Question

5. Discuss when you would use discriminant analysis instead of multiple regression analysis. Explain the difference between metric and non-metric variables.

Answer 1

Multiple regression is an extension of simple linear regression. It is used when we want to predict the value of a variable based on the value of two or more other variables. The variable we want to predict is called the dependent variable. In many ways discriminant analysis matches multiple regression analysis. The main difference between these two is that regression analysis deals with a continuous dependent variable, while discriminant analysis must have a discrete dependent variable and they are divided into groups. You plot each independent variable versus the group variable.

Equation of multiple regression is: Discriminant analysis is: Suppose you have data for K groups, with Nk observations per group. Let N represent the total number of observations. Each observation consists of the measurements of p variables. The i th observation is represented by Xki. Let M represent the vector of means of these variables across all groups and Mk the vector of means of observations in the kth group. Define three sums of squares and cross products matrices, ST, SW, and SA, as follows,

A discriminant function is a weighted average of the values of the independent variables. The weights are selected so that the resulting weighted average separates the observations into the groups.

Metric data is what most people mean when they talk about numbers( cordinal ), the sorts of numbers we collect when we measure something while Non - metric data refers to all the structured data market researchers use that is not metric data i.e. non - metric data includes information that is ranked(ordinal data)