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(MT-IB 1992-406D long) Let e, €2, .... E, be independent random variables each with the N(0, 1) distribution, and x. x2. . x, be fixed real numbers. Let the random variables Y,, Y,, ..., Y, be given by Y, = a+ Bx, + Te,. Isisn, where a, BeR and o e (0, ) are unknown parameters. Derive the form of the least squares estimator (LSE) for the pair (a, B) and establish the form of the distribution. Explain how to test the hypothesis B=0 against B#0 and how to construct a 95% CI for ß. (General results used should be stated carefully, but need not be proved.)

(MT-IB 1992-406D long) Let e, €2, .... E, be independent random variables each with the N(0, 1) distribution, and x. x2. . x, be fixed real numbers. Let the random variables Y,, Y,, ..., Y, be given by Y, = a+ Bx, + Te,. Isisn, where a, BeR and o e (0, ) are unknown parameters. Derive the form of the least squares estimator (LSE) for the pair (a, B) and establish the form of the distribution. Explain how to test the hypothesis B=0 against B#0 and how to construct a 95% CI for ß. (General results used should be stated carefully, but need not be proved.)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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(MT-IB 1992-406D long) Let e, €2, .... €, be independent random variables each with the N(0, 1) distribution, and x. x2. ..., x, be fixed real numbers. Let the random variables Y,, Y,, ..., Y, be given by Y, = a + Bx, + Te,. Isisn, where a, Be R and o e (0, o) are unknown parameters. Derive the form of the least squares estimator (LSE) for the pair (a, B) and establish the form of the distribution. Explain how to test the hypothesis B=0 against B#0 and how to construct a 95% CI for ß. (General results used should be stated carefully, but need not be proved.)
Transcribed Image Text:(MT-IB 1992-406D long) Let e, €2, .... €, be independent random variables each with the N(0, 1) distribution, and x. x2. ..., x, be fixed real numbers. Let the random variables Y,, Y,, ..., Y, be given by Y, = a + Bx, + Te,. Isisn, where a, Be R and o e (0, o) are unknown parameters. Derive the form of the least squares estimator (LSE) for the pair (a, B) and establish the form of the distribution. Explain how to test the hypothesis B=0 against B#0 and how to construct a 95% CI for ß. (General results used should be stated carefully, but need not be proved.)
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