In Problems, construct a scatterplot of the given data. Is there a trend in the data? Are any of the data points outliers? Construct a divided difference table. Is smoothing with a low-order polynomial appropriate? If so, choose an appropriate polynomial and fit using the least-squares criterion of best fit. Analyze the goodness of fit by examining appropriate indicators and graphing the model, the data points, and the deviations.
In the following data, X represents the diameter of a ponderosa pine measured at breast height, and Y is a measure of volume—number of board feet divided by 10 (see Problem 4, Section 4.2).
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4.2.4: Consider the “pace of life” data from Problem 1, Section 4.1. Consider fitting a 14thorder polynomial to the data. Discuss the disadvantages of using the polynomial to make predictions. If a computer is available, determine and graph the polynomial.
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