(Computer exercise) Researchers measured the diameters of 20 trees in a central Amazon rain forest and used 14C-dating to determine the ages of these trees. The data are given in the following table.27 Consider the use of diameter, X, as a predictor of age, Y.

(a) Make a scatterplot of Y = age versus X = diameter and fit a regression line to the data.
(b) Make a residual plot from the regression in part (a). Then make a normal quantile plot of the residuals. How do these plots call into question the use of a linear model and regression inference procedures?
(c) Take the logarithm of each value of age. Make a scatterplot of Y = log (age) versus X = diameter and fit a regression line to the data.
(d) Make a residual plot from the regression in part (c). Next, make a normal quantile plot of the residuals. Based on these plots, does a regression model using a log scale, from part (c), seem appropriate?

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Diameter (cm) Age (yr) Diameter (cm) Age (yr) 180 120 100 225 140 142 139 150 110 150 1372 1167 895 842 722 657 582 562 562 552 115 140 180 112 100 118 82 130 97 110 512 512 455 352 352 249 249 227 227 172