## Wednesday, 31 August 2011

### Discriminant Analysis

We use linear discriminant analysis when we classify objects into two or more groups based on knowledge of some variables or characteristics related to them. Discriminant analysis is somewhat similar to regression analysis. There is a dependant variable and some independent variables used to predict the independent variable in both the techniques. But in discriminant analysis, the dependant variable is categorical not metric.

Applications

1. Selecting MBA students based on some known scores in selection tests.

2. Purchase pattern of products in two categories – national brands and private labels. The independent variables taken for this could be annual income and household size.

3. Dividing a group of people into buyers and non – buyers

4. Selecting a potential candidate for the job or not.

5. It is used by credit rating agencies to rate individuals as high lending risk or low lending risk.

CALCULATION

Discriminant or discriminant function analysis is a parametric technique to determine which weightings of quantitative variables or predictors best discriminate between 2 or more than 2 groups of cases and do so better than chance (Cramer, 2003). The analysis creates a discriminant function which is a linear combination of the weightings and scores on these variables. The maximum number of functions is either the number of predictors or the number of groups minus one, whichever of these two values is the smaller.

Zjk = a + W1X1k + W2X2k + ... + WnXnk

Where:

Zjk = Discriminant Z score of discriminant function j for object k.

a = Intercept.

Wi = Discriminant coefficient for the Independent variable i.

Xj = Independent variable i for object k.

Again, caution must be taken to be clear that sometimes the focus of the analysis is not to predict but to explain the relationship, as such, equations are not normally written when the measures used are not objective measurements.

Name : Varun Aggarwal

Marketing Group 6