High School

Given a linear time series trend, [tex]Y = 5.2 + 3.1t[/tex], developed from a data set ranging from the years 2000 to 2009, what is the forecast for 2013 if the time series started in 2000?

A. 45.5
B. 51.7
C. 39.3
D. 42.4
E. 48.6

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.

  1. 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.

  2. For the year 2013, we calculate [tex]t[/tex] as:

    [

t = 2013 - 2000 = 13
]

  1. 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]

  2. 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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