EXAMINATION Luleå Unversty of Technology N008N Econometrcs Date: 011-05-16 (A1016) Tme: 09.00-13.00 Ad: Calculator and dctonary Teacher on duty (complete telephone number) Robert Lundmark (070-1735788) Teacher on duty (complete telephone number) Grade scale: Total number of questons: Important nformaton: Passed (G): At least 4 ponts. Passed wth honors (VG): At least 3 ponts. The exam conssts of 4 questons, 40 ponts n total. Please make sure you have receved all questons. Also, check so that the last pages contan a t crtcal values table, F dstrbuton table and a Durbn-Watson table. Please present your answer n a clear and logcal manner. Your answers wll be graded by ther qualty, not by the number of words. General nstructons Read all questons before you start and plan your tme for each queston. Begn to formulate the problem and then answer the queston wth complete solutons n a clear and nstructve manner, e.g. explan (short) wth words what you are dong. Gve the economcal nterpretaton of your result, f t s possble. Do not forget to state your assumptons when you feel that such s necessary to make. Answer the questons n ether Swedsh or Englsh. All new answers should begn on a separate page. Wrte your name on every paper sheet you hand n. Wrte clearly! Do not use red pencl! After examnaton The result of your examnaton s posted on your Student portal. Examnaton results are posted wthn 15 workdays after the examnaton and no later den 1 workdays before next re-examnaton day. For the courses wth more than 60 students takng the examnaton the results are posted wthn 0 workdays latest after the examnaton but no later than 1 workdays before the next re-examnaton day. Uppgfter tll tryckeret Projektnummer: 40 491 Hur många ex: 5 Hur många sdor: 6 Dubbel- eller enkelsdgt: Dubbelsdgt
Queston 1 (5 ponts) +----------------------------------------------------+ Ordnary least squares regresson Model was estmated May 09, 011 at 03:49:6PM LHS=Q Mean = 84.34783 Standard devaton = 17.51337 WTS=none Model sze Number of observs. Parameters = = 3 4 Degrees of freedom = 19 Resduals Sum of squares = Standard error of e = 38.06451 1.415413 Ft R-squared =.8943590 Model test Adjusted R-squared =.8934683 F[ 3, 19] (prob) =1116.39 (.0000) Dagnostc Log lkelhood = -38.4915 Restrcted(b=0) = -97.9757 Ch-sq [ 3] (prob) = 119.09 (.0000) Info crter. LogAmemya Prd. Crt. =.8551861 Autocorrel Akake Info. Crter. = Durbn-Watson Stat. =.8516143.8893940 Rho = cor[e,e(-1)] =.5553030 +----------------------------------------------------+ +---------+--------------+----------------+--------+---------+----------+ Varable Coeffcent Standard Error t-rato P[T>t] Mean of X +---------+--------------+----------------+--------+---------+----------+ Constant 14.667836 14.06 I.9765941.050 59.66087 P S -.4057959 1.0441549-11.671 11.80 3.134783.50000 Q = I = P = S = demand for ce-cream Sweden (# of ce-creams per month) real monthly ncome for households n Sweden (1,000 SEK) real prce of ce-creams, n 000 value (kronor per ce-cream) a season dummy varable set to 1 for the summer months (June, July and August) and 0 for the remanng months. a) Explan and argue for why we have ncluded a season dummy varable n the regresson. (1p) b) Based on the regresson results above formally test the statstcal sgnfcance of all the estmated coeffcents. Make sure to clearly state the hypotheses you are testng. (1p) c) Make an economc nterpretaton of the coeffcents of I and P. (1p) d) How does the season dummy varable affect the demand for ce-cream? (1p) e) Based n the Durbn-Watson statstc, does the model suffer from autocorrelaton? Clearly state the hypothess that you are testng and explan n words and/or fgures how you perform the autocorrelaton test. (1 ponts) Queston (10 ponts) Usng econometrcs s not always unproblematc. We have n class covered several problems that mght cause problems usng econometrcs. I want you to explan what the followng problems are, what s causng them and how they can be solved. a) Heteroscedastcty (p) b) Autocorrelaton (p) c) Measurement error (p) d) Omtted varable bas (p) e) Multcollnearty (p)
Queston 3 (10 ponts) There are many ways to use the F-test. One s to test for extra explanatory power after ncludng more extra explanatory varables to the model. The F-statstcs for ths test can be calculated usng the followng expresson: F k 1, n k d. f. RSS 1 RSS extra d. f. used RSS d. f. Model 1: Pˆ 6,5 0, 14Q RSS 1 = 67 k 1 = n 1 =570 Model : Pˆ 6,5 0,14Q 0, 19I RSS = 146 k =3 n =570 Based on the regresson results above, please perform the approprate F-test to formally test f addng the varable I to the model enhances the models explanatory power. Make sure to clearly state the hypothess you are testng and the F-crt value used. Also, make sure to explan n words what you are dong and the conclusons you can make based n the test. Queston 4 (15 ponts) Assume we have a true model that can be expressed as: y 1 x u and where our predcted model takes the form: ˆ y b1 b x Please derve a calculable expresson for b 1 and b by mnmsng the resdual sum of squares (RSS). n mn RSS e where e y yˆ 1 Make sure to also explan n words what you are dong. 3