You are working as a statistician doing oversight for a food-safety and nutrition board, as part of a governmental investigation. The agency has selected 43 types of cereal produced by three companies (General Mills (G), Kellogg's (K), and Quaker (Q)). Eight numerical nutritional characteristics have been measured for each cereal. These 8 variables are calories, protein, fat, sodium, fiber, carbohydrates, sugar, and potassium. In addition, the data file gives the name of each cereal and the company that produced the cereal. Use the output from the analysis attached to answer the following questions:

1. Are there notable associations/relationships between some of the variables? If so, describe them
2. Can we find a few indices that describe the variation in the data set using a lesser dimension than the original set of variables? If so, what are those indices? Is there a convenient interpretation of any of the indices?
3. What is the best model suggested by BIC and the number of groups? How would you characterize the groups? What proportion of the cereals were produced by Kellog's?