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 at any rate 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 paper test on Relapse Analysis and Marks or on the other hand any comparative theme just for you Request Now Gauge . 5 imprints) (b) Prove that r2 = byx bxy , where byx is the least-squares (LS) incline 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 connection among's X and Y . (5 imprints) (c) Present four option in†¡ ation/joblessness relapses. (5 imprints) (d) Give one purpose behind autocorrelated unsettling influences. (5 imprints) (e) Explain how we may utilize the Breusch-Godfrey measurement to test assessed residuals for sequential connection. (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 mistakes 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 monetary translation for the anticipated connections bet ween ostensible (in†¡ ation) vulnerability, genuine (yield development) vulnerability, yield development, and in†¡ ation. Talk about †¦ve testable theories with respect to bidirectional causality among these four factors. (25 imprints) + yt b) A specialist evaluates a direct 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 regular theories †¦t into a general straight structure: Rb = r, where R is a (q k) grid 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 methodology is then to dismiss the theory Rb = r if the registered F esteem surpasses a preselected basic value† Discuss. (20 imprints) (b) The aftereffects of least-squares estimation (in light of 30 quarterly perceptions) of the relapse of the real 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 financing cost, and rt is the normal desire for rt held toward the finish of the previous quarter. FiguresX enclosures are assessed standard blunders. in X (rt r )2 = 52. The example information on r give rt =30 = 10, According to the discerning desires theory 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 genuine estimations of the pace of enthusiasm on three-month U. S. Treasury Bills. (Note: In the above condition all the suppositions of the old style direct relapse model are satis†¦ed). 15 imprints) Continued (Turn more than) 2 4. (a) What are the presumptions of the old style straight relapse model? (10 imprints) (b) Prove that the change covariance network of the (k 1) least-squares vector b is: var(b) = 2 (X 0 X) 1 , where 2 is the difference of the unsettling influences and X is the (n k) grid 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 imprint s) (X 5. (an) Explain how we may utilize White measurement to test for the nearness of heteroscedasticity in the evaluated 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 mistakes 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 Step by step instructions to refer to Regression Analysis and Marks, Essay models