We obtain the following quadratic trend equation:

𝑌
^
𝑖
=
100
−
10
𝑋
𝑖
+
15
𝑋
𝑖
2

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:

𝑌
^
𝑖
=
100
−
10
𝑋
𝑖
+
15
𝑋
𝑖
2

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

BlackTom AI · Accepted Answer

First, identify how the year 2014 maps to the X variable in the given trend equation. The data for years 2004–2013 are coded as X values 0 through 9, in order, so the next year (2014) corresponds to X = 10.

Next, substitute X = 10 into the quadratic trend equation: Ŷ = 100 − 10X + 15X^2.

Compute each term: 100 is the intercept, −10X with X = 10 gives −10(10) = −100, and 15X^2 with X = 10 gives 15(10^2) = 15(100) = 1500.

Combine the terms: Ŷ = 100 − 100 + 1500 = 0 + 1500 = 1500.

Thus, the forecast for 2014, based on the provided model and the coding scheme, is 1500.

Note on the answer options: the provided data shows an answer value of 1500, but the options field is empty in this input, so there are no listed alternatives to evaluate in this context. If options were present, each would need to be checked by substituting X = 10 into the model and comparing the resulting Ŷ values to the given options.

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

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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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