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Suppose you want to study the behavior of sales of a product, say, auto- mobiles over a number of years and suppose someone suggests you try the following models:
Yt = β0 + β1 tYt = α0 + α1 t + α2 t2
where Yt = sales at time t and t = time, measured in years. The ?rst model postulates that sales is a linear function of time, whereas the second model states that it is a quadratic function of time.
a. Discuss the properties of these models.
b. How would you decide between the two models?
c. In what situations will the quadratic model be useful?
d. Try to obtain data on automobile sales in the United States over the past 20 years and see which of the models ?ts the data better.
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