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In this course, you will learn the theory behind dimension reduction, and get some hands-on practice using Principal Components Analysis (PCA) and Exploratory Factor Analysis (EFA) on survey data.

### Module 1: Data Series

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

1. Exploratory Data Analysis
2. Principal Component Analysis
3. Exploratory Factor Analysis
4. Cluster Analysis

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?

1. False
2. True

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

1. PCA explains the total variance
2. EFA explains the common variance
3. EFA identifies measures that are sufficiently similar to each other to justify combination
4. PCA captures latent constructs that are assumed to cause variance

### Module 2: Data Refinement

1. Which of the following options is true?

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

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

1. False
2. True

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

1. Parallel analysis
2. Percentage of Common Variance
3. Scree Test
4. Kaiser-Guttman Rule

### Module 3: Exploring Data

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

1. Customer satisfaction surveys
2. Personality tests
3. Performance evaluations
4. Image analysis

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

1. Regmax
2. Varimax
3. Softmax
4. Promax

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

1. False
2. True

### Machine Learning – Dimensionality Reduction Final Exam Answers

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

1. To identify higher-order dimensions
2. To identify outliers
3. To reduce the number of variables
4. To segment the market
5. None of the above

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?

1. 60
2. 3
3. 20
4. 24
5. The answer cannot be determined

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

1. Principal axis factoring
2. Confirmatory factor analysis
3. Exploratory factor analysis
4. Two of the above
5. None of the above

1. Covariance between the two factors
2. Correlations between each variable and its factor
3. Correlations between each variable and its component
4. Two of the above
5. None of the above

5. When would you use PCA over EFA?

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

6. What is uniqueness?

1. A measure of replicability of the factor
2. The amount of variance not explained by the factor structure
3. The amount of variance explained by the factor structure
4. The amount of variance explained by the factor
5. None of the above

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

1. Maximum likelihood
2. Principal component analysis
3. Cluster analysis
4. Factor analysis
5. None of the above

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?

1. 45
2. 5
3. 60
4. 2
5. None of the above

9. When would you use an orthogonal rotation?

1. When correlations between the variables are large
2. When you observe small correlations between the variables in the dataset
3. When you think that the factors are uncorrelated
4. All of the above
5. None of the above

10. When would you use confirmatory factor analysis?

1. When you want to validate the factor solution
2. When you want to explain the variance in the matrix accounting for the measurement error
3. When you want to identify the factors
4. Two of the above
5. None of the above

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

1. Newman-Frank Test
2. Percentage of common variance explained
3. Scree test
4. Kaiser-Guttman
5. None of the above

12. What is one assumption of factor analysis?

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

13. What is an eigenvector?

1. The proportion of the variance explained in the matrix
2. A higher-order dimension that subsumes all of the lower-order errors
3. A higher-order dimension that subsumes similar lower-order dimensions
4. A higher-order dimension that subsumes all lower-order dimensions
5. None of the above

14. What is a promax rotation?

1. A rotation method that minimizes the square loadings on each factor
2. A rotation method that maximizes the variance explained
3. A rotation method that maximizes the square loadings on each factor
4. A rotation method that minimizes the variance explained
5. None of the above

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

1. 80% of variance explained
2. 50% of variance explained
3. 3 variables
4. 1 unit
5. None of the above

16. Why would you try to reduce dimensions?

1. Individuals need to be placed into groups
2. Variables are highly-correlated
3. Many variables are likely assessing the same thing
4. Two of the above
5. All of the above

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

1. At most 20
2. At least 20
3. As many as the number of factors you can extract
4. Not enough information
5. None of the above

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

1. Eigenvector
2. Commonality
3. Similarity
4. Communality
5. None of the above

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

1. ggplot2
2. FA
3. psych
4. factAnalis
5. None of the above

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

1. Parallel Analysis
2. Scree test
3. Newman-Frank Test
4. Percentage of common variance explained
5. All of the above

### Wrap Up

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