(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...

Extracted 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.)