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Multivariate analysis Homework Help

Multivariate analysis is a statistical method used to explore and analyze data sets that have multiple variables. It includes over twenty different techniques that researchers can use to manipulate complex data. The technique you use depends on the type and complexity of data you are dealing with and the problem you are attempting to solve. Multivariate analysis is one of the most common techniques for analyzing big data today. It is used for research and development, quality control and assurance, process control and optimization, as well as market and consumer research.

How multivariate analysis helps researchers

The multivariate analysis makes manipulating data much easier for both researchers and data analysts. With this technique, one can:

Obtain an overview or summary of a table:

With multivariate analysis, one can perform factor analysis and principal component analysis to view a summary of a given table. Using these techniques, one can easily recognize patterns in data such as trends, outliers, groups, etc. The patterns are usually presented as two plots.
How multivariate analysis helps researchers

Analyze and explain groups of data in a table:

This technique is referred to as classification and discriminant analysis. It enables researchers to identify the differences between groups and find out which group each table row belongs to.

Find out how different columns of data in a table are related:

To do this, data analysts perform partial least squares and multiple regression analysis. This helps them to identify relationships, for instance, between operation conditions of a process and the quality of the product. They use one set of columns (variables) to forecast another to allow for effective optimization and to identify columns that are more essential in the relationship.

Types of multivariate analysis

There are many different types of multivariate analysis, all meant to perform different statistical operations. The most common ones include:

Additive tree:

This is simply a method of displaying data clusters in a graph. It is applied where data in a table represents the same unit both in rows and columns.
Types of multivariate analysis

Canonical correlation analysis:

When you want to find the correlation between two sets of data, canonical correlation analysis is one way to go about it. The method is similar to the correlation coefficient in that it identifies the association between variables. The only difference is that canonical correlation analysis particularly identifies the correlation between two sets of variables.

Cluster analysis:

This technique examines how data is clustered (gathered) using parameters like age, income, education level, household size, etc. It enables researchers to analyze various groups of data and draw inferences from them effectively.

Factor analysis:

Sometimes researchers take a huge amount of data and shrink it into smaller sets of data that are more understandable and manageable. This process is referred to as factor analysis and it helps identify hidden patterns. Factor analysis shows how different patterns overlap and displays the properties that are prevalent in most patterns.

Independent component analysis:

This technique is used both in mathematics and signal processing to illustrate a multivariate function by its subcomponents or hidden factors. The component signals involved are usually independent non-Gaussian signals and the objective of applying independent component analysis is to enable the subcomponents to represent the composite signal accurately.

Generalized Procrustes Analysis (GPA):

The GPA is a technique for comparing two sets of shapes or configurations. It was initially invented to match two shapes from the factor analysis but the technique was later stretched to generalized Procrustes analysis to allow the comparison of more than two shapes.


Multivariate analysis of variance is an analysis of variance with more than one dependent variable. Data analysts use it to determine whether modifying the independent variable changes the dependent variable (response variable).

Pros and cons of multivariate analysis

Every data analysis technique has advantages or disadvantages over other techniques. Below are some of the upsides and downsides of using multivariate analysis for data manipulation:


The technique considers multiple factors of the independent variable that affect the variability of the response variable, which means the results obtained are more accurate.

The results drawn from multivariate analysis are more realistic and closer to real-life situations.


One is required to perform a series of rather complex analyses to get satisfactory results

Collecting and tabulating a large number of variables is an overwhelming and time-consuming process