Suppose that we have postulated the model

Chapter 11, Problem 10E

(choose chapter or problem)

Suppose that we have postulated the model

          \(Y_{1} \beta_{1} x_{1} \varepsilon_{1}\)                 \(i=1,2, \ldots, n\)

where the εi ’s are independent and identically distributed random variables with E(εi ) = 0. Then \(\overline{y_{1}}=\overline{\beta_{1} x_{1}}\) is the predicted value of y when \(x=x_{1}\) and \(S S Z=\sum_{i=1}^{n}\left[y_{1}-\bar{\beta}_{1} x_{1}\right]^{2}\). Find the least-squares estimator of \(\beta_{1}\). (Notice that the equation \(y=\beta_{x}\) describes a straight line passing through the origin. The model just described often is called the no-intercept model.)

Equation transcription:

Text transcription:

Y_{1} \beta{1} x{1} \varepsilon{1}

i=1,2, \ldots, n

\overline{y{1}}=\overline{\beta{1} x{1}}

x=x{1}

S S Z=\sum{i=1}^{n}\left[y{1}-\bar{\beta}{1} x{1}\right]^{2}

\beta{1}

y=\beta{x}