In Applied Multivariate Techniques (John Wiley and Sons, 1996), Subhash Sharma considers a study in which 143 respondents rated three brands of laundry detergents on 12 product attributes using a 5-point Likert scale. The 12 product attributes are:
V1: Gentle to natural fabrics
V2: Won’t harm colors
V3: Won’t harm synthetics
V4: Safe for lingerie
V5: Strong, powerful
V6: Gets dirt out
V7: Makes colors bright
V8: Removes grease stains
V9: Good for greasy oil
V10: Pleasant fragrance
V11: Removes collar soil
V12: Removes stubborn stains
Table 3.13 is a matrix containing the pairwise correlations between the variables, and Figure 3.36 is the SPSS output of a factor analysis of the detergent data. (1) Examining the "EIGENVALUE" column, and recalling that the eigenvalue of a factor is the variance of the factor, explain why the analyst chose to retain two factors. (2) Discuss why factor 1 can be interpreted to be the ability of the detergent to clean clothes. (3) Discuss why Factor 2 can be interpreted to be the mildness of the detergent.
Table 3.13
V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12 V1 1.000000.419010.518400.566410.181220.174540.230340.306470.240510.211920.274430.20694 V2 0.419011.000000.575990.498860.186660.246480.229070.225260.219670.258790.321320.25853 V3 0.518400.575991.000000.643250.290800.344280.410830.340280.328540.388280.394330.36712 V4 0.566410.498860.643251.000000.383600.396370.376990.403910.423370.365640.336910.36734 V5 0.181220.186660.290800.383601.000000.579150.594000.676230.692690.438730.554850.65261 V6 0.174540.246480.344280.396370.579151.000000.577560.701030.622800.621740.598550.57845 V7 0.230340.229070.410830.376990.594000.577561.000000.676820.684450.541750.783610.63889 V8 0.306470.225260.340280.403910.676230.701030.676821.000000.698130.685890.711150.71891 V9 0.240510.219670.328540.423370.692690.622800.684450.698131.000000.585790.646370.69111 V10 0.211920.258790.388280.365640.438730.621740.541750.685890.585791.000000.622500.63494 V11 0.274430.321320.394330.336910.554850.598550.783610.711150.646370.622501.000000.63973 V12 0.206940.258530.367120.367340.652610.578450.638890.718910.691110.634940.639731.00000