Consider the relationship between Y , the number of accidents on a heavily traveled highway, and x,

Question:

Consider the relationship between Y , the number of accidents on a heavily traveled highway, and x, the number of cars traveling on the highway. After a little thought it would probably seem to most that the linear model Y = α + βx + e would be appropriate. However, as there does not appear to be any a priori reason why Var(Y ) should not depend on the input level x, it is not clear that we would be justified in using the ordinary least squares approach to estimate α and β. Indeed, we will now argue that a weighted least squares approach with weights 1/x should be employed—that is, we should choose A and B to minimize

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