1 | P a g e PRACTICE EXAM QUESTION 1 (3 + 4 + 4 + 2 = 13 marks) 2 | P a g e QUESTION 2 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: 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. Using the information above answer the following questions. (a) For a m = 2 common factors model how much of the 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  matrix based on the information in Table 9.1? (e) Show that (2 + 3 + 2 + 2 + 4 = 13 marks) 3 | P a g e QUESTION 3 From the Table of data given below using SAS we obtain the following summary statistics. (a) What does the MANOVA test procedure perform in PROC DISCRIM in SAS? (b) Interpret the Wilk’s Lambda value produced by SAS. (c) Suppose a new applicant has an undergraduate GPA of x1 = 3.21 and x2=497. How would this applicant be classified assuming equal prior probabilities? HINT: Use the fact that the inverse of the pooled covariance matrix equals Recall that and similarly for the other groups. (d) What does the LDF function describe? (e) Write out the LDF for each group. (f) What is the Overall error count or rate? (g) What is the error rate for each group? (h) Explain what the prior probabilities refer to and give their values. (2 + 1.5 + 4 + 2 + 1.5 + 0.5 + 1 + 0.5 = 13 marks) 4 | P a g e QUESTION 4 (6 + 4 + 3= 13 marks) 5 | P a g e Useful to know this