# . Provide (type and/or paste) your answers in the indicated area. 2. This is an individual… – NO PLAGIARISM

Assignment #2 (due Sep. 10)BSAD 251, Fall 2019Prof. T. Noordewier

NAME: _______________________________________

INSTRUCTIONS:

1. Provide (type and/or paste) your answers in the indicated area.2. This is an individual assignment (i.e., to be done on your own, without assistance)

Question #1:

Consider the following information:

Marketing researchers at Generation, Inc., a maker of mobile electric generators, think it likely that customers differ in terms of the importance that they attach to the following two electric generator attributes: (1) that the generator produces low levels of atmospheric emissions (or pollutants), and (2) that the generator operates at a low noise level. A sample of five representative Generation customers (i.e., buyers) reveals the following set of preferences for these two attributes/benefits:

ID emissions noisePaul 2.10 3.00Sally 4.00 6.00John 4.30 7.00Mary 5.00 5.00Zack 4.00 2.20

where:(1) the measurement scale is continuous, and ranges from 1=very unimportant to10=very important(2) the first column indicates a respondent’s i.d. (i.e., customer’s name)(3) the second column (i.e., x-axis, or “emissions”) is the importance weight attached to“generates low levels of atmospheric emissions”(4) the third column (i.e., y-axis, or “noise”) is the importance weight attached to“operates at a low noise level”

For Question #1, parts (a) through (j), perform manually (with the help of a calculator or spreadsheet) a k-means cluster analysis of the Generation, Inc. data. For purposes of this question, set k= 2 and use the coordinate point (4,2) as initial centroid #1 and the coordinate point (2,3) as initial centroid #2 (where the coordinate points are indicated by (x,y) = (emissions, noise), as usual). Perform and report below all numeric calculations to 3 decimal places of precision (e.g., 3.468).

(a) Which customers are assigned to starting centroid #1, and what is the Euclidean distance between each of these customers and starting centroid #1? In your answer clearly indicate each customer’s id, and the Euclidean distance (to 3 decimal places) between the customer and starting (i.e., initial) centroid #1.Buyer id: _________ Distance: ____________Buyer id: _________ Distance: ____________Buyer id: _________ Distance: ____________Buyer id: _________ Distance: ____________Buyer id: _________ Distance: ____________

(Note: here, and below, complete for as many customers as appropriate)

(b) Which customers are assigned to starting centroid #2, and what is the Euclidean distance between each of these customers and starting centroid #2? In your answer clearly indicate each customer’s id, and the Euclidean distance (to 3 decimal places) between the customer and starting centroid #2.

Buyer id: _________ Distance: ____________Buyer id: _________ Distance: ____________Buyer id: _________ Distance: ____________Buyer id: _________ Distance: ____________Buyer id: _________ Distance: ____________

(c) Following your assignment (in parts “a” and “b” above) of customers to the two starting centroids, what are the revised (i.e., updated) centroid coordinate values for centroid #1 and centroid #2? (Note: let’s refer to these revised values as “1st iteration”-revised centroids) (Provide answer in (x,y) format)

1st iteration-revised centroid #1: ___________1st iteration-revised centroid #2: ___________

(d) Next, based on your answer to part (c), and continuing the k-means clustering process, which customers should be assigned to the 1st iteration-revised centroid #1, and what is the Euclidean distance between each of these customers and the 1st iteration-revised centroid #1?Buyer id: _________ Distance: ____________Buyer id: _________ Distance: ____________Buyer id: _________ Distance: ____________Buyer id: _________ Distance: ____________Buyer id: _________ Distance: ____________

(e) Similarly, based on your answer to part (c), which customers should be assigned to the 1st iteration-revised centroid #2, and what is the Euclidean distance between each of these customers and the 1st iteration-revised centroid #2?

Buyer id: _________ Distance: ____________Buyer id: _________ Distance: ____________Buyer id: _________ Distance: ____________Buyer id: _________ Distance: ____________Buyer id: _________ Distance: ____________

(f) Based on your customer assignments in parts “d” and “e” above, what are the 2nd iteration-revised centroid values, for centroid #1 and centroid #2?

2nd iteration-revised centroid #1: ___________2nd iteration-revised centroid #2: ___________

(g) Next, based on your answer to part “f” above, and continuing the k-means clustering process, which customers should be assigned to the 2nd iteration-revised centroid #1, and what is the Euclidean distance between each of these customers and the 2nd iteration-revised centroid #1?Buyer id: _________ Distance: ____________Buyer id: _________ Distance: ____________Buyer id: _________ Distance: ____________Buyer id: _________ Distance: ____________Buyer id: _________ Distance: ____________

(h) Similarly, based on your answer to part “f” above, which customers should be assigned to the 2nd iteration-revised centroid #2, and what is the Euclidean distance between each of these customers and the 2nd iteration-revised centroid #2?

Buyer id: _________ Distance: ____________Buyer id: _________ Distance: ____________Buyer id: _________ Distance: ____________Buyer id: _________ Distance: ____________Buyer id: _________ Distance: ____________

(i) Based on your customer assignments in parts “g” and “h” above, what are the 3rd iteration-revised centroid values, for centroid #1 and centroid #2?

3rd iteration-revised centroid #1: ___________3rd iteration-revised centroid #2: ___________

(j) Are any additional iterations needed in this k-means clustering problem? Yes or no? Why or why not?

Yes or no (circle one)

Explain why or why not: _______________________________________________________

Question #2:

Using the same information as contained in Question #1 above (i.e., using the same preference data from the same five representative Generation customers), use SPSS to answer the following questions, parts (a) through (c). Answer all questions to 3 decimal places of precision (e.g., 3.468).

(a) Using SPSS, create and paste below a simple scatterplot of the Generation, Inc. data. In the plot, display the label (i.e., ID) of each respondent, and make “emissions” the x-axis variable and “noise” the y-axis variable.

Copy and paste the SPSS-produced simple scatterplot here

(b) Use SPSS to perform a k-means cluster analysis of the Generation, Inc. data, setting k=2. Let SPSS determine the starting centroid values for each cluster. Using the cluster labels produced by SPSS (i.e., the labels “1” or “2”), what are the starting centroid values used by SPSS?

(i) For cluster 1: emissions _______ noise _______

(ii) For cluster 2: emissions _______ noise _______

Copy and paste here the SPSS-produced initial centroid value output

(c) From SPSS output, what is the change in Euclidean distance between the SPSS-chosen initial and SPSS-calculated 1st iteration-revised centroid values for cluster #2?

Change in distance (for cluster #2 only) = _______________

Copy and paste here the SPSS-produced output that shows this change in distance

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