Question

1,2)- The international bank UBS regularly produces a report (UBS, 2009) on prices and earnings in the main cities of the world (see table). bigmac2009 rice2009 bigmac2003 rice2003 Amterdam 19 11 16 9 Athens 30 27 21 19 Auckland 19 13 19 9 Bangkok 45 27 50 25 Bancerlona 21 8 22 10 Two of the measures they include are commodity prices, namely 1 kg of rice, the price of a Big Mac hamburger at McDonalds. An interesting feature of reporting prices is that prices are measured in the minutes of labor required for a typical" worker in that location to earn enough money to buy the product. The use of work minutes corrects at least in part currency fluctuations, prevailing wage rates and local prices. Data includes measurements of rice, bread and Big Mac prices from the 2003 and 2009 reports. 2003 was before the Great Recession hit much of the world around 2006, and 2009 may reflect changes in prices due to recession. Doing the accounts by hand or using the Phyton programming language: (a) Make a scatter plot of y = rice2009 versus x = rice2003, rice prices in 2009 and 2003, respectively... (b) Find the least squares estimators BO and B1 of the regression equation y = BO + B1x, where y = rice2009 and x = rice 2003... (c) Make a scatter plot again but using logarithmic scales, that is, make the scatter plot of y = log(rice2009) versus x = log(rice2003)... (d) Find the least squares estimators BO and B1 of the regression equation log(rice2009) = BO + B1 log(rice 2003)... -----> (1) (e) For model (1) calculate the constants Var (BO) and Var (B1), Cov (BO, B1), RSS and the estimator S2 of 02... Now, comparing the data of y = bigmac2009 versus x = bigmac2003 , MacDonald's Big Mac hamburger prices in 2009 and 2003, respectively: (1) Make a scatter plot of y = bigmac2009 versus x = bigmac2003, rice prices in 2009 and 2003, respectively... (g) Find the least squares estimators BO and B1 of the regression equation y = BO + B1x where y =bigmac2009 and x = bigmac2003.. (h) Make a scatter plot again but using logarithmic scales, that is, make the scatter plot of y = log(bigmac2009) versus x = log(bigmac2003)... (1) Find the least squares estimators BO and B1 of the regression equation log(bigmac2009) = BO + B1 log(bigmac2003)... -----> (2) (I) For model (2) calculate the constants Var (0) and Var (B1), Cov (BO, B1), RSS and the estimator S2 of 02...

Answer 1

Answert! Given data: bigmae 9019 Nice 2018 bigmac 2009 orice 2009 Amteadam 16 9 PWR19 27 21 19 30 P19/ 13 AVA et Jg 9 Athens Auckland Bangkok Hos Banceolona 45 1627 a largon so 3,25 21 8 22 POUZD y = oice 2009 vedSUS x = dice 2008 Scotteer plot of Соседі 30+ 25 +9 Coop goisol pul cunvalincom ordak onship absenue belcover and a oor 20 + vice price 15 2009 10 dler fle Coos golpo POP Case = (your gio) pol 210 fe3 5 + + + + 25 30 IS 20 35 o hseoving seatea plot x 9 if we orice porice 2003 b) kos By linear relation between and obseave neglect some point. The linear dregoression is given by g= potpixte whene y = nice 2009 and Juice 2009 exuperdotegundo gpl Inoili falus ou calculation: y = 14.2 san variance of x Syy variance ofy Say covariance between x and y = 14.4 = 52.8 83.2 61.4 -

Ocz d) After taking log: Elbedo the sienoored model TER2010 - 2011 log (you'eice 2009) » Bot p. log (ouce 2003) + & cohere y-log oice 2009 9 - logarice 2003 team 2322 intercept Bo- pre orogoresion coefficient. le Sxa = 0.2276 Syy =, 0:80026 - அவன் team EIN(018) Vaizelo. four logarithmic cidata 00024 F2.83 Q= 2.57 207 G = 2.726792 Dozen, Com Bo = g-pid - 9 - 88 Say PROJ 0.07648 and pi GIOCO 8uotud 0.07648 t fice 2003) Peda:0:- Bi = Saa =103042 Bo The fitted model is given by suction 2010 - Ya log log (oice 2009) FE2820-0 = 2 foor model. 0:07 608 B = 1.08042 2010.0 09 ( * + 70 Sax logarithmic vepo)- vepi) coulpoisid Since go is unknocon, which can be estimated by orespdual sam of squcore Syy-pisay - Te Sax ०२ eising Ssores = 0.8002632 103042 x 0.2345897

n- LOT 5-2 Q Ssses - 0.058537 RSS = 0.058597 ( Residuced, sum of equare) The estimated 22, is groen by or in the Ale soes when p=k+1 =1+1=2 orggade SODE 90 pole he = 0.058537 0.0195124, $0991 de 20.01g SiQUoC 11:35 vipo) = 09/** ) = % in Saa 0.0195120 Š + (2.5+207)2 VIBO viße) = 0.5735000 0.2276642 indtional not Lepietie 0.0195124 = 0.917825 = San 20. 2276642 couißoß.) = = {2:57209) °(0:0195124) 02276642 coulßo: P.) = -0.56699 QUEO:ê bpb Result: 80 = 0.07648 =logoue e Lobom both got (nego) is 0457 35020 = 0.4178 05 VOB) CODE (രാര് സി Couch vipi) - Son ruoto.o pie Code RSS = 0.058537 abond sonstopol vor § 2 = 0.019512u. OU 120 800 focs م )