Question: Suppose we have a stochastic model Y i = x i + i Where the is are independent with mean 0 and variance

Suppose we have a stochastic model

Y_i = βx_i + ε_i

Where the εi’s are independent with mean 0 and variance σ²x_i. Show that the weighted least squares estimator of β is ˆβ = y̅/¯x. Is the standard error for ˆβ that comes from weighted least squares the same as that for ˆB in (4.10)?

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