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exam1solutionsinclass - ISYE6414 Summer 2010 Exam I Dr Kobi...

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Unformatted text preview: ISYE6414 Summer 2010 Exam I Dr. Kobi Abayomi June 10, 2010 You must show all work to receive full credit. kQK] >0 1 A Climatologist investigates the effect of Solar Radiation, Wind, and Temperature on Ozone +i levels. She takes n = 153 daily observations from May 1st until September 30th. The multiple regression output is: Fill in the missing values above. Write the estimated linear model. A +5 {.2 494.34 +0.0;759L Xu , 3.33 X;; +1447“ X23 2 For the model Y1- : [30 + [31XZ- —|— 61; with Q ~ N(O, 02) the following statistics are computed: 9 i=1 9 9 255?: 324 = 2y? 1'21 i=1 9 9 i=0: i +5- !) Compute the least squares estimates [30,51 J.)Compute the SSE, SSR, and SST. Compute the R2 value. Compute the observed F- statistic and perform the appropriate hypothesis test. 'HO +§ ?) Compute the prediction error for a single response a; = x0 for this model. Compute a prediction interval for a single response when :1: = 5 2(X;~T<‘)C -~~9’) 2 209-96...) 443 01": :(Xr—Yfi 20(7):- : 33.54 2 0-0!“ J Ln = 0 A) SST = g: C‘flwfl >317‘ SSR = éQQ'Wf-t 5f§xf=w SSE—‘~/‘H.0$' ,Q‘: i: = earl-*5“ H" A” V" H" ‘3’” Fag?“ x = 7} 5.7567 ,. Reject H. 3) ‘66 laxo i 1;.oatm—a. ‘Spgi 5;"4=MSE‘(’+%+(3%9 H§E=%= 95713: 30.3.? >0 3 + ‘ In a regression of Number of New Accounts (Y) on Size of Minimum Deposit (X) the following ANOVA table is computed: Source l SS l df l MS Regression g] 40.4,. 1 $1 4-0 4- Error 14,7416 9 I637. 74 ‘l‘ ’5' Lack of Fit 13,593.13 4 35 98. 4(- Pure Error [(48 5 2.3.7. 4 Total 19,882 10 Test the hypothesis 51— — 0 vs. the two sided alternative; test the hypothesis E(Y ) = fi0+fl1X vs. the two sided alternative What a1e your conclusions? /- FL: PIT—‘0 VS Ha: Fl 4:0 s ._ +7 F= 11%;: 3.883 < 5.757%?) "5-” 51¢th Ho 2.11. : eéy)= p. +p.x vs. In .~ ECY) + F» +sz +7 91.]. F: ,HSLF :______35q, 2/ .‘3 , (1/5 ‘9’ ‘ MSPE £27,4- 4 >51: ) 7 -‘. l’éjto'b Ho 6 4 This data is collected X y 1 13.59141 2 36.94528 3 100.42768 4 272.99075 5 742.06580 Here is a scatter plot with a linear fit o o to o o > <1" 0 o N o 1 2 3 4 5 X I) Suggestan appropriate transformation and compute the new regression of Y on X using the transformed values. Perform these tests on your model: :1) I)H0251=0andH)HO:Y=fi0+fi1X+e 3) Interpret the coefficients of your model in terms of the original, untransformed data. >0 )This page intentionally left blank I +3 An «Ppmpr‘ld’a ‘lnns‘firn‘mlim : K’s ex/JX) b; _ :(X ——x',~~)c:j a) +1; ? Zéx~ ——~x ”T Y" ~/~7'7¢0 IO ‘ + 5')" ~£ =S’ b.=-/.7047./o no ’) I) H. . ISM—0 vs. H,:p,:¢=o +15 F: 55R >> F.4t-(l’3) I lecmxe QEQO M$ PE gr V7] ”a J7me 4!“ Model ‘H‘fir JA'ILA Mt]? SSLFAD, S‘féko (If you eff/Am “r 7‘» have ’ (10“ qef 'fiul” CNJI‘h) +2 .9) 77‘? an?! (LII-Mae Ty» €xP(X) make: 75 c/unje 5— ,‘q'fNWS/W?! 5 Show work Assume Q ~ N(0, 02) I) . For the model K: = 50 + filXi + 67; with , 21:1 6 z 0. .1). For the above model7 when R2 : 0, yi : g). 3). For the above model, when the 65 are independent, they are also independent if 1 / X is substituted for X. 47)- What is an appropriate transformation for this model Y;- : exp{fio +fi1X1-Y1 +fi2Xi,2+eZ-} i X Extra Credit: For the model K- : e$p{fio + 31X“ + flQXiag + 61-}, what is the expected Change in the response variable for a unit change in X1? +1; I) M7h283=2(‘1;-'b.—b.><z)‘ a}: =23(7;—-b.~hx;)=0 ~<D Se == zLj;—b.—b.><:) =0 (2'6?) +§ A) o=p‘=_§_55_lfi ,‘IJ‘eto $51230. .ssR=:()?,~—7)“=o mam: 5‘: =31“ fir all a. CmrI- neceuartlj ‘j;==‘? firm-‘5 +5” 4) '{Ji=9n‘31=P°*P:Xn *P>Xf=+57 Erlm) E[ Yi/X,=1,H — {($11} = czf (p,+/2,(2,+I) + PM; ~o‘f (Ad-POO +P3Xz) ’3 (9/3"!) ‘fo(/5p+fl.x/ +I3+X2.) +5 ~’— (y’all) wrap» 4—13.)“ Mb) 10 ...
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