Analytical Methods in Economics and Finance | My Assignment Tutor

Unit Code: MAE256 Unit Name: Analytical Methods in Economics and Finance FinalExamination T1, 2020__________________________________________________DEAKIN UNIVERSITYFACULTY OF BUSINESS AND LAWDepartment of EconomicsFINAL EXAMINATION TRIMESTER 1, 2020Unit Code: MAE256Unit Name: Analytical Methods in Economics and FinanceEstimated Reading and Working Time: 2 hours and 15 minutesEstimated time for preparing and submitting your final responsesto CloudDeakin Dropbox: 45 minutesThis is an Open Book Scheduled Online Release Examination. You mustupload your final responses as a Microsoft Word Doc and a pdf file toCloudDeakin Dropbox within 3 hours from the start time scheduled inthe exam timetable.This exam consists of five (5) questions. Answer all the questions. This exam papercarries a total of 60 marks. (This is converted to 60% of your total assessment inthis unit).Preparing and submitting your answers:๏‚ท Download the exam answer sheet word document and input your answers inthat document by typing your response below each question number in thedesignated area.๏‚ท Please insert appropriate diagrams and calculations if necessary in that area.Legibly draw/hand-write relevant graphs or calculations on a piece of whitepaper, scan it and insert it in the document along with your typed responseto each question.๏‚ท For instructions on scanning and inserting images in the word document,please refer to Exam Preliminary Information Document that was released onthe unit site prior to the exam period.๏‚ท Upload the completed exam answer sheet word document along with a pdfcopy of the same in the CloudDeakin Dropbox prior to cut-off timeNOTE: UPON SUBMISSION TO CLOUDDEAKIN, ALL ASSESSMENT WILL BE SUBMITTED THROUGHTURNITIN for the purposes of detecting collusion and/or plagiarism. If your work is found to breachAcademic Integrity Standards, it will be reported to the Academic Integrity Committee (AIC) and theconsequences may result in a Fail for the unit or worse (exclusion from your course).Unit Code: MAE256 Unit Name: Analytical Methods in Economics and Finance FinalExamination T1, 2020__________________________________________________Answer all the questions below.Question 1 (this question has three parts, (a), (b) and (c)) (a)Consider the following probability distribution function for thediscrete random variable X. Calculate E(3X2 + 5). X234f(X)0.450.340.21 (3 Marks)(b) The following joint probability distribution function table showsthe likelihood of the number of times (X) different age groupsof people (Y) have left their house each week for any reasonduring the COVID-19 crisis. Note that X = 1, 2 and 3. Thevariable Y = 1 (Young), 2 (Middle aged), 3 (Old) and 4 (Veryold). Calculate Cov (X,Y). X123Y10.170.130.0820.240.040.0330.140.010.0240.080.020.03 (5 Marks)(c) During the COVID-19 pandemic, it has been observed that fora selected group of countries, the number of new casesrecorded has a normal distribution with a mean of 102, and astandard deviation of 127. Find: (i)(ii)P(50 < X < 150)What is the probability that on any one day in one ofthese countries, less than 10 new cases will berecorded?(4 Marks) (3 + 5 + 4 = 12 Marks)Unit Code: MAE256 Unit Name: Analytical Methods in Economics and Finance FinalExamination T1, 2020__________________________________________________Question 2 (this question has two parts, (a) and (b)) (a)Using firm level data of Indian manufacturing, the followingmodel of employment (EMP) is estimated. ๐‘™๐‘œ๐‘”ฬ‚(๐ธ๐‘€๐‘ƒ) = 0.36 + 0.0183 (๐ธ๐‘‹๐‘ƒ)Where EMP is measured in thousand persons and EXPrepresents firm specific exports measured in million dollars. (i)(ii)Interpret the coefficient of EXP.Based on the model presented above, what is thepredicted employment for a firm with export of 1.75million dollars?(4 marks) (b) In April 2020, many people across the world died beinginfected by COVID-19. To examine the factors affectingnumber of deaths, data were collected on the followingselected variables for 100 countries.DEATH: Total number of deaths due to COVID-19 in eachcountry in April 2020TEMP: Average temperature (in Celsius) in April 2020POPSC: The number of senior citizens, aged over 65SH: A dummy variable that takes a value of 1 if a country islocated in southern hemisphere or 0 otherwise.The estimated model is given below. Standard errors are inparentheses.log(๐ท๐ธ๐ด๐‘‡๐ป ฬ‚ ) = 7.022 โ€“ 0.0297 log(๐‘‡๐ธ๐‘€๐‘ƒ) + 0.053(๐‘ƒ๐‘‚๐‘ƒ๐‘†๐ถ) โ€“ 194.83๐‘†๐ป(3.62) (0.088) (0.002) (36.55)n = 100 R2 = 0.696 (i)Test whether log(TEMP) can significantly explainlog(DEATH) at the 1% level.Test whether the variable SH has a negative effect, thatis, the countries located in southern hemisphere have(ii) significantly lower death relative to other countries. Use5% level of significance.(iii) Interpret the goodness of fit of this model. (8 Marks)(4 + 8 = 12 Marks)Unit Code: MAE256 Unit Name: Analytical Methods in Economics and Finance FinalExamination T1, 2020__________________________________________________Question 3 (this question has four parts, (a), (b), (c) and (d))Consider the following house sale price regression modellog(pricei )= ฮฒ0+ ฮฒ1 agei + ฮฒ2 bedroomsi + ฮฒ3 bathsi+ ฮฒ4 pooli+ ฮฒ5fireplacei + ฮฒ6 waterfronti + uiwhereprice: sale price in thousands of dollars,age: age of the house in years,bedrooms: number of bedrooms in the house,baths: number of bathrooms in the house,pool: a dummy(binary) variable which takes the value of 1 if thehouse has a swimming pool and the value of 0 otherwise,fireplace: a dummy(binary) variable which takes the value of 1 if thehouse has a fireplace and the value of 0 otherwise.waterfront: a dummy (binary) variable which takes the value of 1 ifthe house has a waterfront view the value of 0 otherwise,Estimation results using 1080 observations and modified versionsof the regression model obtained by dropping some of the variablesare displayed in the table below. House Sale Price EstimatesDependent Variable: log(price)Independent VariablesCoefficients Estimates and (StandardErrors)Equation 1Equation 2Equation 3Intercept5.6836.6765.682(0.052)(0.021)(0.054)Age-0.004-0.005(0.001)(0.001)Bedrooms0.1360.132(0.017)(0.018)Baths0.4070.489(0.022)(0.022)Pool0.1090.278(0.038)(0.051)Fireplace0.1920.422(0.022)(0.028)Waterfront0.2110.433(0.040)(0.054)N (number ofobservations)108010801080 Unit Code: MAE256 Unit Name: Analytical Methods in Economics and Finance FinalExamination T1, 2020__________________________________________________a) Using Equation 1 estimates calculate the predicted dollar valueof a brand-new 3 bedroom, 2 bathroom house which has a poolbut does not have a fireplace or a waterfront view. (2 Marks)b) According to Equation 1 estimates, keeping all else constant,predict the new approximate sale value of a $500,000 house if itis renovated to extend for an additional bedroom. (2 Marks)c) Interpret the coefficient estimate of binary (dummy) variable poolin Equation 1 and determine if having a swimming pool is asignificant factor in determining house sale price at 1% level ofsignificance. (4 Marks)d) Test whether all of the continuous variables included in Equation1 are jointly significant at 5 % level of significance. State your nulland alternative hypotheses clearly. (4 Marks)(2 + 2 + 4 + 4 = 12 Marks) SSR (Sum of SquaredResiduals)114.799218.207127.887R-squared0.6130.2650.569 Unit Code: MAE256 Unit Name: Analytical Methods in Economics and Finance FinalExamination T1, 2020__________________________________________________Question 4 (This question has two parts, (a) and (b))(a) The plot presented below, depicts the average wage (y) paidto American football players (USD$โ€™000 per game) from 2004to 2019 based on annual data. The variable x in the fittedmodel, as shown in the chart represents time. What is theaverage annual growth of wages of American football players?Is there any seasonality in this time series variable?(3 Marks)(b) You have been asked by a car dealership located inMelbourne to model their monthly sales (SALES) as a functionof how much is spent on advertising (ADV) and the averageprice of the cars (P) each month. You decide to estimate thefollowing regression model using the historical database of thedealership over the period July 2010 โ€“ April 2020.๐‘†๐ด๐ฟ๐ธ๐‘†๐‘ก = ๐›ฝ0 + ๐›ฝ1๐ด๐ท๐‘‰๐‘ก + ๐›ฝ2๐ด๐ท๐‘‰๐‘ก-1 + ๐›ฝ4๐‘ƒ๐‘ก + ๐‘ข๐‘ก (i)Given the below sample regression function, interpretthe effects of past monthโ€™s advertising on current monthโ€™s sales. Conduct a test of overall significance ofthe model. The standard errors are in parentheses.๐‘†๐ด๐ฟ๐ธ๐‘† ฬ‚ ๐‘ก = 3253.67 + 179.35๐ด๐ท๐‘‰๐‘ก + 4157.86๐ด๐ท๐‘‰๐‘ก-1 โ€“ 2010.62๐‘ƒ๐‘ก(452.01) (932.11) (316.39) (183.27)n = 126 R2 = 0.67(5 Marks)y = 2.1647x โ€“ 4269.7Rยฒ = 0.15930204060801001201402000 2005 2010 2015 2020Average cost ($USD) per player per gameUnit Code: MAE256 Unit Name: Analytical Methods in Economics and Finance FinalExamination T1, 2020__________________________________________________(ii) You also separately estimate the following exponentialtrend model for cars sales. Interpret how the seriesSALES is trending over time.๐‘™๐‘œ๐‘”(ฬ‚๐‘†๐ด๐ฟ๐ธ๐‘†๐‘ก) = 7.73 + 0.039๐‘ก(2 Marks) (iii)You further realise that sales may have been affected inthe months of January 2020 to April 2020 due to theoutbreak of corona virus. How would you model andexamine this impact?(2 Marks) (3 + 9 = 12 Marks)Unit Code: MAE256 Unit Name: Analytical Methods in Economics and Finance FinalExamination T1, 2020__________________________________________________Question 5 (This question has three parts, (a), (b) and (c)) (a)Consider the following time series model. What do you inferabout the nature of the time series Yt?๐‘Œ๐‘ก = ๐œŒ1๐‘Œ๐‘ก-1 + ๐‘ข๐‘ก Where ๐œŒ๐‘ก = 1(3 Marks) (b) The following model of household credit (CRED) on realwages (W) is estimated for the state of New South Wales(NSW) using quarterly data over a period of 2000 to 2018,๐‘™๐‘œ๐‘”(๐ถ๐‘… ฬ‚๐ธ๐ท๐‘ก) = -4.634 + 0.0798W๐‘ก + 0.0294๐‘Š๐‘ก-1Using the following excerpt of the data, what is the predictedhousehold credit in the second quarter of 2018? TimeReal Wage index (W)2018Q1110.212018Q2110.52 (4 Marks)(c) Suppose you are examining how exchange rate ofSingaporean dollars with US dollars (EX) is affected with oilprice (OP) and Singaporean domestic interest rates (R). Youare particularly interested to test if there was any structuralbreak in your model of exchange rate in 2001, the year of 9-11 twin tower attacks. You obtain annual data on the variablesover the period 1980-2015 and estimate the following modelsfor the entire sample and for the sub samples of 1980-2001and 2002-2015:๐ธ๐‘‹๐‘ก = ๐›ฝ0 + ๐›ฝ1๐‘‚๐‘ƒ๐‘ก + ๐›ฝ2๐‘…๐‘ก + ๐‘ข๐‘กYour calculated F statistic for the structural break test is givenby F= 21.In view of the above information, answer the followingquestions: (i)If the unrestricted SSR is 270 and SSR of the estimatedmodel of 1980-2001 is 190 then what is the SSR of theestimated model for the 2002-2015 period?What would you infer about the presence of structuralbreak in the model of Singaporean dollar exchange rate(ii)at the 5% level of significance?(5 Marks) (3 + 4 + 5 = 12 Marks)Unit Code: MAE256 Unit Name: Analytical Methods in Economics and Finance FinalExamination T1, 2020__________________________________________________Appendix:Formulae sheet๐›ƒฬ‚๐Ÿ = ๐ง โˆ‘ ๐—๐ข๐˜๐ข-โˆ‘ ๐—๐ข โˆ‘ ๐˜๐ข๐ง โˆ‘ ๐—๐ข ๐Ÿ-(โˆ‘ ๐—๐ข)๐Ÿ ; ๐›ƒฬ‚๐ŸŽ = โˆ‘ ๐—๐ง๐ข ๐Ÿโˆ‘โˆ‘๐—๐˜๐ข ๐Ÿ๐ขโ€“โˆ‘(โˆ‘๐—๐—๐ข โˆ‘๐ข)๐Ÿ๐—๐ข๐˜๐ขAlternative formulae for ๐›ƒฬ‚๐ŸŽ and ๐›ƒฬ‚๐Ÿ๐›ƒฬ‚๐ŸŽ = ๐˜ฬ… โ€“ ๐›ƒฬ‚๐Ÿ๐—ฬ… ๐›ƒฬ‚๐Ÿ = โˆ‘(๐—๐ข โ€“ ๐—ฬ…) (๐˜๐ข โ€“ ๐˜ฬ…)โˆ‘(๐—๐ข โ€“ ๐—ฬ…)๐Ÿ๐•๐š๐ซ(๐›ƒฬ‚๐ŸŽ) = ๐›”ฬ‚๐Ÿ โˆ‘ ๐—๐ข ๐Ÿ๐ง โˆ‘(๐—๐ข โ€“ ๐—ฬ…)๐Ÿ ๐•๐š๐ซ(๐›ƒฬ‚๐Ÿ) = โˆ‘(๐—๐ข๐›”ฬ‚-๐Ÿ ๐—ฬ…)๐Ÿ๐›”ฬ‚๐Ÿ = โˆ‘ ๐ฎฬ‚๐ข๐Ÿ๐ง โ€“ ๐ค โ€“ ๐Ÿ ๐ญ =๐›ƒฬ‚๐ฃ โ€“ ๐›ƒ๐ฃ๐ฌ๐ž(๐›ƒฬ‚๐ฃ) ~๐ญ(๐ง-๐Š-๐Ÿ)Test of q joint hypothesis๐… =(๐’๐’๐‘๐ซ โ€“ ๐’๐’๐‘๐ฎ๐ซ)/๐ช๐’๐’๐‘๐ฎ๐ซ/(๐ง โ€“ ๐ค โ€“ ๐Ÿ) ~๐…(๐ช,๐ง-๐ค-๐Ÿ)Test of overall significance๐… =๐‘น๐Ÿ/๐ค(๐Ÿ โ€“ ๐‘น๐Ÿ)/(๐ง โ€“ ๐ค โ€“ ๐Ÿ) ~๐…(๐ค,๐ง-๐ค-๐Ÿ)Where, in the above formulae, K is number of regression parameters excludingthe intercept and q is the number of restrictions. SSRr and SSRur representresidual sum of the squares from the restricted and unrestricted regressions,respectively. ๐‘๐Ÿ =โˆ‘(๐˜ฬ‚๐ข โ€“ ๐˜ฬ…)๐Ÿ=๐’๐’๐„๐’๐’๐“ = ๐Ÿ โ€“โˆ‘ ๐ฎฬ‚๐ข๐Ÿ= ๐Ÿ โ€“๐’๐’๐‘โˆ‘(๐˜๐ข โ€“ ๐˜ฬ…)๐Ÿโˆ‘(๐˜๐ข โ€“ ๐˜ฬ…)๐Ÿ๐’๐’๐“ ๐‘นฬ…๐Ÿ = ๐Ÿ โ€“ ๐‘บ๐‘บ๐‘นโ„๐’ โ€“ ๐’Œ โ€“ ๐Ÿ๐’๐’๐“โ„๐’ โ€“ ๐Ÿ = ๐Ÿ โ€“๐ˆ๐Ÿ๐’๐’๐“โ„๐’ โ€“ ๐Ÿ๐‚๐จ๐ซ๐ซ๐ž๐ฅ๐š๐ญ๐ข๐จ๐ง = ๐›’ =๐‚๐จ๐ฏ(๐—, ๐˜)โˆš๐ฏ๐š๐ซ(๐—)๐ฏ๐š๐ซ(๐˜)=โˆ‘(๐—๐ข โ€“ ๐—ฬ…)(๐˜๐ข โ€“ ๐˜ฬ…)โ„๐งโˆš(โˆ‘(๐—๐ข โ€“ ๐—ฬ…)๐Ÿโ„๐ง) (โˆ‘(๐˜๐ข โ€“ ๐˜ฬ…)๐Ÿโ„๐ง) =โˆ‘(๐—๐ข โ€“ ๐—ฬ…)(๐˜๐ข โ€“ ๐˜ฬ…)โˆšโˆ‘(๐—๐ข โ€“ ๐—ฬ…)๐Ÿ โˆ‘(๐˜๐ข โ€“ ๐˜ฬ…)๐ŸWhere, SSE represents regression sum of squares or explained sum ofsquares.Note: n represents sample size in both cross section and time series data.Unit Code: MAE256 Unit Name: Analytical Methods in Economics and Finance FinalExamination T1, 2020__________________________________________________Page 10 of 15Statistical TablesTable A1 Cumulative Areas under the Standard NormalDistribution z0123456789-3.00.00130.00130.00130.00120.00120.00110.00110.00110.00100.0010-2.90.00190.00180.00180.00170.00160.00160.00150.00150.00140.0014-2.80.00260.00250.00240.00230.00230.00220.00210.00210.00200.0019-2.70.00350.00340.00330.00320.00310.00300.00290.00280.00270.0026-2.60.00470.00450.00440.00430.00410.00400.00390.00380.00370.0036-2.50.00620.00600.00590.00570.00550.00540.00520.00510.00490.0048-2.40.00820.00800.00780.00750.00730.00710.00690.00680.00660.0064-2.30.01070.01040.01020.00990.00960.00940.00910.00890.00870.0084-2.20.01390.01360.01320.01290.01250.01220.01190.01160.01130.0110-2.10.01790.01740.01700.01660.01620.01580.01540.01500.01460.0143-2.00.02280.02220.02170.02120.02070.02020.01970.01920.01880.0183-1.90.02870.02810.02740.02680.02620.02560.02500.02440.02390.0233-1.80.03590.03510.03440.03360.03290.03220.03140.03070.03010.0294-1.70.04460.04360.04270.04180.04090.04010.03920.03840.03750.0367-1.60.05480.05370.05260.05160.05050.04950.04850.04750.04650.0455-1.50.06680.06550.06430.06300.06180.06060.05940.05820.05710.0559-1.40.08080.07930.07780.07640.07490.07350.07210.07080.06940.0681-1.30.09680.09510.09340.09180.09010.08850.08690.08530.08380.0823-1.20.11510.11310.11120.10930.10750.10560.10380.10200.10030.0985-1.10.13570.13350.13140.12920.12710.12510.12300.12100.11900.1170-1.00.15870.15620.15390.15150.14920.14690.14460.14230.14010.1379-0.90.18410.18140.17880.17620.17360.17110.16850.16600.16350.1611-0.80.21190.20900.20610.20330.20050.19770.19490.19220.18940.1867-0.70.24200.23890.23580.23270.22960.22660.22360.22060.21770.2148-0.60.27430.27090.26760.26430.26110.25780.25460.25140.24830.2451-0.50.30850.30500.30150.29810.29460.29120.28770.28430.28100.2776-0.40.34460.34090.33720.33360.33000.32640.32280.31920.31560.3121-0.30.38210.37830.37450.37070.36690.36320.35940.35570.35200.3483-0.20.42070.41680.41290.40900.40520.40130.39740.39360.38970.3859-0.10.46020.45620.45220.44830.44430.44040.43640.43250.42860.4247-0.00.50000.49600.49200.48800.48400.48010.47610.47210.46810.4641โ€‡0.00.50000.50400.50800.51200.51600.51990.52390.52790.53190.5359โ€‡0.10.53980.54380.54780.55170.55570.55960.56360.56750.57140.57530.20.57930.58320.58710.59100.59480.59870.60260.60640.61030.61410.30.61790.62170.62550.62930.63310.63680.64060.64430.64800.65170.40.65540.65910.66280.66640.67000.67360.67720.68080.68440.68790.50.69150.69500.69850.70190.70540.70880.71230.71570.71900.72240.60.72570.72910.73240.73570.73890.74220.74540.74860.75170.75490.70.75800.76110.76420.76730.77040.77340.77640.77940.78230.78520.80.78810.79100.79390.79670.79950.80230.80510.80780.81060.81330.90.81590.81860.82120.82380.82640.82890.83150.83400.83650.83891.00.84130.84380.84610.84850.85080.85310.85540.85770.85990.86211.10.86430.86650.86860.87080.87290.87490.87700.87900.88100.88301.20.88490.88690.88880.89070.89250.89440.89620.89800.89970.90151.30.90320.90490.90660.90820.90990.91150.91310.91470.91620.91771.40.91920.92070.92220.92360.92510.92650.92790.92920.93060.9319 Unit Code: MAE256 Unit Name: Analytical Methods in Economics and Finance FinalExamination T1, 2020__________________________________________________Page 11 of 15 1.50.93320.93450.93570.93700.93820.93940.94060.94180.94290.94411.60.94520.94630.94740.94840.94950.95050.95150.95250.95350.95451.70.95540.95640.95730.95820.95910.95990.96080.96160.96250.96331.80.96410.96490.96560.96640.96710.96780.96860.96930.96990.97061.90.97130.97190.97260.97320.97380.97440.97500.97560.97610.97672.00.97720.97780.97830.97880.97930.97980.98030.98080.98120.98172.10.98210.98260.98300.98340.98380.98420.98460.98500.98540.98572.20.98610.98640.98680.98710.98750.98780.98810.98840.98870.98902.30.98930.98960.98980.99010.99040.99060.99090.99110.99130.99162.40.99180.99200.99220.99250.99270.99290.99310.99320.99340.99362.50.99380.99400.99410.99430.99450.99460.99480.99490.99510.99522.60.99530.99550.99560.99570.99590.99600.99610.99620.99630.99642.70.99650.99660.99670.99680.99690.99700.99710.99720.99730.99742.80.99740.99750.99760.99770.99770.99780.99790.99790.99800.99812.90.99810.99820.99820.99830.99840.99840.99850.99850.99860.99863.00.99870.99870.99870.99880.99880.99890.99890.99890.99900.9990 ๏‚ท Examples: If Z ~ Normal(0,1), then P(Z โ‰ค -1.32) = .0934 and P(Z โ‰ค 1.84) =.9671.Unit Code: MAE256 Unit Name: Analytical Methods in Economics and Finance FinalExamination T1, 2020__________________________________________________Page 12 of 15Table A2: Critical Values of the t Distribution Significance Level1-Tailed:.10.05.025.01.0052-Tailed:.20.10.05.02.01Degrees ofFreedom13.0786.31412.70631.82163.65721.8862.9204.3036.9659.92531.6382.3533.1824.5415.84141.5332.1322.7763.7474.60451.4762.0152.5713.3654.03261.4401.9432.4473.1433.70771.4151.8952.3652.9983.49981.3971.8602.3062.8963.35591.3831.8332.2622.8213.250101.3721.8122.2282.7643.169111.3631.7962.2012.7183.106121.3561.7822.1792.6813.055131.3501.7712.1602.6503.012141.3451.7612.1452.6242.977151.3411.7532.1312.6022.947161.3371.7462.1202.5832.921171.3331.7402.1102.5672.898181.3301.7342.1012.5522.878191.3281.7292.0932.5392.861201.3251.7252.0862.5282.845211.3231.7212.0802.5182.831221.3211.7172.0742.5082.819231.3191.7142.0692.5002.807241.3181.7112.0642.4922.797251.3161.7082.0602.4852.787261.3151.7062.0562.4792.779271.3141.7032.0522.4732.771281.3131.7012.0482.4672.763291.3111.6992.0452.4622.756301.3101.6972.0422.4572.750401.3031.6842.0212.4232.704601.2961.6712.0002.3902.660901.2911.6621.9872.3682.6321201.2891.6581.9802.3582.617๏‚ฅ1.2821.6451.9602.3262.576 ๏‚ท Examples: The 1% critical value for a one-tailed test with 25 df is 2.485. The5% critical value for a two-tailed test with large (> 120) df is 1.96.๏‚ท Source: This table was generated using the Stataยฎ function invttail.Unit Code: MAE256 Unit Name: Analytical Methods in Economics and Finance FinalExamination T1, 2020__________________________________________________Page 13 of 15Table A3: 1% Critical Values of the F Distribution Numerator Degrees of Freedom12345678910DenominatorDegrees ofFreedom1010.047.566.555.995.645.395.205.064.944.85119.657.216.225.675.325.074.894.744.634.54129.336.935.955.415.064.824.644.504.394.30139.076.705.745.214.864.624.444.304.194.10148.866.515.565.044.694.464.284.144.033.94158.686.365.424.894.564.324.144.003.893.80168.536.235.294.774.444.204.033.893.783.69178.406.115.184.674.344.103.933.793.683.59188.296.015.094.584.254.013.843.713.603.51198.185.935.014.504.173.943.773.633.523.43208.105.854.944.434.103.873.703.563.463.37218.025.784.874.374.043.813.643.513.403.31227.955.724.824.313.993.763.593.453.353.26237.885.664.764.263.943.713.543.413.303.21247.825.614.724.223.903.673.503.363.263.17257.775.574.684.183.853.633.463.323.223.13267.725.534.644.143.823.593.423.293.183.09277.685.494.604.113.783.563.393.263.153.06287.645.454.574.073.753.533.363.233.123.03297.605.424.544.043.733.503.333.203.093.00307.565.394.514.023.703.473.303.173.072.98407.315.184.313.833.513.293.122.992.892.80607.084.984.133.653.343.122.952.822.722.63906.934.854.013.543.233.012.842.722.612.521206.854.793.953.483.172.962.792.662.562.47๏‚ฅ6.634.613.783.323.022.802.642.512.412.32 ๏‚ท Example: The 1% critical value for numerator df = 3 and denominator df = 60is 4.13.Unit Code: MAE256 Unit Name: Analytical Methods in Economics and Finance FinalExamination T1, 2020__________________________________________________Page 14 of 15Table A4: 5% Critical Values of the F Distribution Numerator Degrees of Freedom12345678910DenominatorDegrees ofFreedom104.964.103.713.483.333.223.143.073.022.98114.843.983.593.363.203.093.012.952.902.85124.753.893.493.263.113.002.912.852.802.75134.673.813.413.183.032.922.832.772.712.67144.603.743.343.112.962.852.762.702.652.60154.543.683.293.062.902.792.712.642.592.54164.493.633.243.012.852.742.662.592.542.49174.453.593.202.962.812.702.612.552.492.45184.413.553.162.932.772.662.582.512.462.41194.383.523.132.902.742.632.542.482.422.38204.353.493.102.872.712.602.512.452.392.35214.323.473.072.842.682.572.492.422.372.32224.303.443.052.822.662.552.462.402.342.30234.283.423.032.802.642.532.442.372.322.27244.263.403.012.782.622.512.422.362.302.25254.243.392.992.762.602.492.402.342.282.24264.233.372.982.742.592.472.392.322.272.22274.213.352.962.732.572.462.372.312.252.20284.203.342.952.712.562.452.362.292.242.19294.183.332.932.702.552.432.352.282.222.18304.173.322.922.692.532.422.332.272.212.16404.083.232.842.612.452.342.252.182.122.08604.003.152.762.532.372.252.172.102.041.99903.953.102.712.472.322.202.112.041.991.941203.923.072.682.452.292.172.092.021.961.91๏‚ฅ3.843.002.602.372.212.102.011.941.881.83 Unit Code: MAE256 Unit Name: Analytical Methods in Economics and Finance FinalExamination T1, 2020__________________________________________________Page 15 of 15Table A5: 10% Critical Values of the F Distribution Numerator Degrees of Freedom12345678910DenominatorDegrees ofFreedom103.292.922.732.612.522.462.412.382.352.32113.232.862.662.542.452.392.342.302.272.25123.182.812.612.482.392.332.282.242.212.19133.142.762.562.432.352.282.232.202.162.14143.102.732.522.392.312.242.192.152.122.10153.072.702.492.362.272.212.162.122.092.06163.052.672.462.332.242.182.132.092.062.03173.032.642.442.312.222.152.102.062.032.00183.012.622.422.292.202.132.082.042.001.98192.992.612.402.272.182.112.062.021.981.96202.972.592.382.252.162.092.042.001.961.94212.962.572.362.232.142.082.021.981.951.92222.952.562.352.222.132.062.011.971.931.90232.942.552.342.212.112.051.991.951.921.89242.932.542.332.192.102.041.981.941.911.88252.922.532.322.182.092.021.971.931.891.87262.912.522.312.172.082.011.961.921.881.86272.902.512.302.172.072.001.951.911.871.85282.892.502.292.162.062.001.941.901.871.84292.892.502.282.152.061.991.931.891.861.83302.882.492.282.142.051.981.931.881.851.82402.842.442.232.092.001.931.871.831.791.76602.792.392.182.041.951.871.821.771.741.71902.762.362.152.011.911.841.781.741.701.671202.752.352.131.991.901.821.771.721.681.65๏‚ฅ2.712.302.081.941.851.771.721.671.631.60 ยฉ Cengage Learning, 2013๏‚ท Example: The 10% critical value for numerator df = 2 and denominator df =40 is 2.44.๏‚ท Source: This table was generated using the Stataยฎ function invFtail.END OF EXAMINATION

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