370 CHAPTER 3 Polynomial and Rational Functions SOLUTION (a) The best-fitting quadratic function for the data is y = -0.0139x2 + 0.209x + 2.74. The regression coordinates screen and the graph are shown in Figure 38. (b) The best-fitting cubic function is shown in Figure 39 and is y = 0.00220x3 - 0.0502x2 + 0.363x + 2.63. (c) The best-fitting quartic function is shown in Figure 40 and is y = 0.000585x4 - 0.0107x3 + 0.0384x2 + 0.166x + 2.70. (d) With the statistical diagnostics turned on, the value of R2 is displayed with the regression results on the TI-84 Plus each time that a regression model is executed. By inspecting the R2 value for each model above, we see that the quartic function provides the best fit because it has the largest R2 value of 0.9293106696. S Now Try Exercise 99. Figure 38 −1 12 0 5 Figure 40 −1 12 0 5 Figure 39 −1 12 0 5 NOTE In Example 8(d), we selected the quartic function as the best model based on the comparison of R2 values of the models. In practice, however, the best choice of a model should also depend on the set of data being analyzed as well as analysis of its trends and attributes.
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