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

The problem gives a quadratic trend equation and asks for the forecast for the year 2014.
First, identify how the year codes map to X values. The data span 2004 through 2013 and are coded 0 to 9, so 2004 corresponds to X = 0, 2005 to X = 1, ..., and 2013 to X = 9.
To forecast 2014, we extend this coding: 2014 would be X = 10 (since 2004 + 10 years = 2014).
Next, plug X = 10 into the trend equation Ŷi = 100 − 10Xi + 15Xi^2:
- Compute the linear term: −10 × X = −10 × 10 = −100.
- Compute the quadratic term: 15 × Xi^2 = 15 × (10)^2 = 15 × 100 = 1500.
- The constant term is 100.
Combine them: Ŷ = 100 + (−100) + 1500 = 0 + 1500 = 1500.
Thus, the forecast for 2014 is 1500.
Note: The provided data includes an answer value of 1500, but the options list is empty in this prompt, so the calculation above is the basis for the forecast. If options were present, we would compare 1500 to them to select the correct choice.

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 ___________.

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