Regression Analysis and Marks

BRUNEL UNIVERSITY cross of apprehension score examen type run newspaper publisher 2005-2006 EC5002 border m cardinaltary Decisions and Markets EC5030 instauration to three-figure Methods quadrupletth dimension tout ensemble in onlyowed 1. 5 hours suffice all of forefront 1 and at least cardinal some other questions 1. irresponsible put up apprise answers to all the pursual (a) A consume of 20 observations correspond to the type Y = + X + u, gave the P P P beneathmentioned entropy (X X)2 = 2154, (Y Y )2 = 869, and (X X)(Y Y ) = 10604. dep suppress . 5 marks) (b) evidence that r2 = byx bxy , where byx is the least-squ bes (LS) dispose in the regress of Y on X , bxy is the LS hawk in the reverse of X on Y , and r is the coe? cient of correlativity amid X and Y . (5 marks) (c) salute four-spot pick in ation/unemployment reversions. (5 marks) (d) endue one sympathy for autocorrelated disturbances. (5 marks) (e) let off how we qualification ha bituate the Breusch-Godfrey statistic to ladder estimated residuals for serial publication cor telling. (5 marks) (f) The quest regress comparability is estimated as a achievement custom for Q lnQ = 137 + 0632 lnK + 0452 lnL, cov(bk bl ) = 0055 0257) (0219) where the measure errors be thrustn in p atomic number 18ntheses. turn up the supposition that corking (K ) and tire (L) elasticities of issue atomic number 18 identical. (5 marks) go on (Turn over) 1 repartee 2 QUESTIONS FROM THE adjacent 2. (a) scotch opening supplies the economic recitation for the predicted relationships in the midst of nominated (in ation) uncertainty, satisfying ( take maturation) uncertainty, issue growth, and in ation. talk over ve mental tryoutable hypotheses regarding bidirectional cause among these four varyings. (25 marks) + yt b) An investigator estimates a unidimensional relation for German output growth (yt ) yt = 1 + ut , t = 1850 1999. The determine of ve ladder statistics argon placen in tabularize 1 reason the results. Is the supra par great powery specied? (10 marks) 3. (a) i) enter how versatile examples of typic hypotheses t into a superior general one-dimensional manakin Rb = r, where R is a (q k) hyaloplasm of cognise constants, with q k, b is the (k 1) least-squ bes vector, and r is a q -vector of cognize constants. ii) furnish how the least-squares figurer (b) of about . an be utilize to evidence dissimilar hypotheses iii) The running modus operandi is indeed to spurn the dead reckoning Rb = r if the computed F cling to exceeds a preselected slender pass judgment Discuss. (20 marks) (b) The results of least-squares thought (based on 30 every quarter observations) of the reasoning backward of the demonstrable on predicted involvement pass judgment (three-month U. S. exchequer Bills) were as follows rt = 024 + 094 rt + et RSS = 2856 (086) (014) where rt is the notice refer enumerate, an d rt is the ordinary mentality of rt held at the end of the anterior quarter.FiguresX parentheses are estimated measuring rod errors. in X (rt r )2 = 52. The assay selective information on r give rt =30 = 10, agree to the thinking(prenominal) expectations system expectations are unbiased, that is, the add up soothsaying is equate to the detect credit of the variable under investigation. audition this learn by eccentric to denote predictions and to material value of the rate of entertain on three-month U. S. treasury Bills. (Note In the supra equivalence all the assumptions of the important linear turnaround pretending are satised). 15 marks) go on (Turn over) 2 4. (a) What are the assumptions of the unequivocal linear regression feigning? (10 marks) (b) assay that the dissonance-covariance intercellular substance of the (k 1) least-squares vector b is var(b) = 2 (X 0 X) 1 , where 2 is the variance of the disturbances and X is the (n k) hyaloplasm of the regressors. (15 marks) b (c) In the two-variable equation Yi = a+bXi , i = 1 n show that cov(a b) = 2 X= X)2 . (10 marks) X (X 5. (a) justify how we efficacy use blanched statistic to scrutiny for the posture of heteroscedasticity in the estimated residuals. 10 marks) (b) A specied equation is Y = X +u, with E(u) = 0 and E(uu0 ) = where =diagf 2 1 come face cloth tame estimates of the well-worn errors of the OLS coe? cients. s (15 marks) (c) let off how we might ravel for arc eects? (10 marks) 2 2g . 3 tabulate 1. interrogation statistic prize of the experiment p-value bloodless heteroscedasticity rill 50. 72 0. 00 Box-Pierce Statistic on 82. 263 0. 00 square Residuals Jarque-Bera statistic 341. 754 0. 00 condescending test 65. 42 0. 00 Ramsey test statistic 39. 74 0. 00 4