2 a Scatter Diagram 0 5 10 15 20 0 20 40 60 80 100 120 Advertising Sales b i x i y 2 i x 2 i y i i y x 23 9.6 529 92.16 220.8 46 11.3 2,116 127.69 519.8 60 12.8 3,600 163.84 768.0 54 9.8 2,916 96.04 529.2 28 8.9 784 79.21 249.2 33 12.5 1,089 156.25 412.5 25 12.0 625 144.00 300.0 31 11.4 961 129.96 353.4 36 12.6 1,296 158.76 453.6 88 13.7 7,744 187.69 1205.6 90 14.4 8,100 207.36 1296.0 99 15.9 9,801 252.81 1,574.1 Total 613 144.9 39,561 1,795.77 7,882.2 = n 1 i i x = 613 = n 1 i i y = 144.9 = n 1 i 2 i x = 39,561 = n 1 i i i y x = 7,882.2 - - = = = = n y x y x 1 n 1 s n 1 i i n 1 i i n 1 i i i xy = 66 . 43 12 9 . 144 )( 613 ( 2 . 882 , 7 1 12 1 = - - 191
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- - = = = n x x 1 n 1 s 2 n 1 i i n 1 i 2 i 2 x = 7 . 749 12 ) 613 ( 561 , 39 1 12 1 2 = - - 2 x xy 1 s s b = = 0582 . 7 . 749 66 . 43 = 08 . 51 12 613 n x x i = = = 08 . 12 12 9 . 144 n y y i = = = x b y b 1 0 - = = 12.08 – (.0582)(51.08) = 9.107 The sample regression line is y ˆ = 9.107 + .0582x The slope tells us that for each additional thousand dollars of advertising sales increase on average by .0582 million. The y-intercept has no practical meaning. 16.3 a i x i y 2 i x 2 i y i i y x 8.5 115 72.25 13,225 977.5 7.8 111 60.84 12,321 865.8 7.6 185 57.76 34,225 1,406.0 7.5 201 56.25 40,401 1,507.5 8.0 206 64.00 42,436 1,648.0 8.4 167 70.56 27,889 1,402.8 8.8 155 77.44 24,025 1,364.0 8.9 117 79.21 13,689 1,041.3 8.5 133 72.25 17,689 1,130.5 8.0 150 64.00 22,500 1,200.0 Total 82.0 1,540 674.56 248,400 12,543.4 = n 1 i i x = 82.0 = n 1 i i y = 1,540 = n 1 i 2 i x = 674.56 = n 1 i i i y x = 12,543.4 - - = = = = n y x y x 1 n 1 s n 1 i i n 1 i i n 1 i i i xy = 40 . 9 10 540 , 1 )( 0 . 82 ( 4 . 543 , 12 1 10 1 - = - - - - = = = n x x 1 n 1 s 2 n 1 i i n 1 i 2 i 2 x = 24 . 10 ) 0 . 82 ( 56 . 674 1 10 1 2 = - - 192
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2 x xy 1 s s b = = 17 . 39 24 . 40 . 9 - = - 20 . 8 10 0 . 82 n x x i = = = 0 . 154 10 540 , 1 n y y i = = = x b y b 1 0 - = = 154.0 – (–39.17)(8.20) = 475.2 The sample regression line is y ˆ = 475.2 – 39.17x b. The slope coefficient tells us that for each additional 1 percentage point increase in mortgage rates, the number of housing starts decreases on average by 39.17. The y-intercept has no meaning. 16.4a
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18 SM_Ch16 - Chapter 16 16.1 a The slope coefficient tells...

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