MS 95 IGNOU MBA Solved Assignment - Write shot notes on a. Regression Analysis b. Discriminant Analysis c. Factor Analysis

Write shot notes on

a.       Regression Analysis

b.      Discriminant Analysis

c.       Factor Analysis

Ans :Regression analysis 

            Regression analysis is one of the most extensively utilized method between

the analytical models of association employed in business research. Regression analysis tries to analyze the connection between a dependent variable and a group of independent variables (one or more). One example is, in demand analysis, demand is versely linked to price for normal commodities. We can write D = A – BP, where D is, the demand which is the dependent variable, P is the unit price of the commodity, an independent variable. It is an example of a simple linear regression equation. The multiple linear regressions model is the prototype of single criterion multiple predictor association model where we wish to research the combined impact of several independent variables upon one dependent variable. In the above example if P is the consumer price index, and Q is the index of industrial production, we might manage to research demand as a function of 2 independent variables P and Q and write D = A – BP + C Q as a multiple linear regression model.

Objectives of Regression Analysis

·         To research a pattern linking the dependent variable and independent variables by establishing a functional relationship between the two. In this equation the level of relationship comes from which is a matter of interest to the researcher in his study.

·         To make use of the well-established regression equation for problems concerning forecasting.

·         To analyze how much of the variation in the dependent variable is described by the group of independent variables. This would allow him to get rid of particular unwanted variables from the system. For instance, if 85% of variation in demand in a research can be stated by price and consumer rating index, the researcher may drop additional factors such as industrial production, extent of imports, substitution effect etc. that may add only 15% of variation in demand provided all the causal variables are linearly independent.

eigenvalue = sum of squared correlations of the discriminant function scores with the p original variables

canonical correlation varies from 0 to 1 never taking on negative values

B)Discriminant Analysis

            More easily interpreted than an eigenvalue, though, is a direct expression of the proportion of between-group separation that is provided by each discriminant function.  This proportion is computed by dividing the eigenvalue for a given discriminant function by the sum of the eigenvalues for all of the discriminant functions.

In SPSS the loadings are called the Cannonical Structure Matrix.

In SPSS the raw canonical coeficients are used to form a discriminant function that can be used to compute discriminant function scores for each person.  The means of these scores form the centroids in the plots.

Advantages of Discrimininant Analysis

Multiple dependent varialbles

Reduced error rates

Easier interpretation of Between-group Differences:  each discriminant function measures something unique and different.

Disadvantages of Discriminant Analysis

Interpretation of the discriminant functions:  mystical like identifying factors in a factor analysis

Assumptions:

each discriminant function formed is distributed normally in each group being compared.

each discriminant function is assumed to show approximately equal variances in each group.

patterns of correlations between avrialbes are assumed to be equivalent from one group to the next

the relationships between variables are assumed to be linear in all groups

no dependent variable may be perfectly correlated to a linear comination of other varialbes (Multicolinearity)

discriminant analysis is extremely senstitive to outliers.

Interpretation of discriminant functions:

begins wiht a series of univariate tests to determine whihc of the original dependent variables have contributed to the overall significance of the discriminant functions.

A discriminant function can be interpreted by determining which groups it best separates.

Correlations between a discriminant function and the original dependent varialbes can reveal what conceptual varialbe the discriminant function represents.

C)Factor Analysis

           Factor analysis attempts to identify underlying variables, or factors, that explain the pattern of correlations within a set of observed variables. Factor analysis is often used in data reduction to identify a small number of factors that explain most of the variance that is observed in a much larger number of manifest variables. Factor analysis can also be used to generate hypotheses regarding causal mechanisms or to screen variables for subsequent analysis (for example, to identify collinearity prior to performing a linear regression analysis).

The factor analysis procedure offers a high degree of flexibility:

• Seven methods of factor extraction are available.

• Five methods of rotation are available, including direct oblimin and promax for nonorthogonal rotations.

• Three methods of computing factor scores are available, and scores can be saved as variables for further analysis.

Example. What underlying attitudes lead people to respond to the questions on a political survey as they do? Examining the correlations among the survey items reveals that there is significant overlap among various subgroups of items--questions about taxes tend to correlate with each other, questions about military issues correlate with each other, and so on. With factor analysis, you can investigate the number of underlying factors and, in many cases, identify what the factors represent conceptually. Additionally, you can compute factor scores for each respondent, which can then be used in subsequent analyses. For example, you might build a logistic regression model to predict voting behavior based on factor scores.

Statistics. For each variable: number of valid cases, mean, and standard deviation. For each factor analysis: correlation matrix of variables, including significance levels, determinant, and inverse; reproduced correlation matrix, including anti-image; initial solution (communalities, eigenvalues, and percentage of variance explained); Kaiser-Meyer-Olkin measure of sampling adequacy and Bartlett's test of sphericity; unrotated solution, including factor loadings, communalities, and eigenvalues; and rotated solution, including rotated pattern matrix and transformation matrix. For oblique rotations: rotated pattern and structure matrices; factor score coefficient matrix and factor covariance matrix. Plots: scree plot of eigenvalues and loading plot of first two or three factors.