## Sunday, 4 September 2011

### Factor Analysis - Just Another Blog

Factor Analysis
Factor analysis is a method for finding out whether a number of variables of interest, are linearly related to a smaller number of unobservable factors.

Factor analysis can be explained in the context of a simple example. Students entering a certain MBA program must take three required courses in Finance, marketing and business policy. Let Y1, Y2, and Y3, respectively, represent a student's grades in these courses. The available data consist of the grades of five students (in a 10-point numerical scale above the passing mark). It has been suggested that these grades are functions of two underlying factors, F1 and F2, tentatively described as quantitative ability and verbal ability, respectively. It is assumed that each Y variable is
linearly related to the two factors, as follows:

Y1 = B10 +B11F1 +B12F2 + e1
Y2 = B20 +B21F1 +B22F2 + e2
Y3 = B30 +B31F1 +B32F2 + e3
The parameters Bij are referred to as loadings. For example, B12 is called the loading of variable Y1on factor F2.In this MBA program, Finance is highly quantitative, while marketing and policy have a strong qualitative orientation. Quantitative skills should help a student in Finance, but not in marketing or policy. Verbal skills should be helpful in marketing or policy but not in Finance.

Factor analysis is a collection of methods used to examine how underlying constructs influence the responses on a number of measured variables.

There are basically two types of factor analysis:
·         Exploratory and Confirmatory.

1) Exploratory factor analysis (EFA) attempts to discover the nature of the constructs influencing
a set of responses.

2) Confirmatory factor analysis (CFA) tests whether a specified set of constructs is influencing re-sponses in a predicted way.

Factor analyses are performed by examining the pattern of correlations between the observed measures. Measures that are highly correlated (either positively or negatively) are likely influenced by the same factors, while those that are relatively uncorrelated are likely influenced by different factors.

Today in class we did factor analysis on the data sheet which had information about various variables affecting car sales and found out correlation between these variables. Satisfactory co-relation between variables is more than 0.5 and variables with higher co-relation are clubbed together to form a cluster.

Dishant Sharma
Marketing 2 Group