Unit 12: Multivariate Analysis - Practice Quiz

1 What is the main purpose of classification in multivariate analysis?

2 Which type of data is normally required to train a supervised classification model?

3 In a classification problem, the dependent variable is usually:

4 What is the basic objective of factor analysis?

5 Principal component analysis primarily explains which type of variance?

6 Principal axis factoring mainly focuses on:

7 Which factor extraction method estimates parameters by maximizing a likelihood function?

8 Which matrix is commonly examined at the beginning of factor analysis?

9 What does the Kaiser-Meyer-Olkin (KMO) measure assess?

10 According to the Kaiser criterion, which factors are generally retained?

11 Why is factor rotation performed?

12 Which of the following is an orthogonal rotation method?

13 What does an oblique rotation allow?

14 What is the main objective of cluster analysis?

15 Which diagram commonly displays the results of hierarchical clustering?

16 What must usually be specified before applying the -means clustering method?

17 What is discriminant analysis mainly used to predict?

18 A discriminant function is usually formed as:

19 What does multidimensional scaling commonly produce?

20 What is conjoint analysis primarily used to study?

21 A researcher wants to predict customer loyalty from satisfaction, perceived value, and service quality. How should this multivariate problem be classified?

22 A study examines 15 attitude variables without specifying any variable as an outcome and seeks a smaller set of underlying dimensions. Which classification is most appropriate?

23 A researcher wants to summarize the total variance in 12 observed variables into a few weighted composites. Which method is most suitable?

24 A researcher is interested in latent constructs that explain only the shared variance among measured variables. Which method best matches this objective?

25 A researcher wants to test the statistical fit of a factor model and construct confidence intervals, assuming approximate multivariate normality. Which extraction method is most appropriate?

26 A dataset produces a Kaiser-Meyer-Olkin value of and a significant Bartlett's test with . What is the best conclusion?

27 After extraction, one variable has a communality of , while all other variables have communalities above . What does the value indicate?

28 The first six eigenvalues from a correlation matrix are , , , , , and . Under the Kaiser criterion, how many factors should initially be retained?

29 A theory states that anxiety and depression are related latent constructs. Which rotation is most appropriate when extracting these factors?

30 After varimax rotation, a variable has loadings of , , and on three factors. How should the variable usually be interpreted?

31 A retailer knows in advance that customers must be divided into four market segments and has a large numerical dataset. Which method is most appropriate?

32 Income is measured in dollars and age is measured in years. Before clustering customers using Euclidean distance, what should the researcher generally do?

33 A researcher uses single-linkage hierarchical clustering and obtains a long sequence of cases joined through close neighbors. Which known tendency does this illustrate?

34 A bank has historical data in which applicants are already labeled as low, medium, or high credit risk. It wants to classify new applicants using financial ratios. Which technique is appropriate?

35 A discriminant function for two groups is . If an observation has and , what is its discriminant score?

36 Box's M test is significant in a discriminant analysis involving several groups. Which assumption is most directly questioned?

37 Consumers rate the pairwise dissimilarity of six smartphone brands. A researcher wants a two-dimensional map in which similar brands appear close together. Which technique should be used?

38 A two-dimensional multidimensional scaling solution has Stress , while a one-dimensional solution has Stress . What is the most reasonable interpretation?

39 In a conjoint study of laptops, a respondent's part-worths are for a low price, for a high-resolution screen, and for a light weight. Ignoring the intercept, what is the total utility of a laptop with all three features?

40 In a conjoint analysis, the utility range for price is , for brand is , and for warranty is . What is the relative importance of price?

41 A researcher has 12 continuous variables and wants to assign observations to one of four groups. The group labels are known for a training sample, but the group covariance matrices may differ. Which classification is most appropriate?

42 A binary classifier estimates . A false negative costs 8 units, a false positive costs 2 units, and correct decisions have zero cost. Under minimum expected loss, how should the observation be classified?

43 Which statement correctly distinguishes principal component analysis from principal axis factoring when both are applied to the same correlation matrix?

44 A dataset contains strongly non-normal indicators, and the researcher wants latent common factors without relying on a multivariate-normal likelihood-ratio test. Which extraction method is most defensible?

45 Under maximum likelihood factor analysis, which result can be formally evaluated when its assumptions are sufficiently satisfied?

46 For three standardized variables, the inverse correlation matrix is

Using , what additional operation is required before computing the KMO values?

47 A sample correlation matrix has eigenvalues . The corresponding mean eigenvalues from parallel random datasets are . How many factors should parallel analysis retain?

48 After extracting a two-factor model, one variable has loadings and . Assuming standardized variables and no additional factor contributions, what are its communality and uniqueness?

49 An unrotated orthogonal loading matrix is transformed as , where . Which quantity is necessarily unchanged for every observed variable?

50 In an oblique factor solution, variable has pattern coefficients , and the factor correlation matrix is . What is the structure coefficient of with the second factor?

51 A researcher expects two substantive constructs to be correlated but applies varimax rotation. What is the most important interpretive risk?

52 A cluster analysis uses Euclidean distance on income measured in dollars and satisfaction measured on a seven-point scale. Income has far greater numerical variance. What is the most defensible preprocessing decision?

53 Under Ward's method with squared Euclidean distance, clusters and contain 4 and 6 cases, and their centroids are 5 units apart. What is the increase in within-cluster sum of squares if they are merged?

54 A hierarchical single-linkage solution joins two dense, well-separated groups through a sequence of sparse intermediate observations. Which diagnosis best explains the result?

55 Two groups have multivariate normal distributions with equal covariance matrices but unequal prior probabilities. Relative to equal priors, how does incorporating the unequal priors affect the linear discriminant boundary?

56 In a three-group discriminant analysis with five predictors, what is the maximum number of nonzero canonical discriminant functions?

57 A study applies quadratic discriminant analysis with 80 predictors but only 25 observations in each group. What is the central estimation problem?

58 A nonmetric multidimensional scaling solution has low stress, but its recovered distances are not linearly related to the original dissimilarities. Why can the solution still be valid?

59 In classical MDS, double-centering the squared dissimilarity matrix produces a matrix with several substantial negative eigenvalues. What is the best interpretation?

60 An effects-coded conjoint model estimates level utilities for a three-level attribute as for level 1 and for level 2. What utility is implied for level 3?