The trend equation for quarter sales data (in millions of dollars)for 1996-2000 is $\hat { \mathrm { y } } _ { t }$ = 6.8 + 1.2t,where t = 1 for the first quarter of 1996.If the seasonal index for the third quarter of 2001 is 1.25,then the forecasted sales for the third quarter of 2001 is:
A) 34.4.
B) 27.52.
C) 43.00.
D) 35.65.

Question

Quizplus · Accepted Answer

To find the forecasted sales for the third quarter of 2001, we need to first find the trend value for that quarter using the trend equation given:

For the third quarter of 2001, t = (5*4) + 3 = 23 (since t = 1 for the first quarter of 1996 and there are 5 years + 2 additional quarters between 1996 and 2001)

Plugging in t = 23 into the trend equation, we get:
$\hat { \mathrm { y } } _ { 23 }$ = 6.8 + 1.2(23) = 32

However, we also need to adjust for the seasonal index for the third quarter of 2001, which is given to be 1.25. This means that sales for the third quarter are 25% higher than average.

Multiplying the trend value by the seasonal index, we get:

Forecasted sales for the third quarter of 2001 = 32 * 1.25 = 40

Therefore, the best choice is C) 43.00.

The Trend Equation for Quarter Sales Data (In Millions of Dollars)for