Regression Analysis and Marks Free Essays

BRUNEL UNIVERSITY Master of Science Degree assessment Specimen Exam Paper 2005-2006 EC5002: Modeling Financial Decisions and Markets EC5030: Introduction to Quantitative Methods Time permitted: 1. 5 hours Answer all of inquiry 1 and in any event two different inquiries 1. Obligatory Provide brief responses to all the accompanying: (an) An example of 20 perceptions relating to the model: Y = + X + u, gave the P following information: (X X)2 = 215:4, (Y )2 = 86:9, and (X X)(Y Y ) = 106:04. We will compose a custom article test on Relapse Analysis and Marks or on the other hand any comparable theme just for you Request Now Gauge . 5 imprints) (b) Prove that r2 = byx bxy , where byx is the least-squares (LS) slant in the relapse of Y on X , bxy is the LS slant in the relapse of X on Y , and r is the coe? cient of relationship among's X and Y . (5 imprints) (c) Present four option in†¡ ation/joblessness relapses. (5 imprints) (d) Give one explanation behind autocorrelated unsettling influences. (5 imprints) (e) Explain how we may utilize the Breusch-Godfrey measurement to test evaluated residuals for sequential relationship. (5 imprints) (f) The accompanying relapse condition is assessed as a creation work for Q: lnQ = 1:37 + 0:632 lnK + 0:452 lnL, cov(bk ; bl ) = 0:055; 0:257) (0:219) where the standard blunders are given in enclosures. Test the theory that capital (K ) and work (L) versatilities of yield are indistinguishable. (5 imprints) Continued (Turn more than) 1 ANSWER TWO QUESTIONS FROM THE FOLLOWING: 2. (an) Economic hypothesis supplies the financial translation for the anticipated connect ions between ostensible (in†¡ ation) vulnerability, genuine (yield development) vulnerability, yield development, and in†¡ ation. Talk about †¦ve testable speculations in regards to bidirectional causality among these four factors. (25 imprints) + yt b) A specialist assesses a straight connection for German yield development (yt ): yt = 1 + ut , t = 1850; : ; 1999. The estimations of †¦ve test measurements are appeared in Table 1: Discuss the outcomes. Is the above condition accurately speci†¦ed? (10 imprints) 3. (an) I) Show how different instances of run of the mill speculations †¦t into a general straight system: Rb = r, where R is a (q k) network of known constants, with q k, b is the (k 1) least-squares vector, and r is a q - vector of known constants. ii) Show how the least-squares estimator (b) of about . a be utilized to test different speculations iii) â€Å"The test method is then to dismiss the theory Rb = r if the registered F esteem surpas ses a preselected basic value† Discuss. (20 imprints) (b) The aftereffects of least-squares estimation (in view of 30 quarterly perceptions) of the relapse of the genuine on anticipated financing costs (three-month U. S. Treasury Bills) were as per the following: rt = 0:24 + 0:94 rt + et ; RSS = 28:56; (0:86) (0:14) where rt is the watched loan cost, and rt is the normal desire for rt held toward the finish of the former quarter. FiguresX enclosures are evaluated standard blunders. in X (rt r )2 = 52. The example information on r give rt =30 = 10, According to the judicious desires speculation desires are fair, that is, the normal expectation is equivalent to the watched acknowledgment of the variable under scrutiny. Test this case by reference to declared expectations and to real estimations of the pace of enthusiasm on three-month U. S. Treasury Bills. (Note: In the above condition all the presumptions of the old style direct relapse model are satis†¦ed). 15 imprints) Continued (Turn more than) 2 4. (a) What are the suspicions of the traditional straight relapse model? (10 imprints) (b) Prove that the change covariance lattice of the (k 1) least-squares vector b is: var(b) = 2 (X 0 X) 1 , where 2 is the fluctuation of the unsettling influences and X is the (n k) network of the regressors. (15 imprints) b (c) In the two-variable condition: Yi = a+bXi , I = 1; : ; n show that cov(a; b) = 2 X= X)2 . (10 i mprints) (X 5. (an) Explain how we may utilize White measurement to test for the nearness of heteroscedasticity in the assessed residuals. 10 imprints) (b) A speci†¦ed condition is Y = X +u, with E(u) = 0 and E(uu0 ) = ; where =diagf 2 ; : ; 1 Derive White’ right gauges of the standard blunders of the OLS coe? cients. s (15 imprints) (c) Explain how we may test for ARCH eâ ¤ects? (10 imprints) 2 2g . 3 Table 1. Test measurement Value of the test p-esteem White heteroscedasticity test 50. 72 0. 00 Box-Pierce Statistic on 82. 263 0. 00 Squared Residuals Jarque-Bera measurement 341. 754 0. 00 ARCH test 65. 42 0. 00 Ramsey test measurement 39. 74 0. 00 4 The most effective method to refer to Regression Analysis and Marks, Essay models