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.

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