Consider the model y = x + , where the intercept of the line is known to be zero. Assume that values (x1, y1) ,

Consider the model y = βx + ε, where the intercept of the line is known to be zero. Assume that values (x1, y1) , . . . , (xn, yn) are observed, and the least-squares estimate β of β is to be computed.
a. Derive the least-squares estimate β in terms of xi and yi.
b. Let σ2 denote the variance of ε (which is also the variance of y). Derive the variance σ2 β of the least-squares estimate, in terms of σ2 and the xi.