Olive oil from Spain, Tunisia, and other countries is imported into Italy and is then re...

Olive oil from Spain, Tunisia, and other countries is imported into Italy and is then repackaged and exported with the label “Imported from Italy.” Olive oils from different places have distinctive tastes. Can the oils from different regions and areas in Italy be distinguished based on their combinations of fatty acids? This question was considered by Forina et al. (1983). The data consists of the percentage composition of 8 fatty acids (palmitic, palmitoleic, stearic, oleic, linoleic, linolenic, arachidic, eicosenoic) found in the lipid fraction of 572 Italian olive oils. There are 9 collection areas, 4 from southern Italy (North and South Apulia, Calabria, Sicily), two from Sardinia (Inland and Coastal), and 3 from northern Italy (Umbria, East and West Liguria). The file olive contains the following variables for each of the 572 samples:

• Region: South, North, or Sardinia

• Area (subregions within the larger regions): North and South Apulia, Calabria, Sicily, Inland and Coastal Sardinia, Umbria, East and West Liguria

• Palmitic Acid Percentage

• Palmitoleic Acid Percentage

• Stearic Acid Percentage

• Oleic Acid Percentage

• Linoleic Acid Percentage

• Linolenic Acid Percentage

• Arachidic Acid Percentage

• Eicosenoic Acid Percentage

Examine this data with the aim of distinguishing between regions and areas by using fatty acid composition.

a. Make a table of the mean and median values of percentages for each area, grouping the areas within regions.

b. Complement the analysis by making parallel boxplots. Which variables look promising for separating the regions?

c. It is possible that the regions can be more clearly separated by considering pairs of variables. Use the variables that appear to be informative from the analysis up to this point to make scatterplots. How well can the regions be separated based on the scatterplots?

d. How well can the areas within regions be distinguished?

e. By interactively rotating point clouds, one can examine relationships among more than two variables at a time. Try this with the software ggobi available at http://www.ggobi.org/.