Question

A quadratic trend equation yt = 900 + 30t - 2.5t2 was fitted to a company's...

A quadratic trend equation yt = 900 + 30t - 2.5t2 was fitted to a company's sales. This result implies that the sales trend: hit a maximum in period t = 30. hit a minimum in period t = 5. hit a minimum in period t = 6. hit a maximum in period t = 6.

Math   Statistics-And-Probability   
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Answer #1

Quadratic trend is given by:

                             (1)

Differentiating (1) with respect to t and equating to 0, we get:

                                            (2)

So,

t = 6

Differentiating (2) again ith respect to t, we get:

Since

is negative, t = 6 gives the maximum.

Thus, the correct option is:

hit a maximum in period t = 6.

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