Problem: Consider fitting a simple linear regression model through the origin, Y = BX ε, to a set of data using the least squares method. Give an example of a situation where fitting the model Y = B1X ε is justified by theoretical or other physical and material considerations. Show that the least squares estimate of B1 is given by B1 = Σ(XiYi) / Σ(Xi^2). Show that the residuals e1, e2, ..., en will not necessarily add up to zero.
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