In the following data, X represents the diameter of a ponderosa pine measured at breast height, and

Question:

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).

X 17 19 20 22 23 25 31 32 36 37 38 39 41 Y 19 25 32 51 57 71 141 123 187 192 205 252 248 294 33

In Problems 6-12, 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.

Data from problem 4

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. Make a scatterplot of the data. Discuss the appropriateness of using a 13th-degree polynomial that passes through the data points as an empirical model. If you have a computer available, fit a polynomial to the data and graph the results.

X Y 17 19 20 22 23 25 31 32 33 36 37 38 39 41 19 25 32 51 57 71 141 123 187 192 205 252 248 294