HW3 Solution

HW3 Solution - 2,7 Page i _ Solution 3 Stat 128 mu (1 The...

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Unformatted text preview: 2,7 Page i _ Solution 3 Stat 128 mu (1 The change in {he mean hardness (Y) when “Hm Maps“? *tr‘me. (X) increqSes me hear 53 b1» (:2 70w 5: 55’ bi i tag, 31-98%} (re-Ir on 9:949) Mm b, 2 2,034 ) 01:0 :2!) fl- {6) Sibd : the? (0 9%- 5/4) : 2,?77 2,034 r: 2 ammo? a (145507) 2.35;?» 4t- (L77) 2.30) Thus, With Confidence @aflf’cgem f?) we est-imam ~thcazt the mezm hardness increases Somewhere betwem b7 and 2-3:: far Each Cielob‘tlonazfl hm" 6” we elapseofl flme bv H0 1 $1 :2 Us. Ha ; g, 3’32 came; 3 £0-23? n4) : t(g??§;f¢)‘2?77 _ ‘r-Z 2‘03 4 test sf“ *:~——..b' _ 42“ GIL?th t 5%} W‘ 09578 Beds on wire 179 “at! 5 2,?77, Grandad? H0 If >2.?77, Cencibde Ha: Decis'm ConcLMe Ho smee HR]: 0378 < 2‘??? P—VCI‘MQ : Pm}; H‘W‘Hi fl”): 0.378} IQPm‘D {1:04) > may} 2.8 (0). .io 2.16 Figure 2a 2 i3 0” P956 4-57 5-. = s v: Ha: 6%, “=00; n: 25' V .“ 195*3 3:579}? ‘3 5% c; 4% .._ - M...- - '. . tag-t 3+ 15:21 T _n HM 003470 Iaéécs‘zz‘? ) de: ‘ , . asiofi Me If 3th S t(,.%; H) : 45(0375-3 23) : 2,35? )CanCIHdGHo,’ if M} > 2,06?) Conciude HQ CORC-iuSion Conduct}, Ho 33mg H5“! = ;,g43223 < 106$ (1, Precflcfion iflflfef‘vai b, Cemoi‘dQ/nce “WWI 700" 0‘ Mm regpame ’J c, Predh‘cfion im‘WVGt/E . CL, 98% Cl 109? the mam hardflfls (Y) Wt!“ ’95 30 A , . , -35» - :{(b.??’- ML) -_- 1 a ,3- 3 = 227’. 2 , “m 2H“ z) ’ yh 68 6 + ‘2 O “H a) 6 = 2.624 2* A _‘ _j__ " 2‘ STA}: NStin+ SSH ]* M35 _ _!o.45<?‘?3 MSE - I01: 453%, n: :5, 5?: 28 , 53m " 3%.} “00905??- i' £230,103 A - I ‘ 36 J- (3 “232 - ' “* - it} 0e458?3 i 6 + SEQ 0&5864- ) 3.121} -: (Joiéggq :owgzzgj- A A . yh i {ii-ggn—238{xh§ (2 53 on Eye 54) :2 . H; )9, fifleflafim .4. Memo} In :‘th "Xh 30_ P5376 3. I j (363*?)2 XL : 22?;62 S'2{Precij 3 MSE if +fi +“‘§'§xx j 2 - Io 4&8?3 ‘if + 7? + “Mm-“(30 6—28)} 1-299: I’m? : “=1452? 3 _ Wm; “ ,JH.;4.:17 : 3 338 4 , Yh i ffif-:,n—2j S€prec1j 2) 22f 62 3.: 2-624K3333) =9 (220 86 J 2338,33), 250' Derive the pimps/fig m (2.6) 3*" the k“ : k; 2 um)?" Z :_ Z : I -—-. ~ 7. _ szx___)a T A 20m «M t X 20w) . h. ’2 F, _ ; mt —— L7Xz 2X3 — nil mange; Z“ ’___72 2: “mm H ;: 06 x) 21(pr z :(Xci2fxafw) 3X62‘ 9&2 2 :MM 3X; m hf? -_- 1 k _,_ :: ZJQ -=~ Jinx: + nx)‘ : } E (gue-Du options ls=72 nodate formdlim=' ; data plastic; input hardness time; datalines; 199.0 16.0 205.0 15.0 196.0 16.0 200.0 16.0 218.0 24.0 220.0 24.0 215.0 24.0 - 223.0 24.0 237.0 32.0 234.0 32.0 235.0 32.0 230.0 32.0 250.0 40.0 248.0 40.0 253.0 40.0 246.0 40.0 30 ; run; proc reg; model hardness=timelclb alpha=0.01; model hardness=timelr clm cli a1pha=0.02; plot hardness*time; run; "AS 60099 The SAS System 1 The REG Procedure Model: MODEL1 Dependent Variable: hardness Number of Observations Read 17 Number of Observations Used 16 Number of Observations with Missing Values 1 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 1 5297.51250 5297.51250 506.51 <.OOO1 Error 14 (146.425001 @M - > Ms“ ”‘ Corrected Total 15 5443.93750 SSE t I: C;2 we a {We 1 - . Root MSE R-Square c.9731 Dependent Mean 225.56250 Adj R-Sq 0.9712 Coeff Var 1.43376 a" - , a0 9 Parameter Estimates $?:: 163.69“0 + 2' 3 >§ _ Parameter Standard Variable DF Estimate Error t Value Pr > |t] I be .. Sim} Intercept 1 163.60000‘ (2.657021 63.45 <.OOO1 time 1 . 2.034381 0.09039- 22.51 <.ooo1 b1 C—w/s’gej Parameter Estimates Variable DF 99% Confidence Limits O Intercept 1 (160.69046 176.50954) 0115* {go time 1 ( 1.76529 2.30346) 0 Ci 1% {5), The SAS System 2 The REG Procedure Model: MODEL2 Dependent Variable: hardness Number of Observations Head 17 Number of Observations Used 16 Number of Observations with Missing Values 1 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model ' 1 5297.51250 5297.51250 506.51 <.0001 Error 14 146.42500 10.45893 Corrected Total 15 5443.93750 Boot MSE 3.23403 R-Square 0.9731 Dependent Mean 225.56250 Adj R-Sq 0.9712 Coeff Var 1.43376 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > |t| Intercept 1 168.60000 2.65702 63.45 <.0001 time 1 2.03438 0.09039 22.51 <.0001 The SAS System 3 The REG Procedure Model: MODEL2 Dependent Variable: hardness Output Statistics Dependent Predicted Std Error Obs Variable Value Mean Predict 98% CL Mean 1 199.0000 201.1500 1.3529 197.5993 204.7007 2 205.0000 201.1500 1.3529 197.5993 204.7007 3 196.0000 201.1500 1.3529 197.5993 204.7007 4 200.0000 201.1500 1.3529 197.5993 204.7007 5 218.0000 217.4250 0.8857 215.1006 219.7494 6 220.0000 217.4250 0.8857 215.1006 219:7494 7 215.0000 217.4250 0.8857 215.1006 '219.7494 8 223.0000 217.4250 0.8857 215.1006 219.7494 9 237.0000 233.7000 0.8857 231.3756 236.0244 10 234.0000 233.7000 0.8857 231.3756 236.0244 11' 235.0000 233.7000 0.8857 231.3756 236.0244 12 230.0000 233.7000 0.8857 231.3756 236.0244 13 - 250.0000 249.9750 1.3529 246.4243 253.5257 14 248.0000 249.9750 1.3529 246.4243 253.5257 15 253.0000 249.9750 1.3529 246.4243 253.5257 16 246.0000 249.9750 _1.3529 246.4243 253.5257 17 . 229.6313 0.8285 {227.4589 231.8056 3 :232: C2; 139 E1113 Output Statistics “411514 X330 . Std Error Student Obs 98% CL Predict Residual Residual Residual 1 191.9496 210.3504 —2.1500 2.937 ~0.732 2 191.9496 210.3504 3.8500 2.937 1.311 3 191.9496 210.3504 -5.1500 2.937 -1.753 4 191.9496 210.3504 ~1.1500 2.937 -O.391 5 208.6248 226.2252 0.5750 3.110 0.185 6 208.6248 226.2252 2.5750 3.110 0.828 7 208.6248 226.2252 -2.4250 3.110 -0.780 8 208.6248 226.2252 5.5750 3.110 1.792 9 224.8998 242.5002 3.3000 3.110 1.061 10 224.8998 242.5002 0.3000 3.110 0.0965 11 224.8998 242.5002 1.3000 3.110 0.418 12 224.8998 242.5002 -3.7000 3.110 -1.190 13 240.7746 259.1754 0.0250 2.937 0.00851 14 240.7746 259.1754 ~1.9750 2.937 -0.672 15 240.7746 259.1754 3.0250 2.937 1.030 16 240.7746 259.1754 -3.9750 2.937 -1.353 17 (220 . 8695 238 . 3930) . $52 Wang/1011011. 111181101 X1le with X :30 The SAS System 4 The REG Procedure Model: MODEL2 Dependent Variable: hardness Output Statistics Cook's Obs -2-1 0 1 2 D 1 1 *1 1 0.057 2 1 1** 1 0.182 3 1 ***1 1 0.328 4 1 1 1 0.016 5 1 1 1 0.001 6 1 1* 1 0.028 7 1 *1 1 0.025 8 1 1*** 1 0.180 e 1 1** 1 0.048 10 1 1 1 0.000 11 1 1 1 0.007 12 1 **1 1 0.057 13 1 1 1 0.000 14 1 *1 1 0.048 15 1 |** | 0.112 16 | **| | 0.194 17 Sum of Residuals 7 0 Sum of Squared Residuals 146.42500 Predicted Residual 88 (PRESS) 194.01315 hardness : 000.0 %2.03440ime 200' - N ' 15 qu - fl 0.9m 2504 000$ _ 0.020 T RMSE 3.234 2400 m 2300 + 05.0 10.5 20.0 22.5 25.0 27.5 30.0 32.5 35.0 37.5 40.0 time ...
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This note was uploaded on 11/09/2009 for the course STAT 118 taught by Professor ** during the Fall '09 term at GWU.

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HW3 Solution - 2,7 Page i _ Solution 3 Stat 128 mu (1 The...

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