The document describes types of data analysis: univariate (one variable), bivariate (two variables), and multivariate (more than two variables), emphasizing the differences in complexity and relationships among variables. It highlights the purpose of multivariate analysis, which is to explore interdependencies and relationships among multiple variables, useful in various fields including economics and psychology. Techniques discussed include principal components analysis (PCA) and factor analysis (FA), focusing on data reduction and covariate relationships.

1. Multivariate Analysis

2. Univariate Data
► This type of data consists of only one variable.
► The analysis of univariate data is thus the simplest form of analysis since the information
deals with only one quantity that changes.
► It does not deal with causes or relationships .
► The main purpose of the analysis is to describe the data and find patterns that exist
within it.
► The example of a univariate data can be Marks of students ,income of salaried class.

3. Bivariate data
► This type of data involves two different variables.
► The analysis of this type of data deals with causes and relationships
► the analysis is done to find out the relationship among the two variables.
► Example of bivariate data can be height and weight of a group of
individuals , income and expenditure of middle clas

4. Multivariate Data
► Multivariate data arise whenever analysis is based on more than two
variables.
► The values of these variables are all recorded for each distinct item,
individual or experimental unit.
► Data based on pathological test ( Haemoglobin Count, Blood Sugar ,ESR,
Potassium, Cholesterol)

5. Objective of Multivariate data analysis
(p variates)
► Studying the p variables individually is not sufficient as it will not
take into account the correlations among the variables.
► Multivariate analysis is more meaningful as it involves the
relationships and interdependence among all the p variables.
► Some areas of study where MA methods are used are
- Economics, Insurance , Financial Services , Linguistics ,Psychology
etc.

6. Some of the Multivariate techniques
► Discriminant Analysis
► Principal Components Analysis (PCA)
► Factor Analysis (FA)
► Canonical analysis
► Cluster Analysis
► Multivariate Analysis of Variance and Covariance
► Multivariate Regression Analysis

7. Contd.
► In this paper we will be focusing on first three methods.
► We will also be doing Multivariate normal distribution.
► We have already covered Bivariate normal distribution.
► For now a brief introduction of PCA and FA

8. PCA
► A PCA is concerned with explaining the variance – covariance
structure of a set of variables through a few linear combinations
of these variables.
► Its general objectives are (i) Data Reduction (ii)Interpretation.
► P C’s serve as intermediate steps in much larger investigations eg . Multiple
regression and cluster analysis

9. Factor Analysis
► F A is a data reduction technique for investigating interdependencies or
correlations or covariances.
► The essential purpose of FA is to describe ,if possible, the covariance
relationships among many variables in terms of a few underlying, but
unobservable variables called factors.
► Details in my next PPT.