DSC 410/510 - Multivariate Statistical Methods

Assignment 11 (deadline: 4pm on Monday, November 8)

Practical matters

Three-group Illustrative Example from p296-314:

• Reproduce the analysis described in the book by working through "hatco3group.sas" (available from the handouts page of the class web-site). This provides SAS code and instructions for running a discriminant analysis on the hatco data (available in the "hatco.xls" spreadsheet).
• Send an e-mail to ipardoe at lcbmail.uoregon.edu with answers to the following questions:
  1. Slide 25 in the class notes describes how to calculate the proportion of variation in the response variable (X₁₄) that can be explained by this discriminant analysis. In particular, if the first and second canonical correlations are called C₁ and C₂ respectively, then the explained variation = C₁² + C₂²(1-C₁²). What is the result of this calculation for this analysis (hint: if you're a careful reader the answer can be found in the book).
  2. Consider the following results:
     

     centroids	function 1	function 2
     X14=1: new task	-1.482	-0.579
     X14=2: modified rebuy	-0.473	1.206
     X14=3: straight rebuy	1.592	-0.247

     These numbers are the unrotated centroids in Table 5.18 (labeled "class means on canonical variables in SAS"). They relate to the plot drawn using the last piece of code in "hatco3group.sas." Thus, function 1 mainly discriminates straight rebuys from modified rebuys and new tasks, while function 2 then discriminates modified rebuys from new tasks. Next, consider the following results:
     

     loadings	function 1	function 2
     X1: delivery speed	0.650
     X2: price level		0.824
     X3: price flexibility	0.721
     X5: overall service		0.817

     These numbers are the largest magnitude unrotated loadings in Table 5.18 (labeled "pooled within canonical structure in SAS" for variables used in the analysis, or calculated separately using Excel for other variables). Which statement best describes how these loadings can be used in conjunction with the above centroid results:
     1. modified rebuys tend to be distinct from new tasks mainly through higher perceptions of Hatco on delivery speed and price flexibility; straight rebuys tend to be distinct from modified rebuys and new tasks mainly through higher perceptions of Hatco on price level and overall service
     2. straight rebuys tend to be distinct from modified rebuys and new tasks mainly through higher perceptions of Hatco on delivery speed and price flexibility; modified rebuys tend to be distinct from new tasks mainly through higher perceptions of Hatco on price level and overall service
     3. straight rebuys tend to be distinct from modified rebuys and new tasks mainly through higher perceptions of Hatco on price level and overall service; modified rebuys tend to be distinct from new tasks mainly through higher perceptions of Hatco on delivery speed and price flexibility
     4. modified rebuys tend to be distinct from straight rebuys and new tasks mainly through higher perceptions of Hatco on delivery speed and price flexibility; straight rebuys tend to be distinct from new tasks mainly through higher perceptions of Hatco on price level and overall service

This assignment is worth 15 points rather than the usual 10.