Suppose you want to study the behavior of sales of a product, say, automobiles over a number of years and suppose someone suggests you try the following models Y t 0 1 t Y t 0 1 t 2 t 2 where Y t sales at time t and t time, measured in years The first model postulates that sales is a linear functio...

a In the first model where sales is a linear function of time the rate of chan ...

Suppose you want to study the behavior of sales of a product, say, automobiles over a number

Question:

Suppose you want to study the behavior of sales of a product, say, automobiles over a number of years and suppose someone suggests you try the following models:

Y_t = β₀ + β₁t

Y_t = α₀ + α₁t + α₂t²

where Y_t = sales at time t and t = time, measured in years. The first 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 fits the data better.