I need to write 2-page response to question 3.66.

I do not understand what the questions are asking (questions 1, 2, and 3).

3.10 Factor Analysis (Optional and Requires Section 3.4) 193 Exercises for Section 3.10 CONCEPTS Table 3.16 is a matrix containing the pairwise 3.64 What is the purpose of factor analysis? correlations between the variables, and Figure 3.50 3.65 Why does factor analysis do factor rotation? is a software package output of a factor analysis of the detergent data. (1) Examining the "EIGENVALUE" column in Figure 3.50, and METHODS AND APPLICATIONS recalling that the eigenvalue of a factor is the 3.66 In Applied Multivariate Techniques (John Wiley and variance of the factor, explain why the analyst chose Sons, 1996), Subhash Sharma considers a study in to retain two factors. (2) Discuss why Factor I can which 143 respondents rated three brands of laundry be interpreted to be the ability of the detergent detergent on 12 product attributes using a 5-point to clean clothes. (3) Discuss why Factor 2 can be Likert scale. The 12 product attributes are: interpreted to be the mildness of the detergent. V1: Gentle to natural fabrics Makes colors bright 3.67 Table 3.17 shows the output of a factor analysis of the V2: Won't harm colors V8: Removes grease stains ratings of 82 respondents who were asked to evalu- V3: Won't harm synthetics ate a particular discount store on 29 attributes using a V9: Good for greasy oil V4: Safe for lingerie 7-point Likert scale. Interpret and give names to the v10: Pleasant fragrance V5: Strong, powerful V11: Removes collar soil five factors. V6: Gets dirt out V12: Removes stubborn stains TABLE 3.16 Correlation Matrix for Detergent Data V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12 V1 1.00000 0.41901 0.51840 0.56641 0.18122 0.17454 0.23034 0.30647 0.24051 0.21192 0.27443 0.20694 V2 0.41901 1.00000 0.57599 0.49886 0.18666 0.24648 0.22907 0.22526 0.21967 0.25879 0.32132 0.25853 V3 0.51840 0.57599 1.00000 0.64325 0.29080 0.34428 0.41083 0.34028 0.32854 0.38828 0.39433 0.36712 V4 0.56641 0.49886 0.64325 1.00000 0.38360 0.39637 0.37699 0.40391 0.42337 0.36564 0.33691 0.36734 V5 0.18122 0.18666 0.29080 0.38360 1.00000 0.57915 0.59400 0.67623 0.69269 0.43873 0.55485 0.65261 V6 0.17454 0.24648 0.34428 0.39637 0.57915 1.00000 0.57756 0.70103 0.62280 0.62174 0.59855 0.57845 V7 0.23034 0.22907 0.41083 0.37699 0.59400 0.57756 1.00000 0.67682 0.68445 0.54175 0.78361 0.63889 V8 0.30647 0.22526 0.34028 0.40391 0.67623 0.70103 0.67682 1.00000 0.69813 0.68589 0.71115 0.71891 v9 0.24051 0.21967 0.32854 0.42337 0.69269 0.62280 0.68445 0.69813 1.00000 0.58579 0.64637 0.69111 V10 0.21192 0.25879 0.38828 0.36564 0.43873 0.62174 0.54175 0.68589 0.58579 1.00000 0.62250 0.63494 V11 0.27443 0.32132 0.39433 0.33691 0.55485 0.59855 0.78361 0.71115 0.64637 0.62250 1.00000 0.63973 V12 0.20694 0.25853 0.36712 0.36734 0.65261 0.57845 0.63889 0.71891 0.69111 0.63494 0.63973 1.00000 Source: Data from Subhash Sharma, Applied Multivariate Techniques (New York Wiley, 1996). FIGURE 3.50 A Software Package Output of a Factor Analysis of the Detergent Data INITIAL STATISTICS: ROTATED FACTOR MATRIX: VARIABLE COMMUNALITY FACTOR EIGENVALUE PCT OF VAR CUM PCT FACTOR 1 FACTOR 2 .42052 6.30111 52.5 52.5 VI 12289 .65101 V1 39947 1.81757 15.1 67.7 V2 .13900 V2 64781 .56533 W N .66416 5.5 73.2 V3 V3 24971 78587 56605 57155 4.8 78.0 V4 29387 V4 74118 60467 .55995 4.7 82.6 V5 V5 73261 15469 57927 6 44517 3.7 86.3 V6 V6 .73241 20401 69711 41667 3.5 89.8 V7 V7 .77455 .22464 .74574 8 .32554 2.7 92.5 V8 V8 .85701 9 20629 66607 .27189 2.3 94.8 V9 V9 80879 .59287 19538 10 .25690 2.1 96.9 V10 V10 69326 71281 11 23923 19159 1.6 98.5 V11 V11 77604 64409 12 25024 17789 1.5 100.0 V12 V12 .79240 19822