Chapter 11.3, Problem 10E

Suppose that we have postulated the model

$Y_i={\beta }_1{x}_i+{\epsilon }_{i}i=1,2,\dots ,n,$

where the ε_i’s are independent and identically distributed random variables with E(ε_i) = 0. Then ${\hat{y}}_i={\hat{\beta }}_1{x}_i$ is the predicted value of y when x = x_i and $\text{SSE}={\displaystyle {\sum }_{i=1}^n[y_i-{\hat{\beta }}_1{x}_i]}$. Find the least-squares estimator of β₁. (Notice that the equation y = β_x describes a straight line passing through the origin. The model just described often is called the no-intercept model.)