MBA 740 Module 7

Review Questions

1.       Why is multivariate data analysis particularly useful in big data analysis?

Because big data typically involves many variables measured on many observations at the same time. Multivariate techniques are designed specifically to analyze those complex relationships simultaneously rather than one variable at a time.

2.       What is the key characteristic of identifying multivariate data analysis?

The analysis of three or more variables simultaneously. In other words, a technique is considered multivariate when it examines multiple variables at the same time to understand relationships, patterns, or effects. The defining feature is not just having many variables in a dataset — it’s that the statistical technique analyzes them jointly in a single model rather than separately

3.       What is the concept of a variate in multivariate data analysis.

Variate is the mathematical way in which a set of variables can be represented with one equation.

4.       Define dependence techniques and give examples of multivariate dependence techniques.

Dependence techniques are multivariate procedures that predict some observed dependent variable using a combination of predictors that serve as independent variables.

·       Multiple regression analysis

·       Discriminant analysis

·       Multivariate analysis of variance

·       logistic regression

5.       What distinguishes MANOVA from ANOVA?

The only difference between MANOVA and n-way ANOVA is the inclusion of multiple, related dependent variables as opposed to a single dependent variable.  A key distinction between the two is that MANOVA models produce and additional layer of testing compared to ANOVA

6.       What distinguishes MANCOVA from MANOVA?

MANCOVA is a variation of MANOVA that can include interval or ratio covariates.

7.       What is role of Wilks’ Lambda (Λ) in MANOVA and MANCOVA?

Wilks’ Lambda (Λ) is a multivariate test statistic used to determine whether there are statistically significant differences between group mean vectors on a combination of dependent variables.

In MANOVA, Wilks’ Lambda tests:

Whether the independent variable(s) have a significant overall effect on the combined dependent variables.

In MANCOVA, Wilks’ Lambda assesses:

Whether adjusted group means differ significantly on the combined dependent variables.

8.       How is a cutting score used to determine group membership in discriminant analysis?

Cutting score is a number produced by discriminant analysis that serves as a benchmark to which discriminant scores are compared. A discriminant score above the cutting score places observations in one group while a discriminant score below the cutting score places them in another.

9.       How are MANOVA and discriminant analysis related?

Discriminant analysis shares a lot in common with multivariate analysis, particularly linear regression and MANOVA.  MANOVA tells you whether groups differ.

Discriminant analysis tells you how they differ and helps predict group membership.

10.  What is a confusion matrix?

A confusion matrix is a classification table that compares predicted group membership to actual group membership, showing correct and incorrect classifications and allowing calculation of model accuracy and error rates.

11.  What is the primary difference in applications between discriminant analysis and logistic regression analysis?

The primary difference in application is that discriminant analysis requires multivariate normality and equal covariance matrices and is best used when those assumptions are met, whereas logistic regression does not require these assumptions and is more flexible for predicting categorical outcomes using mixed types of independent variables.

12.  What types of research questions can be addressed by logistic regression?

Logistic regression addresses research questions that involve predicting and explaining categorical outcomes. It estimates the probability of an event occurring, identifies significant predictors of group membership, evaluates odds ratios, and classifies observations into categories without requiring normality assumptions.

13.  What is the likelihood value that is used for in interpreting logistic regression results.

Likelihood value provides a way of indicating the overall significance or predictive capabilities of logistic regression because -2 times the log of the likelihood value (abbreviated as -2LL) takes on the value of 0 when every observation is correctly classified as a success or failure.

14.  What is an entropy or pseudo R-squared?

Entropy (pseudo) R² is an assessment of logistic regression predictive power that functions like the R² in multiple regression.

15.  How does an analyst interpret the statistical significance and meaning of individual independent variables used in logistic regression?

An analyst interprets individual independent variables in logistic regression by examining the p-value (Wald statistic) to determine statistical significance, the sign of the coefficient to determine direction of effect, and the odds ratio (e^β) to assess the magnitude of impact on the likelihood of the outcome occurring.