This is a multivariate analysis problem

In a consumer-preference study, a random sample of customers were asked to rate several attributes of a new product. The responses, on a 7-point semantic differential scale, were tabulated and the attribute correlation matrix constructed. The correlation matrix presented below: Attribute (Variable) 1 2 3 4 5 Taste 1.00 .02 .42 .01 1 Goodbuyformoncy 2 .02 1.00 .13 .71 Flavor 3 .96 .13 1.00 .50 .ll 4 5 Suitableforsnack .42 .71 .50 1.00 Provides lots of energy .01 .85 .11 .79 1.00 A factor analysis was performed on the Correlation matrix and results summarised below. The estimated factor loadings, communalities, and specific variances, are given in Table 9.1. Table 9.1 Estimated factor loadings Specific Communalities variances Variable F1 F2 4; = 1 - h? 1. Taste .56 .82 .98 .02 2. Good buy for money .78 -.53 .88 86 3. Flavor .65 .75 .98 4. Suitable for snack .94 -.10 .89 E 5. Provides lots of energy .80 -.54 .93 .07 Eigenvalues 2.85 1.81 Cumulative proportion of total (standardized) sample variance .571 .932Using the information above answer the following questions. (a) For a m = 2 common factors model how much ofthe total (standardised) variance will be accounted for, JUSTIFY YOUR ANSWER USING THE EIGEN VALUES? (b) Interpret the 2 Factors. (c) What is the L matrix based on the information in Table 9.1? (d) What is the '1' matrix based on the information in Table 9.1? (e) Show that =LL'+'P