Ch 11 - 20E

Chapter 11, Problem 20E

(choose chapter or problem)

Suppose that \(Y_{1}, Y_{2}, \ldots Y_{n}\) are independent normal random variables with \(E\left(Y_{1}\right)=\beta_{0}+\beta_{1} x_{1}\) and \(V\left(Y_{1}\right)=o^{2}\), for i = 1, 2, . . . , n. Show that the maximum-likelihood estimators (MLEs) of \(\beta_{0}\) and \(\beta_{1}\) are the same as the least-squares estimators of Section 11.3.

Equation transcription:

Text transcription:

Y{1}, Y{2}, \ldots Y{n}

E\left(Y{1})=\beta{0}+\beta{1} x{1}

V\left(Y{1})=o^{2}

\beta{0}

\beta{1}