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18.4: L1.05- Section 4

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    Section 4: Using Solver to choose the best kind of model

    Sometimes data has a pattern for which more than one kind of model is a potential match. While visual inspection of the best-fit graphs will usually show which one is best, you can also choose between candidates by seeing which model type has the smallest best-fit standard deviation.

    Example 6: Does a quadratic model fit the population data better than the model in Example 3? Why?

    Solution approach:

    [a] Use Solver with the Quadratic Model worksheet in Models.xls to fit the same data.

    [b] Add the computation of standard deviation to the worksheet.

    [c] Compare the standard deviation σ for the quadratic model with that of the exponential model.

    [reveal-answer q=”249938″]Show Answer[/reveal-answer]
    [hidden-answer a=”249938″]

    An exponential model is a better fit to this data than a quadratic model, because the best-fit exponential model y=3.11\cdot{{(1.0289)}^{x}} has σ = 0.46 million, while the best-fit quadratic model y=0.0051\cdot{{(x-6.536)}^{2}}+3.555 has σ = 0.85 million, which is almost twice as large.

    [/hidden-answer]

    Can you think of another reason that a quadratic model is not likely to be appropriate for this data? (Hints: Where is the vertex of the parabola? What does this imply about the quadratic model’s prediction for years before 1780, the first year given in this dataset?)

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    • Mathematics for Modeling. Authored by: Mary Parker and Hunter Ellinger. License: CC BY: Attribution

    18.4: L1.05- Section 4 is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.

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