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# Machine Learning – Dimensionality Reduction Cognitive Class Answers

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Module 1: Data Series

Question 1: Which of the following techniques can be used to reduce the dimensions of the population?

• Exploratory Data Analysis
• Principal Component Analysis
• Exploratory Factor Analysis
• Cluster Analysis

Question 2: Cluster Analysis partitions the columns of the data, whereas principal component and exploratory factor analyses partition the rows of the data. True or false?

• False
• True

Question 3: Which of the following options are true? Select all that apply.

• PCA explains the total variance
• EFA explains the common variance
• EFA identifies measures that are sufficiently similar to each other to justify combination
• PCA captures latent constructs that are assumed to cause variance

Module 2: Data Refinement

Question 1: Which of the following options is true?

• A matrix of correlations describes all possible pairwise relationships
• Eigenvalues are the principal components
• Correlation does not explain the covariation between two vectors
• Eigenvectors are a measure of total variance, as explained by the principal components

Question 2: PCA is a method to reduce your data to the fewest ‘principal components’ while maximizing the variance explained. True or false?

• False
• True

Question 3: Which of the following techniques was NOT covered in this lesson?

• Parallel analysis
• Percentage of Common Variance
• Scree Test
• Kaiser-Guttman Rule

Module 3: Exploring Data

Question 1: EFA is commonly used in which of the following applications? Select all that apply.

• Customer satisfaction surveys
• Personality tests
• Performance evaluations
• Image analysis

Question 2: Which of the following options is an example of an Oblique Rotation?

• Regmax
• Varimax
• Softmax
• Promax

Question 3: An Orthogonal Rotation assumes that factors are correlated with each other. True or false?

• False
• True

Final Exam Answers – Machine Learning – Dimensionality Reduction Cognitive Class

Question 1: Why might you use cluster analysis as an analytic strategy?

• To identify higher-order dimensions
• To identify outliers
• To reduce the number of variables
• To segment the market
• None of the above

Question 2: Suppose you have 100,000 individuals in a dataset, and each individual varies along 60 dimensions. On average, the dimensions are correlated at r = .45. You want to group the variables together, so you decide to run principle component analysis. How many meaningful, higher-order components can you extract?

• 60
• 3
• 20
• 24
• The answer cannot be determined

Question 3: What technique should you use to identify the dimensions that hang together?

• Principal axis factoring
• Confirmatory factor analysis
• Exploratory factor analysis
• Two of the above
• None of the above

• Covariance between the two factors
• Correlations between each variable and its factor
• Correlations between each variable and its component
• Two of the above
• None of the above

Question 5: When would you use PCA over EFA?

• When you want to use an orthogonal rotation
• When you are interested in explaining the total variance in a variance-covariance matrix
• When you have too many variables
• When you are interested in a latent construct
• None of the above

Question 6: What is uniqueness?

• A measure of replicability of the factor
• The amount of variance not explained by the factor structure
• The amount of variance explained by the factor structure
• The amount of variance explained by the factor
• None of the above

Question 7: Suppose you are looking to extract the major dimensions of a parrot’s personality. Which technique would you use?

• Maximum likelihood
• Principal component analysis
• Cluster analysis
• Factor analysis
• None of the above

Question 8: Suppose you have 60 variables in a dataset, and you know that 2 components explain the data very well. How many components can you extract?

• 45
• 5
• 60
• 2
• None of the above

Question 9: When would you use an orthogonal rotation?

• When correlations between the variables are large
• When you observe small correlations between the variables in the dataset
• When you think that the factors are uncorrelated
• All of the above
• None of the above

Question 10: When would you use confirmatory factor analysis?

• When you want to validate the factor solution
• When you want to explain the variance in the matrix accounting for the measurement error
• When you want to identify the factors
• Two of the above
• None of the above

Question 11: Which of the following is NOT a rule when deciding on the number of factors?

• Newman-Frank Test
• Percentage of common variance explained
• Scree test
• Kaiser-Guttman
• None of the above

Question 12: What is one assumption of factor analysis?

• A number of factors can be determined via the Scree test
• Factor analysis will extract only unique factors
• A latent variable causes the variance in observed variables
• There is no measurement error
• None of the above

Question 13: What is an eigenvector?

• The proportion of the variance explained in the matrix
• A higher-order dimension that subsumes all of the lower-order errors
• A higher-order dimension that subsumes similar lower-order dimensions
• A higher-order dimension that subsumes all lower-order dimensions
• None of the above

Question 14: What is a promax rotation?

• A rotation method that minimizes the square loadings on each factor
• A rotation method that maximizes the variance explained
• A rotation method that maximizes the square loadings on each factor
• A rotation method that minimizes the variance explained
• None of the above

Question 15: What is the cut-off point for the Common Variance Explained rule?

• 80% of variance explained
• 50% of variance explained
• 3 variables
• 1 unit
• None of the above

Question 16: Why would you try to reduce dimensions?

• Individuals need to be placed into groups
• Variables are highly-correlated
• Many variables are likely assessing the same thing
• Two of the above
• All of the above

Question 17: If you have 20 variables in a dataset, how many dimensions are there?

• At most 20
• At least 20
• As many as the number of factors you can extract
• Not enough information
• None of the above

Question 18: What term describes the amount of variance of each variable explained by the factor structure?

• Eigenvector
• Commonality
• Similarity
• Communality
• None of the above

Question 19: What package contains the necessary functions to perform PCA and EFA?

• ggplot2
• FA
• psych
• factAnalis
• None of the above

Question 20: What is the best method for identifying the number of factors to extract?

• Parallel Analysis
• Scree test
• Newman-Frank Test
• Percentage of common variance explained
• All of the above