The trend line $\hat { Y } = 0.65 + 0.005 t$
was calculated from quarterly data for 2000 - 2004,where t = 1 for the first quarter of 2000.The trend value for the second quarter of the year 2005 is 0.75.

Question

The trend line $\hat { Y } = 0.65 + 0.005 t$ 
was calculated from quarterly data for 2000 - 2004,where t = 1 for the first quarter of 2000.The trend value for the second quarter of the year 2005 is 0.75.

Quizplus · Accepted Answer

The trend value for the second quarter of 2005 is calculated by substituting $ t = 22 $ (since $ t = 1 $ for Q1 2000, and Q2 2005 is 21 quarters later) into the equation: $\hat{Y} = 0.65 + 0.005 \times 22 = 0.76$.

The Trend Line Y^=0.65+0.005t\hat { Y } = 0.65 + 0.005 tY^=0.65+0.005t

The Trend Line $\hat { Y } = 0.65 + 0.005 t$