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Questions and Answers
What is the main objective of Principal Components Analysis (PCA)?
What is the main objective of Principal Components Analysis (PCA)?
What distinguishes PCA and FA from regression analysis?
What distinguishes PCA and FA from regression analysis?
In PCA, what makes the computation and interpretation of Principal Components (PCs) relatively simple?
In PCA, what makes the computation and interpretation of Principal Components (PCs) relatively simple?
Which technique transforms the original variables into new, uncorrelated variables called principal components?
Which technique transforms the original variables into new, uncorrelated variables called principal components?
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What is the major objective of selecting factors in Factor Analysis (FA)?
What is the major objective of selecting factors in Factor Analysis (FA)?
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What is the main purpose of principal components analysis?
What is the main purpose of principal components analysis?
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In PCA, how are the coefficients chosen for each new variable (principal component)?
In PCA, how are the coefficients chosen for each new variable (principal component)?
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What does it mean by 'Var (C1) ≥ Var (C2) ≥ ... ≥ Var (CP)' in principal components analysis?
What does it mean by 'Var (C1) ≥ Var (C2) ≥ ... ≥ Var (CP)' in principal components analysis?
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What is the condition for the sum of the squares of coefficients for any principal component in PCA?
What is the condition for the sum of the squares of coefficients for any principal component in PCA?
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How are C1, C2, C3, and further principal components defined in terms of their variance in PCA?
How are C1, C2, C3, and further principal components defined in terms of their variance in PCA?
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How are the variances of individual principal components related to the original total variance in PCA?
How are the variances of individual principal components related to the original total variance in PCA?
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Study Notes
Principal Components Analysis (PCA)
- The main objective of PCA is to reduce the dimensionality of a dataset while retaining most of the information.
Comparison with Regression Analysis
- PCA and Factor Analysis (FA) differ from regression analysis in that they are not used to predict a dependent variable, but rather to identify patterns and relationships in the data.
Characteristics of Principal Components
- The computation and interpretation of Principal Components (PCs) are relatively simple in PCA because the PCs are orthogonal (perpendicular) and uncorrelated.
Technique of PCA
- PCA is a technique that transforms the original variables into new, uncorrelated variables called principal components.
Objective of Factor Analysis (FA)
- The major objective of selecting factors in FA is to identify the underlying factors that explain the patterns and relationships in the data.
Purpose of PCA
- The main purpose of PCA is to identify the directions of maximum variance in the data and to reduce the dimensionality of the dataset.
Coefficients in PCA
- The coefficients for each new variable (principal component) are chosen in such a way that the first principal component has the maximum variance, the second principal component has the second maximum variance, and so on.
Variance of Principal Components
- The variance of the principal components is in descending order, meaning that Var(C1) ≥ Var(C2) ≥ ...≥ Var(CP), where C1, C2, ..., CP are the principal components.
Condition for Coefficients
- The condition for the sum of the squares of coefficients for any principal component in PCA is that it equals 1.
Definition of Principal Components
- C1, C2, C3, and further principal components are defined in terms of their variance, with C1 having the highest variance, C2 having the second highest variance, and so on.
Relationship with Original Variance
- The variances of individual principal components are related to the original total variance in that the sum of the variances of all principal components equals the original total variance.
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Description
Explore the differences between Principal Components Analysis (PCA) and Factor Analysis (FA), two statistical techniques used to identify key factors representing relationships among interrelated variables. Learn about the applications, advantages, and considerations when using PCA and FA.
