Answer :
A. The forecast of demand for the year 2016, based on the given time series trend equation, is 40.
- The given time series trend equation is 25.3 + 2.1t, where t represents the number of years after the base year, 2010. Since t = 1 for the year 2010, we can calculate the value of t for the year 2016 by subtracting the base year from 2016, resulting in t = 2016 - 2010 = 6.
To forecast the demand for the year 2016, we substitute the value of t into the equation:
Demand for 2016 = 25.3 + 2.1 * 6
= 25.3 + 12.6
= 37.9
Therefore, based on the given time series trend equation, the forecasted demand for the year 2016 is 37.9.
In the explanation above, we start by calculating the value of t for the year 2016 by subtracting the base year (2010) from 2016. This gives us t = 6. Next, we substitute the value of t into the time series trend equation to find the demand for the year 2016, which turns out to be 37.9.
It's important to note that the time series trend equation assumes a linear relationship between time (t) and demand. The equation includes a constant term (25.3) and a coefficient for time (2.1), indicating the rate at which the demand is expected to increase over time. By plugging in the value of t for the specific year (2016), we can estimate the corresponding demand value.
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