We obtain the following quadratic trend equation:

ˆ
Y
i=100−10Xi+15X
2
i

The data used was from 2004 through 2013 coded 0 to 9. The forecast for 2014 is ___________.

Question

We obtain the following quadratic trend equation:

ˆ
Y
i=100−10Xi+15X
2
i

The data used was from 2004 through 2013 coded 0 to 9. The forecast for 2014 is ___________.

BlackTom AI · Accepted Answer

First, I will restate what's given and what we need to do. The quadratic trend model is Ŷ_i = 100 − 10 X_i + 15 X_i^2, where X_i is the coded year from 0 to 9 for 2004–2013. The question asks for the forecast for 2014, which corresponds to X_i = 10.

Now, evaluating the model term by term for X_i = 10: the constant term is 100. The linear term is −10 × X_i = −10 × 10 = −100. The quadratic term is 15 × X_i^2 = 15 × 100 = 1500.

Summing these components: Ŷ = 100 − 100 + 1500 = 1500. So the forecast for 2014, according to this quadratic trend equation, is 1500.

Because the provided answer options are missing in the given data, I cannot comment on which option corresponds to 1500 within a set of choices. However, if 1500 were among the options, it would be the value produced by plugging X_i = 10 into the model as shown.

In summary, with X_2014 = 10, the forecast Ŷ_2014 = 100 − 100 + 1500 = 1500. The calculation hinges on substituting the correct coded year into the quadratic expression and performing the arithmetic in order: square term first, then linear, then constant, or simply evaluate step by step as shown.

We obtain the following quadratic trend equation: ˆ Y i=100−10Xi+15X 2 i The data used was from 2004 through 2013 coded 0 to 9. The forecast for 2014 is ___________.Single choice

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