231HW12-S10 - H W [2 (92) TEJE; H02 Hm MP magma t...

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Unformatted text preview: H W [2 (92) TEJE; H02 Hm MP magma t H5157“le “MI 55W = 209755.77 Hamel. : 147730.59 [553(74: [55-10 < 200*?53.?7 ~ 2%??50. 5?) W 1225.; full 4.5;; ? “35> :4 6*}- l3 ‘8? I 1": 2w .3. (A T» i f I v.4 exp \ \J x. “be :~+ '.\3 CT Q\ 4-: >< 9 N L29 N m 0? .\'l A 75% mo— JraZvi u gt?!” {9; iv- to.025,;1§.. » L395“? i 206‘” 0.1707” 7. y “1.55mi, ~ 0,552‘35‘9H XX Tram JMP WW: 3):“ 11:6, L560 2 3.452172 5? = 0420427 , 5 =-. 0.59 6553' ' A W/v flammfflgwl 01' W 4min), 1560 \3 @flwé/ $7366 i Tom/24.. 51; :. 3452(72i [064x 0.120427 1 [3183613, 397650?353 ‘ A W. mleer M. W Wt‘j' w/m «=6, I960 L3 a.wa»~...~9..n.w m n I x a. A A ~ " . . Aim. AWwis, ma» i 750.95% x H?- = SEISm; $143.05“ 012042714; , ;; [2.(76045/ 12658296] . ’ i 9, , , 1 MW agave 2 (M?! W rm MO $5 M’zféy jg»: for), J;ng 034m 1, ‘ ' f 1‘ (“Jim j a" I I} r y; Iv ! {W’Er/ [mar A! 17%me Y 65mg z‘iiiiw my” mm” 3’ . [my immzsj/ (2gb i 51.556276 H fir? {[H‘Um Mari/0X jar ,q mt j w/m J): A 75% (200»J'Motl HI jér “INNS, £21757? H ,. /\ J. . ”%?ixx=5z 33:350 (40,025,25‘ ‘ 5?. I »: [2346243, 10mm A 75% moo-Mm? XW + 1%WU] w :1 [1406357 ,, rm j m A L[fr/277m?er [MM/z = [ 6,8 H415 116 Mai '3" 2mm -r 2. W , 103: A677] 53 c- I x 0.léjoéfi f 291m 33::5/ 16580 {3; 2.682615 i 2.054 x mmf + 0163066: “ , LIME?“ a “3 TM. L w “giFHWL’MI‘z {fifwfififlj J —— [Hm-6}, 5720826] HW 12 Response Y Whole Model Actual by Predicted Plot 400 0 50 100150 200 250 300 350 Y Predicted P<.0001 RSq=0.66 RMSE=56.592 Summary of Fit RSquare RSquare Adj Root Mean Square Error Mean of Response Observations (or Sum Wgts) Analysis of Variance 0.657846 0.629333 56.59163 79.14444 27 Source DF Sum of Squares Mean Square F Ratio Model 2 147780.59 73890.3 23.0719 Error 24 76862.69 3202.6 Prob > .F C. Total 26 22464329 <.0001* Lack Of Fit Source DF Sum of Squares Mean Square F Ratio Lack Of Fit ' 6 69824.462 11637.4 29.7622 Pure Error 18 7038.233 391.0 Prob > F Total Error 24 76862.695 , <.0001* Max RSq 0.9687 Parameter Estimates Term Estimate Std Error t Ratio Prob>|t| lntercept 286.80833 33.12993 8.66 <.0001* X1 45.86667 3.798181 -4.18 0.0003* X2 «1.78625 0.333469 -5.36 <.0001* Residual by Predicted Plot “(6 :1 "a ‘5 a) D: >— —100 Overlay Plot 2.5 2 1.5 1 0.5 0 -O.5 —1 ’~1.5 Studentized Resid Y 1 2 3 Overlay Piot 2.5 2 1.5 1 0.5 ~O.5 —1 -1.5 Studentized Resid Y 1 10 20 O 50 100150 200 250 300 350 Y Predicted 456789 X1 10 11 30 40 50 60 7O 80 90100 X2 Overlay Plot 2.5 2 1.5 1 0.5 O 0.5 -1 —'l.5 —100 -50 O 50 100 150 200 Pred Formula Y 1 Studentized Resid Y 1 The plot of standardized residuals against x1 shows that the standardized residuals are not randomly scattered along horizontal zero line. The variability of standardized residuals when x1 = 6 is smaller than the variability of standardized residuals when x1 = 3 or 10. it shows that probably there exist some non—linear relation between y and XI. The plot of standardized residuals against x2 also shows that the standardized residuals are not randomly scattered along horizontal zero line. The variability of standardized residuals when x2 = 20 is larger than the variability of standardized residuals when x2 = 60 or 100. it shows that probably there exist some non~|inear relation between V and x2. The plot of standardized residuals against predicted y also clearly shows that the standardized residuals are not randomly scattered along horizontal zero line. Therefore, these plots indicate that the current model is not appropriate enough. Response Y Whole Model Actual by Predicted Plot 0 50 100 150 200 250 300 350 Y Predicted P<.0001 RSq=0.89 RMSE=33.587 Summary of Fit RSquare 0.894546 RSquare Adj 0.869438 Root Mean Square Error 33.58678 Mean of Response 79.14444 Observations (or Sum Wgts) 27 Analysis of Variance Source DF Sum of Squares Mean Square F Ratio Model 5 200953.77 40190.8 35.6278 Error 21 23689.51 1128.1 Prob > F C. Total 26 224643.29 <.0001* Lack Of Fit Source DF Sum of Squares Mean Square F Ratio Lack Of Fit 3 16651.280 5550.43 14.1950 Pure Error 18 7038.233 391.01 Prob > F Total Error 21 23689.513 <.0001* Max RSq 0.9687 Parameter Estimates Term Estimate Std Error t Ratio Prob>lt| Intercept 573.87628 56.20158 10.21 <.0001* X1 66.00534 15.81019 -4.17 0.0004* X2 —7.361943 1.134821 -6.49 <.0001* X1_Sq 1.9185185 1.146526 1.67 0.1091 X2_Sq 0.0245729 0.00857 2.87 0.0092* X1 1X2 0.4147804 0.06902 6.01 <.0001* Residual by Predicted Plot R :3 '0 '7) m D: >— 0 50 100 150 200 250 300 350 YPredicted Overlay Plot 1.5 1 0.5 O —0.5 ~1 —1.5 —2 ~25 234567891011 X1 Studentized Resid Y 2 Overlay Plot 1.5 1 0.5 O —O.5 —1 -1.5 —2 —2.5 10 20 30 4O 50 60 70 80 90100 X2 Studentized Resid Y 2 Overlay Plot 1.5 ’l 0.5 O —0.5 ~‘l 4.5 —2 —2.5 . ~50 0 50 100 150 200 250 i Pred Formula Y 2 Studentized Resid Y 2 Compared with (a), the plot of standardized residuals against x1 shows that the standardized residuals seem much more randomly scattered along horizontal zero line. However, it shows that maybe there still exist some non-linear relation between y and x1. Compared with (a), the plot of standardized residuals against x2 also shows that the standardized residuals seem muchmore randomly scattered along horizontal zero line. However, the variability of standardized residuals seems to decrease as x2 increases. Compared with (a), the plot of standardized residuals against predicted y seem much’ more randomly scattered along horizontal zero line. However, it still be not random enough and some non—linear relation between standardized residuals and predicted y can be seen. Therefore, these plots indicate that this new model is more appropriate than the model in (a) but this new model seem still not appropriate enough for the data. (c) Refer to the comparison based on the appearance ofthe plots in (a) and (b) 5 JStepwlse Flt Ftesnunsew . gtepylse Regressive Control a”; ', ProbloEnlerE _ Pu:me L0. _ "l'QIIWIE‘flma‘e‘ ’ . H , MW... ,_ 1 .505 are 0155 015110an 01511110107110 ' Cp me . 231509.513 21 1120.072 0.0015 0.0004 '0 270.4951 lnckaxieted P01001010! Esllmaln ‘ 1100 SS 'Fflalln“ “Plole' ’ 7;} «inletcepl , 573070270 1 'r 0 0.000 1 El 2 x1 , 00.005313 110001.00 17.120 0.00013 [1 2i xz‘ ‘-7.3010120 1 17475.22 ' , 12.005 1000-0 ~13 « 111,50 101051052 1 3150019,, 2.000 0.10000 ', E ii x2_0q 002157292 -1 0274002 0222 ‘ 0.00922 '13 7 111012 1» "011470011 1 10739.73 30.111 5.70040 0 [2.0101110001001100 “$100100” saqsswnsrmm' 011 1 .112 0010100, 0.0003 91091.05 0.4001 01.00 2 .‘X1 51110100 00003 55000.75» 0.0570 17.130 3 X11x2 01110100 - 000000073073 0030213022 , r 5 X230 Enlaied 0.0315 0274.001' 0.0005 , 6.8 ‘ XLSQ Entered (0.1091 3158.649r’jflfifll5 E a m a u m a For the model in (a): RSquare = 0.657846 RSquare Adj = 0.629333 CD = 47.136 For the model in (b): RSquare = 0.894546 RSquare Adj = 0.869438 Cp = 6 Based on the RSquare, Adjusted RSquare and CD, the model in (b) is more appropriate than the model in (a). However, even for the model in (b), the RSquare, Adjusted RSquare are still large enough. So neither model is a really adequate description of the data. (d) See the handwritten. (8) Response Y' Whole Model Actual by Predicted Plot Y' Predicted P<.0001 RSq=0.78 RMSE=0.5966 Summary of Fit RSquare 0.781612 RSquare Adj 0.763413 Root Mean Square Error 0.596553 Mean of Response 3.753478 Observations (or Sum Wgts) 27 Analysis of Variance Source DF Sum of Squares Mean Square -F Ratio Model 2 30.568342 15.2842 42.9481 Error 24 8.541012 0.3559 Prob > F C. Total 26 39.109354 <.0001* Lack Of Fit Source DF Sum of Squares Mean Square F Ratio Lack Of Fit 6 5.2100356 0.868339 4.6924 Pure Error 18 3.3309762 0.185054 Prob > F Total Error 24 8.54101 18 0.0048* Max RSq 0.9148 Parameter Estimates Term Estimate Std Error t-Ratio Prob>|t| Intercept 10.876366 _ 0.787182 13.82 <.0001* X1' -1 .398768 0.232687 —6.01 <.0001* X2' -1.206039 0.170971 ~7.05 <.0001* 0.5. 00. .msEmmm .> o. 5. 1.. 1 a _ Residual by Predicted Plot .0 m .m d e r P .Y 515.05. 5. _> Eme umNzcmuam Overlay Plot 2.25 1.75 X1' 1.5 1.25 5.15.05.45.25. 1 0 mm 1. 7.. .> Emma vazchBw Overlay Plot 4.5 3.5 X2' Overlay Plot 15 Studentized Resid Y' .#,.<'D .0 Nth—3010014 !'\> 01 N 2.5 3 3.5 4 4.5 5 5.5 6 Pred Formula Y' The plot of standardized residuals against xl’ shows that the standardized residuals are not randomly scattered along horizontal zero line. The variability of standardized residuals when x1’ = 2.25 is larger than the variability of standardized residuals when x1’ take other values. lt also shows that probably there exist some non-linear relation between y’ and x1’. The plot of standardized residuals against x2’ also shows that the standardized residuals are not randomly scattered along horizontal zero line. The variability of standardized residuals seems constant. But it shows that possibly there exist some non-linear relation between y’ and x2’. The plot of standardized residuals against predicted y also clearly shows that the standardized residuals are not randomly scattered along horizontal zero line. Therefore, these plots indicate that this model is not appropriate enough. if) 10 Overlay Plot Yr OJ Y‘ combination means .A 01 O Pred Formula Y' A f_'"_r'_‘_l___T-——'T_'_‘T“_"l 1 1.25 1.5 1.75 2 2.25 X1' The 9 predicted values y’what’s based on the model in (e) seem still not close enough to the 9 sample means of y’. 80 the model in (e) is still not appropriate enough for the data. (9) As shown in the ANOVA: Source DF Sum of Squares Mean Square F Ratio Model 2 30.568342 15.2842 42.9481 Error 24 8.541012 0.3559 Prob > F C. Total 26 39.109354 <.0001* F = 42.9481 and the corresponding p-value is very small (<.0001). Since p-value is smaller than 0.05, we could reject Ho. (*0 As shown in the ANOVA table: Lack Of Fit Source Lack Of Fit ‘ Pure Error Total Error DF 6 18 24 Sum of Squares 5.2100356 3.3309762 8.54101 1 8 Mean Square 0.868339 0.185054 F Ratio 4.6924 Prob > F 00048" Max RSq 0.9148 F = 4.6924 and the corresponding p—value is 4.6924. Since p—value < 0.05, We reject Ho that the true regression model is linear. (i), (J), 00 See the handwritten. Also refer to the output of JMP as follows: 4;] Edit Tablas Rows Cd: H303 fl 5145 24352125 i. - . _ i , , I lwé11_rdxiiiiiiav 51005011100110;le l ,1 , Eormillux smilemlzmmcsltlY1 1111.50 ‘ t x2_511 ’ 'X11X2 i V 2 ‘ V2 ' : ' Y' X1' 0 1 3‘ 20 300.2 2034033331 104573011 7. _ 4001 _0ui' 200504054 1007035704: 570444002! 1.005512 0 2 3 20 010.0 203.403333l 2040010333 05 400i 50! 200501054 1.04520051l 573014052? 1.000512: . a :1 3g 2 20 333 203403323; r 2471001551 . 01 _ 400; r 501 ‘ 200504054 - 101300150 5.00014240l 1.000512: 0 4 s 20 00.51 15500333; 40443505 35!, 400; - 1201 15027405 4.0502172; 4501152101 1.7017501 0 5 r 0‘. ’20 125.2l 1550033332 03552200. 35; 400; 170; 15027455 4175144001 4.01412430fi1701750 1: 5 ‘5 20 1424 1155003333; * ~0.2501054L 215i “4003 . 120i 150.27405 055505513 4.050641 1.701750. 0 7 mi 20 20.2; 02.4155557 4.300701] 100' 4001 :00; 512210051 '~1.00540351 3.0055025; 2.302505: 0 0 10! ‘20 20.2! 024150507; 4.2330054?" 100 4001l 200. 51.2210051 .' ' 43.005555“ 3.33032100i 2.3015051 . a 9 10 r 20 101.“ ' 914156667? 0.1974500“ ‘ 100% 400] ‘ZDDE L 5‘1210981 1.0013553El LGMNZHLZJDZSDSl AP'ed-Ffir—nmfiQ} ‘ o 10 :1. 50 57.3 132033333; 7110710451 0 35003 100! 114533333 4.551044! 4200150243 10011512; Asmwmmwz o 11 , 31 50 77.0 r 1320333201 40011471; at r 3500; 100. 11453333 . 2003105 435542505: 1.000512; AM. . ,. o 12 31 50 . 03.0 132033333; 0705241le 0; 3500; ‘100; 41453333: r :0500550 454223030; 1.000512: 4x103. «1 13 « a at :00 43 - 0443333331 074520503 3513 3500; 350; ~42.0777770 0000732001 325120012! 1.701750. 4112-41 ’ _ , o 14 5 . 50 44,5 1 043333333; 0.7102004 35 30001 3501 420777770 005020004; 3.70540010l 1.701750. Amaramiuiav-fi- o 15 0 50 55.0 " 0443333331 03330170 '. 35; 35001, :00 420777770 075505440 4.1001304” 1.701250. ASNWHWWRWW ‘- o 10 10 00 10.7 I 20.0505507L 0.1000753; 100i ‘000; ‘ 125000000 031041523! 2370243741 23025051 ‘V'cl’mhmwmmms" o 17 10 50 30.1 7005555075. 024420055; 100 500% 120000000 1.002230% 352020730! 2.3025051 o 10 10 50 30.1 200555057! .. . 033730500; 100' 1100 120050000 1.24715024 3555122471 2.3025051 J Lawmmmw r o '10 a 100 25.5 misaaaaag * 05504425; 01 300 270050450 002053 3277144731 1.000512; AUWWSMMW I - 20 a 100 22.3 5050333331 07305040} 0; 300 270050450 501550223 3104505501 1.000512; Asmammw ’ ‘ 21 a 100 :40 5050333331 040204530 0 ' r300 L270050450 . 020500200 354951730; 1.000512: _;____ 1 - 22 0! 100 132.0 tzaamaal 4 030770201; 35; 500,’ 531403004 . 000701230} 3400420521 1.701750- 7 ‘ A 23 5 100 25.5[ 1200333332 0234105221 35‘ 1110 531403904 - 055041015 3.24250235l 1.701750 _ a n 24 5 100 32.7 12.0033333{ 0.30504730l 30! 5001 531403504 000371247 3.4073750051701750- me . r 1 101 100 ‘ 2.3 50.403333; 1013543031 100; - 10000: > - 1000; 20.000015 -0.050032| 0032010012; 23025051 35:2?“ , g 101 100 4.4! 50403333; 1.05305713é 100! 10000; 10001 20000015 00054405! 140150454; 2.3025051 Law“, 0 101 100 5.0 ' 1.00074005l' 1003 100006 10001. 20.090015 «0.0404505; 1.75705702l 2.3025051 M 00 - 1 r - 64 54001 540r 230043944 ‘ ,- .-l 2.079441: ' l ’ ’ i : g t“ . x I 12 Fl: Ed: 1385.110»; C '30 9*. Y. A : A; Sumemlzexl . ‘ A X1’ 142' ‘ P700F94muloY1 ResldY’ 00701217701107: LowexflS‘iMele‘ 0mm 95%!71900‘!‘ Lowel95161701771100“:9596170le P7041551“ 1.00661229 1905773227 5726692991 -0.04066H 3146657 512665921 6.22652670: 4.39787627 7.05550771 0.24217944 2 109861229 2.90573227F 57266820011 002264652 314.6667 5.2366592¥ 6126526781 4.39767627; 7.05550771 0142176441 2 109091229 299573227 572699299; 014039043 314.5667~_____ aggggsazi 622552679; 439707921: ' 7.05550771 0.24217944 ‘_ 4 1.79175947 2.99573227 4.757140763 412763059 026.0667 _ 4153074971 5355206541 3463165831 605111566 0.19287081 1.79175947 2179573227 4.75714076 0.27606623 126.0667 __ 435007497 . 5.155206541 3.46316583? - 6.05111566 0.19267061 7 1.79175947 199573227 4.75714076 . ' 0.3569431 126.0667 435907497 5155206541 ’ 1463105831 ‘ 605111566 019267061 2.30758509 2.99573227 4.04261412 4.0694373 50.36667 3.5509565 4525271741 4 1720164451 5.36506376 0.23385724 130258500 2.89573227 _ 4174261412 ’-1.2614867 50.36667 _ 3.5586565 ' 4525271741 172016445 5.36566376 0.23365724 culm‘hm) 330258506 298573227 404261412 167360260 50.36667 3.5506565; ' 452527174 172016445. ' 5.3650636333385724 7W 1.09664226 4.08434456 440172366 4.3404466 79.7 41710374761 I 4.79307314;‘ 34087694511 5.68364646 048961548 A smdenm“ Resmyz‘ 109861220 4.09434450 4.40172366 410616542 797 4.010374761 419307314 1109798451 568364646 016061646 108961229 4.08434455 4.40172386 " 014841325 . 78.7 4.01037476 . . 4783073141 340879945x 569364845 0.18981648 1.79175647 4.08434458 . 143217172 056314328 51.13333 3.183622481 3680720071 117610883 4.66823301 0.12042706 1.70175841 6406434455 ' 3.4321717! 0.6218302 51.13333 346302248 3013072097; 2476109831 468823301 0.12042708 179175947 409434456 ' 143217172 139386275 51.13333 116302248 168072097! 117010983 466823351 012042706 4 Y4? ' A x1'4’é A X257 1 Fred Formula W1" JEludendees'W 130259509 409434450 211794500 00704324 27.90007 134070550 3.00500459é 1.432993% 400302107 077005514 _ 290759509 409434450 ' 271754509 142910592 27.977997 134949559 1090004595. 1.4922903 4.00302107 0.17009514 230259509 409434455 171794509 190900949 27.90667 137079559 ' 309000459: 4.4922993 - 400302707 047005514 Amwergsmmw . 109991229 460517019. 173594974 . 47.910596 27.05997 1329799591 4.2445273; ' 247199099 5.09959503 0.22233599 4.3999,“me 1.09661229 4.00517019 - 370504044 ' 4.2303993 27.09057 ' 132975959 . 414452735. 247790005 5.0999990: 022233599 ‘pmdsgy‘ug: ' 4.099612sz 499517019 379564074 ’-9.420370: 97.95557 . 3925775999!r 494452731 ‘ 147109995; 5.09959593 0.22233599 . ‘ 77......” 479175947 499517079 2.91509021 ..1.17762569 30.35957 ' 1470053753 v 3.xa1azsasi 1.537993”; 409790377 019721995 1.79175947 460517019 181609621 0.74401499 ' 30.35567 147005375; 1151330655 1.53730314i ' 4.09400927 0.1572758?» 1.79175947 4.60517019 ' 1016090217 137229329 3036657 1470053751 3461388661 ‘ 1.53738314' 409400527 016721885 130258509 460517019 110156957 ~~2.2770905 4.186607 198146235! 154167679} 019404935 ' 140900078 0.21324072 130256509 460517018 210156957 ‘ 4.1127654 4.166657 166146235. 154167679} .r0.794049351 140900978 021324072 130258509 450517019 . 210156957 , -0.E189226 4.155667 1661462351 2541676791 0794048351 ' 140900978 011324072 ‘ 107044154 438202663 250261545 - - -i '1 - ' 015306839 13 ...
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231HW12-S10 - H W [2 (92) TEJE; H02 Hm MP magma t...

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