Statistics Homework Solutions 207

Statistics Homework Solutions 207 - 207 SUPPLEMENTARY...

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Unformatted text preview: 207 SUPPLEMENTARY EXERCISES FOR CHAPTER 8 3 182. 3 182 0 0088901 , or (0.0314, 0.0880). 0. ¡ 0 is is t 3 945. ¨ ¡ ¡ ¡ ¡ 0 029, but this is the value for a two-tailed test. ¨ 0 029 2 0 0145. ¡ £ ¡ ¨ ¡ For the one-tailed test, P ¨ The output gives P 0 versus H1 : β2 ¡ ¨ From the output, the test statistic for testing H0 : β2 0 versus H1 : β2 § ¨ 0. We therefore test H0 : β2 ¡ ¤ (d) The reaction rate is decreasing with time if β2 ¨ A 95% confidence interval is 0 059718 ¥ ¡ 025 ¨ t3 It is reasonable to conclude that the reaction rate decreases with time. β1 x 1 β2 x 2 ¢ ¢ β0 β3 x 1 x 2 ¢ ¡ y ε. ¢ 21. 23. (a) The 17-variable model containing the independent variables x 1 , x2 , x3 , x6 , x7 , x8 , x9 , x11 , x13 , x14 , x16 , x18 , x19 , x20 , x21 , x22 , and x23 has adjusted R2 equal to 0.98446. The fitted model is 1569 8 24 909x1 196 95x2 8 8669x3 2 2359x6 0 077581x7 0 057329x8 1 3057x9 12 227x11 44 143x13 ¢ ¡ ¨ ¨ ¡ 21 656x19 18 253x20 ¨ ¨ ¢ ¨ ¢ ¢ ¨ ¨ ¡ ¨ ¢ ¢ ¨ ¨ ¨ ¢ ¨ ¡ 0 97071x16 74 775x18 37 553x22 329 8x23 ¨ ¨ ¡ ¨ ¢ 4 1883x14 82 591x21 ¨ ¡ ¡ ¡ ¨ ¢ ¨ ¡ y ¢ (b) The 8-variable model containing the independent variables x 1 , x2 , x5 , x8 , x10 , x11 , x14 , and x21 has Mallows’ C p equal to 1.7. The fitted model is 20 4x10 ¡ ¨ ¢ 0 024247x8 7 1313x11 ¨ ¨ ¢ 121 96x5 ¢ ¨ ¢ 76 499x2 2 4466x14 ¨ ¨ ¢ 24 782x1 ¢ ¨ 665 98 47 85x21 ¨ ¨ ¡ ¡ y ¡ (c) Using a value of 0 15 for both α-to-enter and α-to-remove, the equation chosen by stepwise regression is y 927 72 142 40x5 0 081701x7 21 698x10 0 41270x16 45 672x21. ¨ ¨ ¢ ¨ ¢ ¨ ¢ ¨ ¢ ¨ ¢ ¨ ¡ ¡ (d) The 13-variable model below has adjusted R2 equal to 0.95402. (There are also two 12-variable models whose adjusted R2 is only very slightly lower.) 0 358x7 ¢ 14 46x6 ¨ ¨ ¡ 313 31x3 0 078746x8 ¡ ¨ ¡ 8663 2 ¨ ¨ 13 998x9 230 24x10 188 16x13 5 4133x14 1928 2x15 8 2533x16 294 94x19 129 79x22 3020 7x23 ¨ ¢ ¨ ¨ ¢ ¡ ¨ ¨ ¨ ¢ ¡ ¨ ¢ ¢ ¨ ¨ ¢ ¡ ¡ z ...
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This note was uploaded on 12/20/2011 for the course STA 3163 taught by Professor Mattgilg during the Fall '11 term at UNF.

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