Porridge Foods is a health-foods company considering a venture in the breakfast foods market. As part of its market research, Porridge Foods has collected data on 11 quantitative variables for 77 breakfast cereals contained in the file breakfast.

Porridge Foods is interested in applying principal components analysis to summarize the information in these data. The following table lists the 11 quantitative variables.

a. What percentage of the variation is explained by the first principal component?

b. What percentage of variation is explained by the second principal component?

c. Provide interpretations for how the first principal component and the second principal component respectively describe the breakfast cereals. Support your narrative with observations from a combined analysis of the scatter plot of the principal components and the weights of the original variables in each of the principal components.

Transcribed Image Text:

Variable Description Calories Protein Fat Sodium Fiber Carbo Sugars Potass Vitamins Weight Cups Rating Calories per serving Grams of protein Grams of fat Milligrams of sodium Grams of dietary fiber Grams of complex carbohydrates Grams of sugars Milligrams of potassium Percentage of FDA recommended vitamins and minerals Weight in ounces of one serving Number of cups in one serving Consumer reports rating of the cereal