exam1solutionsinclass

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

This preview shows pages 1–7. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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 ...
View Full Document

{[ snackBarMessage ]}

What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern