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Answer :
To forecast the value of the linear time series trend for the year 2013, we first need to determine the value of the variable [tex]t[/tex] for that year.
The time series starts in the year 2000, so [tex]t = 0[/tex] corresponds to the year 2000. Each subsequent year increases [tex]t[/tex] by 1.
For the year 2013, we calculate [tex]t[/tex] as:
[
t = 2013 - 2000 = 13
]
Substitute [tex]t = 13[/tex] into the linear trend equation:
[tex]Y = 5.2 + 3.1t[/tex]
[tex]Y = 5.2 + 3.1 \times 13[/tex]
Calculate:
[tex]Y = 5.2 + 40.3 = 45.5[/tex]
Therefore, the forecast for 2013 according to the given linear time series trend is [tex]45.5[/tex].
The correct multiple choice option is a. 45.5.
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