attributes. These attributes, developed through focus groups, a pretest, and used in previous studies, The primary database, consisting of $100$ observations on $18$ separate variables, is based on a market

segmentation study of HBAT customers. HBAT sells paper products to two market segments: the

newsprint industry and the magazine industry. Also, paper products are sold to these market

segments either directly to the customer or indirectly through a broker. Two types of information were

collected in the surveys. The first type of information was perceptions of HBAT's performance on $13$ Figure $1$

b$.$ Interpret the following factor matrix:

are the most influential in the selection of suppliers in the paper industry. Respondents included

purchasing managers of firms buying from HBAT, and they rated HBAT on each of the $13$ attributes

using a $0-10$ scale, with $10$ being "Excellent" and $0$ being "Poor". The second type of information

relates to purchase outcomes and business relationships $($e$.$g$.,$ satisfaction with HBAT and whether

the firm would consider a strategic alliance$/$partnership with HBAT$).$ A third type of information is

available from HBAT's data warehouse and includes information such as size of customer and length

of purchase relationship.

Exploratory factor analysis can identify the structure of a set of variables as well as provide a process

for data reduction. In our example, the perceptions of HBAT on $13$ attributes $($ X$6$ to X$18)$ are examined

for the following reasons:

Data Summarization with Interpretation $-$ Understand whether these perceptions can be

"grouped". Even the relatively small number of perceptions examined here presents a complex

picture of $78$ separate correlations. By grouping the perceptions and then engaging in the steps

of factor interpretation, HBAT will be able to see the big picture in terms of understanding its

customers and what dimensions the customers think about HBAT.

Data Reduction $-$ Reduce the $13$ variables to a smaller number of composite factors. If the $13$

variables can be represented in a smaller number of composite variables, then the other

multivariate techniques can be made more parsimonious. Of course, this approach assumes

that a certain degree of underlying order exists in the data being analysed.

a$.$ Using the Table $1$ and Figure $1$ below how many factors should the researcher keep and

why? $(3)$

Table $1$

Factor Initial Eigenvalues