# problem-4.6

problem-4.6 A table shows the relationship between manufacturer and vitamin type by shelf location:

    ## load and attach data set
    > library(MASS); attach(UScereal)
    > table(mfr, vitamins, shelf)
    , , shelf = 1

    , , shelf = 3

       vitamins
    mfr 100% enriched none
      G 3    6        0
      K 2    8        0
      N 0    1        0
      P 0    6        0
      Q 0    1        1
      R 0    1        0

The most obvious relationship is that 100% fortified cereal appears only on the highest shelf. This leaves space for the kid-desirable, sugar-laden cereals on the coveted second shelf.
The bubble plot is produced with the commands

    > plot(calories ~ sugars, data=UScereal, cex=2*sqrt(fat))

There appears to be a linear relationship between sugars and calories, as expected. The larger bubbles appear to be above the smaller ones, indicating that more fat implies more calories as well.
A pairs plot (pairs(UScereal)) shows many relationships. For example, the fibre, shelf plot shows some relationship. A better plot than the scatterplot for showing a factor and a numeric variable is the boxplot:

    > boxplot(fibre ~ shelf, data=UScereal)

The high-fiber cereals live on the top shelf for presumably the same reason that the fortified cereals do.