The paper Population Pressure and Agricultural Intensity (Annals of the Association of American Geographers [1977]: 384396) reported

Question:

The paper €œPopulation Pressure and Agricultural Intensity€ (Annals of the Association of American Geographers [1977]: 384€“396) reported a positive association between population density and agricultural intensity. The following data consist of measures of population density (x) and agricultural intensity (y) for 18 different subtropical locations:

a. Construct a scatterplot of y versus x. Is the scatterplot compatible with the statement of positive association made in the paper?
b. The scatterplot in Part (a) is curved upward like segment 2 in Figure 5.38, suggesting a transformation that is up the ladder for x or down the ladder for y. Try a scatterplot that uses y and x2. Does this transformation straighten the plot?
c. Draw a scatterplot that uses log(y) and x. The log(y) values, given in order corresponding to the y values, are 0.95, 0.85, 0.78, 1.70, 0.70, 2.00, 0.85, 1.15, 1.15, 1.00, 1.70, 1.15, 1.70, 2.18, 1.00, 1.83, 2.00, and 2.00. How does this scatterplot compare with that of Part (b)?
d. Now consider a scatterplot that uses transformations on both x and y: log(y) and x2. Is this effective in straightening the plot? Explain.