5.49 The paper “Population Pressure and Agricultural Intensity” (Annals of the Association of American Geographers [1977]: 384–396) reported a positive relationship 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:

x 1.0 26.0 1.1 101.0 14.9 134.7 y 9 7 6 50 5 100 x 3.0 5.7 7.6 25.0 143.0 27.5 y 7 14 14 10 50 14 x 103.0 180.0 49.6 140.6 140.0 233.0 y 50 150 10 67 100 100

a. Construct a scatterplot of y versus x. Is the scatterplot compatible with the statement of positive relationship made in the paper?

b. 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.