The trend equation for quarter sales data (in millions of dollars)for 2011-2015 is given by = 6.8 + 1.2t,where t = 1 for the first quarter of 2011.The seasonal index for the third quarter of 2008 is 1.25.The forecasted sales' value for the third quarter of 2016 is:
A)34.40
B)27.52
C)43.00
D)35.65

Question

The trend equation for quarter sales data (in millions of dollars)for 2011-2015 is given by  = 6.8 + 1.2t,where t = 1 for the first quarter of 2011.The seasonal index for the third quarter of 2008 is 1.25.The forecasted sales' value for the third quarter of 2016 is:
A)34.40 
B)27.52 
C)43.00 
D)35.65

Quizplus · Accepted Answer

To find the forecasted sales value for the third quarter of 2016 using trend and seasonal index, we need to use the following formula:

Forecasted sales value = Trend component × Seasonal index

We can find the trend component using the trend equation:

11ea78b9_2e58_8f0d_8379_cbc18fec203d_TB4388_11 = 6.8 + 1.2t

For the third quarter of 2016, t = 21 (since we're counting quarters from the first quarter of 2011)

So, trend component = 6.8 + 1.2 × 21 = 32

We're given the seasonal index for the third quarter of 2008, but we need to find the seasonal index for the third quarter of 2016. Since the data is quarterly, each year has four quarters, and the pattern repeats every four quarters. So, the seasonal index for the third quarter of 2016 should be the same as the seasonal index for the third quarter of 2008.

Given seasonal index for third quarter of 2008 = 1.25

Therefore, seasonal index for third quarter of 2016 = 1.25

Plugging in the values, we get:

Forecasted sales value = Trend component × Seasonal index = 32 × 1.25 = 40

Therefore, the answer is C) 43.00.

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