4.1 Breakfast Cereals. Use the data for the breakfast cereal example in Section 4.7 to explore and summarize the data as follows: (Note that a few records contain missing values; since there are just a few, a simple solution is to remove them first. You can use the Missing Data Handling utility in XLMiner.) a. Which variables are quantitative/numerical? Which are ordinal? Which are nominal? b. Create a table with the average, median, min, max, and standard deviation for each of the quantitative variables. This can be done through Excels functions or Excels Tools > DataAnalysis > DescriptiveStatistics menu. c. Use XLMiner to plot a histogram for each of the quantitative variables. Based on the histograms and summary statistics, answer the following questions: i. Which variables have the largest variability? ii. Which variables seem skewed? iii. Are there any values that seem extreme? 171 d. Use XLMiner to plot a side-by-side boxplot comparing the calories in hot versus cold cereals. What does this plot show us? e. Use XLMiner to plot a side-by-side boxplot of consumer rating as a function of the shelf height. If we were to predict consumer rating from shelf height, does it appear that we need to keep all three categories of shelf height? f. Compute the correlation table for the quantitative variable (use Excels Tools > DataAnalysis > Correlation menu). In addition, use XLMiner to generate a matrix plot for these variables. i. Which pair of variables is most strongly correlated? ii. How can we reduce the number of variables based on these correlations? iii. How would the correlations change if we normalized the data first? g. Consider the first column on the left in Figure 4.11. Describe briefly what this column represents