The linear trend forecasting equation for an annual time series containing 42 values (from 1976 to 2017) on net sales (in $billions) is Yi = 1.2 +0.5Xi.

Question

What is the fitted trend value for the tenth year, and what is the fitted trend value for the most recent year?

Answer 1

To find the fitted trend value for the tenth year, we substitute X = 10 into the equation:

Y10 = 1.2 + 0.5(10)
Y10 = 1.2 + 5
Y10 = 6.2

Therefore, the fitted trend value for the tenth year is $6.2 billion.

To find the fitted trend value for the most recent year, we substitute X = 42 (since the data is from 1976 to 2017) into the equation:

Y42 = 1.2 + 0.5(42)
Y42 = 1.2 + 21
Y42 = 22.2

Therefore, the fitted trend value for the most recent year is $22.2 billion.