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HW6 Solution

# HW6 Solution - 3.9 lelrrl—ItlTerit—E‘Tllnllmll 2 3 4...

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Unformatted text preview: 3.9 lelrrl—ItlTerit—E‘Tllnllmll 2 3 4 5 6 7 8 9 '10 '11 a) It shows nonlinear pattern, which indicates the linear assumption is violated. b) No transformation on X will alleviate the problem, but adding a second order term X”? into the regression might solve the problem. 33w j . 5% 12a, W 4%? f Eifuil. 0.? 3x . .m \$.34 g nyk an,” afvv a... a. 5/ The SAS System 21:33 Sunday, November 8, 2009 21 The REG Procedure Model: MODEL1 Dependent Variable: y Number of Observations Head 16 Number of Observations USed 16 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 1 213.99470' 213.99470 234.98 <.0001 Error 14 12.7496? 0.91069 Corrected Total 15 226.7443? Root MSE 0.95430 R-Square 0.9438 Dependent Mean 102.18125 Adj R-Sq 0.9398 Coeff Var 0.93393 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > gt] Intercept 1 -7.73852 7.17464 -1.08 0.2990 X 1 53.95332 3.51967 15.33 <.0001 The SAS System 21:33 Sunday, November 8, 2009 23 The REG Procedure Model: MODEL1 Dependent Variable: y Output Statistics Dependent Predicted Std Error Std Error Student Cook‘s Obs Variable Value Mean Predict Residual Residual Residual -2-1 0 1 2 0 1 102.9000 102.9737 0.2441 -0.0737 0.923 —0.0799 | ] | 0.000 2 101.5000 101.5709 0.2419 -0.0709 0.923 —0 0768 I 1 | 0.000 3 100.8000 100.2760 0.2690 0.5240 0.916 0.572 | |* | 0.014 4 98.0000 97.4165 0.3918 0.5835 0.870 0.671 | |* I 0.046 5 97.3000 97.0388 0.4117 0.2612 0.861 0.303 | | | 0.011 6 93.5000 94.0714 0.5804 -0.5714 0.758 —0.754 ] *1 | 0.167 7 97.5000 99.4128 0.2992 -1.9128 0.906 ~2.111 { ****| | 0.243 8 102.2000 103.0276 0.2449 -0.8276 0.922 -0.897 | *| I 0.028 9 105.0000 105.6714 0.3298 —0.6714 0.896 -0.750 | *| 1 0.038 10 107.2000 106.2648 0.3576 0.9352 0.885 1.057 | |** 1 0.091 11 105.1000 103.2974 0.2494 1.8026 0.921 1.957 | l*** | 0.140 12 103.9000 103.4053 0.2516 0.4947 0 921 0.537 | 1* | 0.011 13 103.0000 102.0565 0 2387 0.9435 0.924 1.021 1 1** | 0.035 14 104.8000 104.4844 0.2819 0.3156 0.912 0.346 1 | | 0.006 15 105.0000 105.6714 0.3298 -0.6714 0.896 -0.750 | *| | 0.038 16 107.2000 108.2611 0.4628 -1.0611 0.835 —1.271 | **| | 0.249 Sum of Residuals 0 Sum of Squared Residuals 12.74967 Predicted Residual 88 (PRESS) 16.46858 The SAS System 21:33 Sunday, November 8, 2009 22 The EEG Procedure Model: MODEL1 Dependent Variable: y Durbin-Watson D 0.857 Number of Observations 16 1st Order Autocorrelation 0.527 \$45 a? ‘5‘: 5 ﬁ- a 13%;} “ﬂ? {3% ~ ' :31 a F x 1‘: “Aw. KL CD I J...__....|..W.A..J ’7 + ‘1|\||\||\I|i\IV‘EI\Il\E|%‘|\\ll\\||§\E|\‘|1\lill\||\|\\|i\|§‘i|l\[||\\§l§\ll 123455789WHW21|415 CJ‘J time 4‘AkALWmWﬁM.NV‘.‘..V, c4 ...
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