Multivariate analysis deals with the observation and analysis of more than one variable at a time this technique is utilized in performing trade studies in design and analysis across a number of dimensions and at the same time taking into account the effect that the variable has on the responses of interest(Hair,2010).This type of analysis has several uses. These uses include; Capability-based design, inverse design, alternatives analysis, etc.

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Multivariate analysis can be used in quantitative studies in various different ways. These include:

## Organizing and counting of the data that is surveyed.

All social researcher find the raw data as being invariable. This is because it is impossible for them to collect all the data from all the regions. Organization of the data is however very important for the detection of any unknown factors, verifications of the assumptions made and much more. For quantitative analysis, organization of data is very important especially for numerical processes that have to be done such as to simplify on the explanation of the phenomenon (Hair, Black, Babin, Anderson, & Tatham, 2006).

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The data thus has to be standardized before analysis is done. Open questions needs some criteria to be set for categorizing the answers. The data can be summarized by conducting some cross tabulation and some statistics.

## Summarizing of data by multivariate analysis

Using the basic analysis, it might be quite hard to understand the tendency of what is being surveyed when the raw data contains a lot of information and questions. Basic analysis becomes problematic once someone has to deal with more than two variables. In this case, multivariate analysis can be used to analyze complicated information which the human mind cannot adequately comprehend. Its calculation is very intricate though this type of analysis has popularized as computers developed. (Hair*et al* 2006).Some of the major methods of this type of analysis include;

- The principle component analysis- it summarizes multivariate information into simpler values.
- The multiple linear regression analysis- it estimates other variables basing on some of the fixed variables.
- Factor analysis- uses multivariate data to estimate the potential data
- Discriminant analysis-it determines which group a certain data belongs basing on some fixed variables(Johnson, & Wichern, 1992)

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Multivariate regression works on deriving a formula that describes how some variables change in relation to change in other variables. General linearmodels can be used for the linear relations which makes used of different matrixes with the formula written as;

Y= XB+U

Y represents a matrix which contains a series of multivariate measurements, X represents a matrix which can be a design matrix, B is also a matrix with parameters which can be estimated and U represents a matrix which contains noise or errors(Morrison,1990). The general linear model can used a number of statistical models such as Analysis of Variance (ANOVA), ordinary linear regression, the T and F-test and many more. Multiple linear regression can also be used. According to (Morrison, 1990), is a generalized form of linear regression which considers more than one independent variable and restricts the dependent variable to one. These are used when the errors (matrix U), input in the equation do not follow a multivariate normal distribution. This type of multivariate statistical test may be useful in future research as it will aid in monitoring the changes of variables especially the numeric variable.