The paper Population Pressure and Agricultural Intensity

Chapter 0, Problem 5.59

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The paper Population Pressure and Agricultural Intensity (Annals of the Association of American Geographers [1977]: 384396) 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:x 1.0 26.0 1.1 101.0 14.9 134.7y 9 7 6 50 5 100x 3.0 5.7 7.6 25.0 143.0 27.5y 7 14 14 10 50 14x 103.0 180.0 49.6 140.6 140.0 233.0y 50 150 10 67 100 100a. Construct a scatterplot of y versus x. Is the scatterplotcompatible with the statement of positive associationmade in the paper?b. The scatterplot in Part (a) is curved upward like segment2 in Figure 5.31, suggesting a transformation that isup the ladder for x or down the ladder for y. Try a scatterplotthat uses y and x2. Does this transformation straightenthe plot?c. Draw a scatterplot that uses log(y) and x. The log(y)values, given in order corresponding to the y values, are0.95, 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. Howdoes this scatterplot compare with that of Part (b)?d. Now consider a scatterplot that uses transformations onboth x and y: log(y) and x2. Is this effective in straighteningthe plot? Explain.