Ronald Fisher published an analysis on the sizes of iris sepals and petals. The data, collected over several years by Edgar Anderson, were used to show that these measurements could be employed to differentiate between species of irises. The data set Versicolor contains four measurements (sepal length, sepal width, petal length, and petal width) on 50 versicolor irises. The petals are colorful and flashy, while the sepal (under the petals) tends to be less colorful. Conduct a principal component analysis on the Versicolor data. Be sure to use the correlation matrix instead of the covariance matrix.
a. List the four eigenvalues. How many eigenvalues are greater than one? Kaiser recommended retaining the principal components with corresponding eigenvalues greater than one. 4 However, this should be a general guideline, not an absolute rule.
b. What is the percentage of the variation explained by the first principal component?
c. What is the percentage of the variation explained by the first two principal components combined?
d. A scree plot is a simple graphic used to display the eigenvalues for each successive principal com-ponent. In this graph, the number of each principal component is plotted on the horizontal axis and the corresponding cumulative eigenvalue is plotted on the vertical axis. Use the software instructions to create a scree plot for the data.