Consider the Amazon tree data from Exercise 12.6.9. The researchers in this study were interested in how age, Y, is related to X = "growth rate," where growth rate is defined as diameter/age (i.e., cm of growth per year).
(a) Create the variable "growth rate" by dividing each diameter by the corresponding tree age.
(b) Make a scatterplot of Y = age versus X = growth rate and fit a regression line to the data.
(c) Make a residual plot from the regression in part (b). 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?
(d) Take the logarithm of each value of age and of each value of growth rate. Make a scatterplot of Y = log(age) versus X = log(growth rate) and fit a regression line to the data.
(e) Make a residual plot from the regression in part (d). Then make a normal quantile plot of the residuals. Based on these plots, does a regression model in log scale, from part (d), seem appropriate?