Multivariate Analysis - -deals with the statistical analysis of observations where there are multiple responses on each observational unit.
-Multivariate Analysis - -This essentially models reality where each situatio
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Multivariate Analysis - -deals with the statistical analysis of observations where there are multiple responses on each observational unit.
-Multivariate Analysis - -This essentially models reality where each situation, product, or decision involves more than a single variable.
-quantum of data - -Despite the ____________________ available, the ability to obtain a clear picture of what is going on and make intelligent decisions is a challenge.
-process the information in a meaningful fashion - -When available information is stored in database tables containing rows and columns, Multivariate Analysis can be used to __________________
-USES OF MVDA - -- Consumer and market research
- Quality control and quality assurance across a range of industries such as food and beverage, paint, pharmaceuticals, chemicals, energy, telecommunications, etc.
- Process optimization and process control
- Research and development
-TYPES OF MVDA - -1. Principal Component Analysis/ Factor Analysis
2. Classification and Discriminant Analysis
3. Multiple Regression Analysis or Partial Least Squares
-Principal Component Analysis/ Factor Analysis - -Obtain a summary or an overview of a table
-Principal Component Analysis/ Factor Analysis - -identify the dominant patterns in the data, such as groups, outliers, trends, and so on
-Factor Analysis and Principal Components Analysis - -a class of procedures used for data reduction and summarization.
-interdependence technique - -Factor Analysis and Principal Components Analysis is an _____________________: no distinction between dependent and independent variables.
-Uses of Factor Analysis - -- To identify underlying dimensions, or factors, that explain the correlations among a set of variables.
- To identify a new, smaller, set of uncorrelated variables to replace the original set of correlated variables.
-Factor score coefficients - -The first set of weights that are chosen so that the first factor explains the largest portion of the total variance
-Bartlett's test of sphericity - -used to test the hypothesis that the variables are uncorrelated in the population (i.e., the population corr matrix is an identity matrix)
-Correlation Matrix - -a lower triangle matrix showing the simple correlations, r, between all possible pairs of variables included in the analysis. The diagonal elements are all 1.
-Communality - -Amount of variance a variable shares with all the other variables. This is the proportion of variance explained by the common factors.
-Eigenvalue - -Represents the total variance explained by each factor.
-Factor loadings - -Correlations between the variables and the factors.
-Factor Matrix - -contains the factor loadings of allthe variables on all the factors
-Factor Scores - -are composite scores estimated for each respondent on the derived factors.
-Kaiser-Meyer-Olkin (KMO) measure of sampling adequacy - -Used to examine the appropriateness of factor analysis. High values (between 0.5 and 1.0) indicate appropriateness. Values below 0.5 imply not.
-Percentage of Variance - -The percentage of the total variance attributed to each factor.
-Scree Plots - -is a plot of the Eigenvalues against the number of factors in order of extraction.
-Principal Component Analysis - -An exploratory technique used to reduce the dimensionality of the data set to 2D or 3D
-Principal Component Analysis - -• Can be used to:
-Reduce number of dimensions in data
-Find patterns in high-dimensional data
-Visualize data of high dimensionality
-Principal Component Analysis Steps - -1. Standardize the data.
2. Obtain the Eigenvalues and Eigenvectors from the covariance matrix or correlation matrix, or perform a Singular Vector Decomposition
3. Sort eigenvalues in descending order and choose the k eigenvectors that correspond to the k largest eigenvalue where k is the number of dimensions of the new feature subspace (k < d).
4. Transform the projection matrix W from the selected k eigenvalues.
5. Transform the original dataset X via W to obtain a k-dimensional feature subspace.
-Classification and Discriminant Analysis - -Analyze groups in the table, how these groups differ, and to which group individual table rows belong.
-Discriminant Analysis - -is used to determine which variables discriminate between two or more naturally occurring groups.
-Analysis of Variance (ANOVA) - -Discriminant function analysis is very similar to ___________________.
-Multiple Regression Analysis or Partial Least Squares - -Find relationships between columns in data tables
-Multiple Regression Analysis or Partial Least Squares - -To use one set of variables (columns) to predict another, for the purpose of optimization, to find out which columns are important in the relationship.
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