ADMS 3330 Midterm - 2008 Winter

ADMS 3330 Midterm - 2008 Winter - AK/ADMS 3330.3.0 Mid Term...

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Unformatted text preview: AK/ADMS 3330.3.0 Mid Term 1 Winter 2008 PART B CONTAINS 22 PAGES - INCLUDING COVER PAGE PLUS TABLES (LAST 3 PAGES). DO NOT DETACH ANY PAGES. Question 1 (13 marks) A professor of economics wants to study the relationship between income ()2 in $10005) and education (x in years). A random sample W is taken and the results are shown below. (Keep computations to two decimal places) Education Cx) 11‘ 8 12 10 13 14 Income ) 40 35 43 41 52 49 7 a) Sketch a scatter diagram of the data to determine whether a linear model appears to be appropriate. 515000) 3 ID‘IIIZIS 13 2 y2 = 11460 andey— — 3008. Compute estimates of the slope and the intercept for the regression of y on x. _ __ _ _ __ ._......____..i..__._.__....,._._. _ __ _ _. .A... 0..- _ “$133.3...” _ _._ _ .. 3'“ Th;[ Z74 3,: m n_\I - __ _ “MS—xi _ - l m _ 2m 1.: “3‘2"? + 2va + ”‘43 “4% i H [2% 4""??? 'f"'3‘?”“?3iw AK/ADMS 3330.3.0 Mid Term Winter 2008 c) Determine the Wand describe what this statistic tells you about the model’s fit. _ 260‘a j W s 3?: 21 ‘ 55L(“’>C35”'*" K3,. =: b x L 39 ti — ,4 m 3 Z::::Z'Igglig.,j @444 $1 @W7c:(§3;'g‘"5m‘° [2 27) ,_ sSté 311G , , ,_ d) Is there evidence at the 5% significance level of a linear relationship between income and education? 6 :o_ _ __ H, @‘ito____ ., __ in- U) w ill Pag onZ #11er a fluidmcfi m leafed; Hs “declare. fiw'q q New ”lawth P AK/ADMS 3380.3.0 Mid Term Winter 2008 Question 2 (12 marks) A real estate agent seeks to develop a model to predict the selling price of a home. At first, the agent believed the most important variable in determining the price of a home is house size in square feet. A first-order model and a W‘ were proposed, and obtained the following output results. Answer questions (a) and (b). SUMMARY OUTPUT First-order model Re oression Statistics — mm_ 0.9868508 R Suare 0.972349 Ad'usted R Suare 0.9692 Standard Error 5.289488] 20 ANOVA df SS Re . ression Residual Total — ‘ Coefficients Standard Error lnterce ut 4535.5548 15.1 8244903 House Size -68.91228 6.679585284 SUMMARY OUTPUT Second-order model Re ression Statistics Multi le R 0.9161795 R Sguare 0.8555501 Adjusted R Sguare 0.8473206 Standard Error 15.9570332 Observations Re ression Standard Error lnterce at House Size1 House Size2 a) Write out the equation for each model. Page 4 of 22 -10.3169 _ 33 MS 10686.84 6032661501 3548624 __ 21976.95 —— t Stat df 2 17 I . 7669.1045 37.40477606 20.50301 1.99E-13 -359.1005 34.19257013 -10.5023 7.51E-09 64.547297 7.576323931 8.519606 1.53E-07 MS 1 18797.96128 18797.96 106.4374 5.51432E-09 3178988723 176.6105 —— 19 21976.95 5.51E-09 5 5 34076E 14 " Natal 'l'f.,'.j:I: :..:: -Qf“I...,.:f.-I. AK/ADMS 3330.3.0 Mid Term Winter 2008 b) Which model seems to fit better? Explain your answer L _ @215" "a z _ 8’“ :2: ("s-815 5556p ,ng4ve3lM t?313m_, =~ 13:. 4...: 733:9, After exploring the above model, the agent thought that house size in square feet, lot size in square feet, and the structure of house are important variables in determining the price of a home. Then, the agent developed a model and got the following output result. The indicator variable is l = 1 if two story or I = 0 if not. Answer questions (c), (d) and (e). SUMMARY OUTPUT 0.666481 0.444196 0.339983 25337.48 8.21E+09 2.74E+09 4.262381 0.021596 1.03E+10 6.42E+08 _— 1.85E+10 — CoeffICIents Standard Error t Stat P-va/ue 70230.9 29272.89 2399179 0.028967 107.6029 . -20.1149 35.20226 —0 57141 0.575661 114 9596 0.936005 0.363184 _ 22052.8 13767.14 1.601845 0.128746 ll Page 5 of 22 AK/ADMS 3330.3.0 Mid Term 9 Winter 2008 c) Write out the regression model that the agent developed. (L __ ___________ g5;35.9.2950.99._9l9___j.__lgiaeflls9_+ 20- llfl,.35>_i_220519’ 314 d) To test the validity of the model, where do you need to check in the output results? ___.9_Jotl51l9_ur,g:§§.._:tl5c5_25;55§§L___dfipmds ”on“ J? iést 9.9-.. 3 _____ ___l-l ______ ‘r __ i: __. _ ___9555955999 5 9 999, 555 95 9 _ “:1: ‘ *5 559:; 995599: 59 "“9995 55 59959 99995;, 9 5999., e) For each one square foot increase in house size, how much does the house price increase on average, provided that the other variables are constant? Page 6 of 22 AK/ADMS 3330.3.0 Mid Term Winter 2008 Question 3 (13 marks) ProFlex, a new manufacturer of high- e-nd golf clubs, decided they wanted to start analyzing their sales data for the ast 10 months. Given the following sales data: 356 a) Use ex 0 ntial smoothing to fo cast sales for theilh month 3E’acriId provide the MSE. Use a smoothing const toLELfor this approach. Please 0 tyour answer in fiox provided. . . ‘ sea :65- Fa=05x550toixbl‘1~ bass L ' E4 0 3 lg Ya + 0 (M3 t). 31% 5‘10 f" o 124 5355 55H! F5f169%:LififliékéfiI};ohm :03X567Jrotx 5511 If; is 56 .2 ‘17. F O 3 :9 TS «Ida (IE: 05x54“: + 07 3‘ 556 2q1_.58’> 2079 r—I 05X__\{5+0'l r5» 27(5ch +07X553 2079~563945 Ft; 0 3 X “is "t o "I X F3 [email protected]‘i;‘..,fi駧:,:.__.:.‘_:_:_fl_iuk:vaIW P 7 f22 J .Fu '- 0 3 X Ylo f 01“ [:lo -ag:é00 5'55 AK/ADMS 3330.3.0 Mid Term » Winter 2008 b) Use @moving average . forecast sales for the 11th month and provide the MSE. Please put your answe n the box provided. _ , -- . i. 360. 013 2' 54013:: +SGS ...... l 5:51 .. , - - i I: . ILYi F) I " 1:11 -" - _____ 9 _-. 5L5; — -- -.-- ...... ,I _____ $511135: .11 028:) ____ _ MSE.: (a (O ‘1 5 - 553%156 1 c) Use a weighted moving average to forecast sapl(es for the 11th month ”51—1-5526 and prOVIde the MSE. Use weights of .6 .3 and .1. Please put your answer in the box provided. flfff:-7-f,:5.516:1;‘11::54I4 " 126116 f:Q11f.'_’§;f:j_ii:If:I:fff :7 ~ I1 3 5171.151337] 57’ 5’ Io M @5wa? - _. 5465727 J72» ., 100315 ‘1 ,. ,_ 0 £156ch 567 621 2| ‘65 1%" 530 5151 5 173-1 .515- 2‘1 d) Which approach prod d‘Fges tnggest forecasting result Ex-onential Smoothin. smctHefi £15th ‘ . Circle the one you selected. WeI hted Movm o Avera-ed \ Mm! Ma 15111621 66-36”- a £11...qu Page 8 of 22 AK/ADMS 3330.3.0 Mid Term Winter 2008 ___—”___— Question 4 (12 marks) Tyrone Wheeler set up TW Tires in 2003. He believed that by offering services such as off- season tire storage and online preebooking of sets of seasonal tires, he could create a significant amount of value added for his clients. He has the following sales records for the past 16 quarters: ___—— a) Assuming a Multiplicative Time-Series Model, com te e scaled seasonal indices for all four seasons. 6) S(Og‘aoé-icfi'ifl'iogflOVEzAOW‘EQEBB‘EM S(tow—HumMowflmlma—om40463 9 go. Gizawocw—rmm) _ fi-vfiéim‘az‘oqtfl?) ,_ _. . «rafthloofi 34.10 84hr? .. -63 i N . Page 9 01°22“ C1( Q2 Q75 @va v Y/ ‘E 5 V . é V Y; \/ AK/ADMS 3330.3.0 Mid Term Winter 2008 Suppose that we haVe already computed all de-seasonalized sales for the above time periods and fitted a least squares linear regression in which the de-seasonalized demand is the dependent variable and the period, t, is the independent variable. The linear regression have produced the equation Y = 236. 5126 + 10. 2483*t. (’1 ) 3 Farag 6 C. c, b) What IS the MSE forthe four qu rters of 2007? (‘l IL A h“, . hat 05 b .2 . . _ ((5% J quiet; ___________________________ _ -.£t_2.._i_.§(et:(5 _______________ ; ______ _ _..___(1H'D- 3505 . (418 l.._.5et%. Page 10 of 22 AK/ADMS 3330.3.0 Mid Term @ Winter 2008 c) Compute the sales forecasts for all seasons of 2008. 0%? 249035 Ll- _ ____.E x 236m. 312M losétm I15 ____‘.¢:+l L267- M __- .. _.__.\._,3___ _ ..__ ,_ . _ m _‘_t2:§_:_52_2 _&>)_.._8;.005 x. 5:32.9125 ..... Page 11 of 22 AK/ADMS 3330.3.0 Mid Term Winter 2008 Question 5 (13 marks) Jeff, a small investor, has some funds available to invest. He has narrowed his choices to two common stocks, namely Tory Bank and Rocky Auto, and he intends to invest all his money in precisely one of the two stocks. Market can be high or low. His payoffs (gain/loss) stated below depends on what happens to the market. m- State of Nature T— Hi h H $000 Low L $000 mix-— -robabilit Jeff is considering hiring the services of Amy Consultant to obtain better estimates of future market behavior. The reliability of Amy’s forecasts of market favorable (F) and market Unfavorable (U) is as given below: P(F|H)=O.8 WU”) 'flh'oii (U|L) =0.7 (PM \_ 003 min—w PC” 03 PlEuH) 0&4 a) Construct the tree and state the optimal decision strateg without onsulting Amy Consultant. Why? _T05 Bo ,« e a ,1 l4 x 0 I:_—____f_":_”_ii:f;....:“mffff]l..flZ:1::fffmif:_ j ”10 ma 1:. m w l =2: 1+1 [05 has he”; tV j; fiffflifl f.)1.1;””i::f' 'fQ _ Skouic’t d‘ome W mwfi ‘1“ Tag Page 12 of 22 AK/ADMS 3330.3.0 Mid Term Winter 2008 Page 13 of 22 AK/ADMS 3330.3.0 Mid Term Winter 2008 c) What is the expected value of Amy’s forecast? How much should Jeff be willing to pay Amy Consultant? F Stalénfncxlwe " w .m.-.H13h_________._._-___.._‘..._ ”3-. .l,..,,.t__.‘,_t.,.,...l._a- _.,. w .-\__.‘.-.V WWW”. “we..-“ 4‘ , .. W- -Wl....-._. . _...,,_.L-Qfl___-_________.____,._._-_-.“"5”- _,..u.‘..l__,-_., _ WW -m. W._,...-,V.w.~,,m_.__ ._ :L: 1. - _ ' ~ A AK/ADIVIS 3330.3.0 Mid Term Winter 2008 d) Construct a decis' tree for the whole problem. Include all probabilities and payoffs. Pagey15 of 2,2, AK/ADMS 3330.3.0 Mid Term Winter 2008 e) Measure the efficiency of Sample Information. Page 16 of 22 AK/ADMS 3330.3.0 Mid Term Winter 2008 Question 6 (12 marks) .4 ' You are provided you with the following table in which the values are expressed i {W} . Decision 014 Required: a) Which decision would an optimistic decision maker select? min. ,,,,,,, Lost ............... cl; =- 3500 _, .01: :«21390 Jib?" 590 61+“?- $00 —’ ~ QLQQ/E‘Sibfi ".5 F5 chosen x, . __ _ b) What about a conservative decision maker? mm m Ma, _ finalisasfc... Jig? ___.._ma~ggl cflfi “for; _ mafia {fit-13931 m _ __ _._ _ _____________________ “Mm; .m& 3.--- -1314. '—"- WW} .5 _ 9:1; 22%09 ‘ _ € __ g.._% Markejwt_ .Cieu‘? midis} ................. chaser: .. V. MORE NEXT PAGE... Page 17 of 22 AK/ADMS 3330.3.0 Mid Term Winter 2008 (1) Which decision alternative would aMision maker select? Assume that the probabilities of S], S; and 83 are 0.3, 0.2 and 0.5 respectively. MORE NEXT PAGE... Page 18 of 22 AK/ADMS 3330.3.0 Mid Term Winter 2008 e) A decision maker, Selena, expressed the following indifference probabilities. Letting U (500) = 10 and U (6000) @which decision alternative would Selena select? Assume that the probabilities of $1, $2 and 83 are 0.3, 0.2 and 0.5 respectively. " __::I:I:7.:to:é}:'fIf.TT:ffti625::iii—is}:iii-:1::1::1::j‘ffflfff,. Ev=fl3 Foeforsqmsgz4 ' “ Evesclsos' i 7m2iat¢msl152fil ”tommflingm$03.”... . ’iflVfll’aggxaglg7fi55 .. m «2‘ 3.3 we; ‘3. fi‘gm‘l'i" .52 W73} 15'ch END OF PART B. TABLES ON PAGES 20-22. Page 19 of 22 AK/ADMS 3330.3.0 Mid Term Winter 2008 DO NOT DETACH THE TABLES Critical Values of t DEGREES OF FREEDOM t.1on 11.050 15.025 12.706 31.821 63.656 4.303 6.965 9.925 3.182 4.541 5.841 i 2.776, 3.747 4.604 2.571 3.365 4.032 2.447 3.143 3.707 2.365 2.998 3.499 2.306 2.896 3.355 2.262 2.821 3.250 2.228 2.764 3.169 2.201 2.718 3.106 2.179 2.681 3.055 2.160 2.650 3.012 2.145 2.624 2.977 2.131 2.602 2.947 2.120 2.583 2.921 2.110 2.567 2.898 2.101 2.552 2.878 2.093 2.539 2.861 2.086 2.528 2.845 2.080 2.518 2.831 2.074 2.508 2.819 2.069 2.500 2.807 2.064 2.492 2.797 2.060 2.485 2.787 2.056 2.479 2.779 2.052 2.473 2.771 2.048 2.467 2.763 2.045 2.462 2.756 2.042 2.457 2.750 2.030 2.438 2.724 2.021 2.423 2.704 2.014 2.412 2.690 2.009 2.403 2.678 2.000 2.390 2.660 1.994 2.381 2.648 1.990 2.374 2.639 1.987 2.368 . 2.632 1.984 2.364 2.626 1.980 2.358 2.617 1.977 2.353 2.611 1.975 2.350 2.607 1.973 2.347 2.603 1.972 2.345 2.601 1.960 2.326 2.576 Page 20 of 22 AK/ADMS 3330.3.0 Mid Term Winter 2008 Critical Va‘ues of F: A = .025 .43) A P NUMERATOR DEGREES 01= FREEDOM v2 1 2 '3 4 5 6 '7 8 ,9 1' 647.8 799.5 364.2 899.6 921.8 937.1 9432 956.7 963.3. 2 3.851 39.00 39.17 39.25. 39.30 39.33 39.36. 39.37 39.39 3 1744 16.0.4 15.44 15.10 14.83 14.73 14.62 14.54 14.47 4 12.22 10.65 9.98 9.60 9.36 9.20 9.07 319.8, 3.90 5 10.01 3.43. 7.76 7.39 7.15 6.98 6185.- $6.76 6.63 ’6 8.31 7.26 6.60" 6.23 5.99 5.32 5.70 5.60 5.52 7 8.07 6.54 5.89 5.52 5.29 5.12 4.99‘ 4.90 4.32 3 7.57 6.06 5.42 5.05 4.32 4.65 4.53 4.43 4.36 9 7.21 5.71 5.08 4.72 4.43 432 4.20 4.10 4.03 10 6.94 5.46 4.83 4.47 4.24 4.07 3.95 3.85 3.78. 11 6.72 5.26 4.63 4.28 4.04 3.38 3.76 3.66 3.59 12 655- 5.10 4.47 4.12 3.89 3.73 3.61 3.51 3.44 13 6.41 4.97 4.35 4.00 3.77 3.60 3.43 3.39 3.31 .14 6.30 4.86 4.24 3.89 3.66 3.50 3.33 329 3.21 15 6.20 4.77 4.15 3.80 3.53 3.41 3.29 3.20 3.12 16 6.12 4.69. 4.03 3.73 3.50 3.34 3.22 3.12 3.05 g 17 6.04. 4.62 4.01 3.66 3.44 3.23 3.16 3.06 2.93 g 18 5.93 4.56 3.95 3.61 3.38 3.22 3.10 3.01 2.93 :2 19 5.92 4.51 3.90 3.56- 3.33 3.17 3.05 2.96 2.83 *5 20 5.37 4.46 3.8.6 3.51 3.29 3.13 3.01 2.91 2.34 5;; 21 5.83 4.42 3.82 3.43 3.25 3.09 2.97 2.87 2.80 g 22 5.79 4.38 3.78 3.44 3.22 3.05 2.93 2.84 2.76 g 23 5.75 4.35 3.75 3.41 3.13 3.02 2.90 2.31 2.73 g 24 5.72 4.32 3.72 3.33 3.15 2.99 2.37 2.73 2.70 2 25 5.69 4.29 3.69 3.35 3.13 2.97 2.35 2.75 2.63 ‘5‘ 26 5.66 4.27 3.67 3.33 3.10 2.94 2.32 2.73 2.65 g 27 5.63 4.24 3.65 3.31 3.08 2.92 2.30 2.71 2.63 23 5.61 4.22 3.63 3.29 3.06 2.90 2.73 2.69 2.61 29 5.59 4.20 3.61 3.27 3.04 2.33 2.76 2.67 2.59 30 5.57 4.13 3.59 3.25 3.03" 2.37 2.75 2.65 2.57 40 5.42 4.05 3.46 3.13 2.90 2.74 2.62 2.53 2.45 60 5.29 3.93 3.34 3.01 2.79 2.63 2.51 2.41 2.33 120 5.15 3.30 3.23 2.89 2.67 2.52 2.39 2.30 2.22. 06 5.02 3.69 3.12 2.79 2.57 2.41 2.29 2.19 2.11 SOURCE: From M. Merrington and C. M. Thompson, "Tables of Percentage Points of the Inverted Beta (F)9Di5tribution," Biomeh'ika 33 (1943): 73—88. Reproduced by permission of the Biometrika Tmstees. Page 21 of 22 York University Table 6(a) ———--———-—————————.—u___—_—_—____ Critical Values of E A = .05 fl?) NUMERATOR DEGREES 05 FREEDOM 4 S 6 1 161.4 199.5 215.7 224.6 230.2 234.0 236.8 238.9 240.5 2 18.51 19.00 19.16 1.9.25 19.30 19.33 19.35 19.37 19.38 3 10:13 9.55 9.28 9.12 9.01 8.94 8.89 8.85 8.81 4 7.71 6.94 6.59 6:39 6.26. 6.16 6.09 6.04 6.00 5 6.61 5.79 5.41 5.1.9 5.05 4.95 4.88 4.82 4.77 6 5.99 5.14 4.76 4.53 4.39 4.28 4.21 4.15- 4.10 7 5.59 4.74 4.35 4.12 3.97 3.87 3.79 3.73 3.68 8 5.32 4.46 4.07 3.84 3.69 3.58 350 3.44 3.39 9 5.12 4.26 3.86 3.63 3.48 3.37 3.29 3.23 3.18 10 4.96 4.10 3.71 3.48 3.33 3.22 3.14 3.07 3.02 11 4.84 3.98 3.59 3.36 3.20 3.09 3.01 2.95 2.90 12 4.75. 3.89 3.49 3.26 3.11 3.00 2.91 2.85 2.80 g 13 4.67 3.81 3.41 3.18 3.03 2.92 2.83 2.77 2.71 E 14 . 4.60 3.74 3.34 3.11 2.96 2.85 2.76 2.70 2.65 E 15 4.54 3.68 3.29 3.06 2.90 2.79 2.71 2.6.4 2.59 '5 16 4.49. 3.63 3.24. 13.01 2.85 2.74 2.66 2.59 2.54 E 17 4.45. 3.59 3.20 2.96 2.81 2.70 2.61 2.55 2.49 1;; 18 4.41 3.55 3.16 2.93 2.77 2.66 2.58 2.51- 2.46 a 19 4.38 3.52 3.13 2.90 2.74 2.63 2.54 2.48 2.42 e 20 4.35 3.49 3.10. 2.87 2.71 2.60 2.51 2.45 2.39 :2 21 4.32 3.47 3.07 2.84 2.68 2.57 2.49 2.42 2:37 5 22 4.30 3.44 3.05 2.82 2.66 2.55 2.46 2.40 2.34 :21 2.3 4.28 3.42 3.03 2.30 2.64 2.53 2.44 2.37 2.32 “ 24 1 4.26 3.40 3.01 2.78 2.62 2.51 2.42 2.36 2.30 25 4.24 3.39 2.99 2.76 2.60 2.49 2.40 2.34 2.28 26 . 4.23 3.37 2.98 2.74 2.59 2.47 2.39 2.32 2.27 27 4.21 3.35 2.96 2.73 2.57 2.46 2.37 2.31 2.25 28 4.20 3.34 2.95 2.71 2.56 2.45 2.36 2.29 2.24 29 4.18 3.33 2.93 2.70 2.55 2.43 2.35 2.28 2.22 30 4.17 3.32 2.92 2.69 2.53 2.42 2.33 2.27 2.21 40 4.08 3.23 2.84 2.61 2.45 2.34 2.25 2.18 2.12 60 4.00 3.15 2.76 2.53 2.37 2.25 2.17 2.10 2.04 120 3.92 3.07 2.68 2.45 2.29 2.17 2.09 2.02 1.96 3.» 3.84 3.00 2.60 2.37 2.21 2.10 2.01 1.94 1.88 SOURCE: From .M Merrington and C. M. Thompson, ”Tables of Percentage Points of the Inverted Beta (IO-Distribution," Biometrikrz 33 (1943): 73—1-88. Reproduced by permission of the Biometrika Trustees. Page 22 of 22 ...
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