QUESTION $5$

$(11)$

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 $13$

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STA$4820/015/0/2024$

attributes. These attributes, developed through focus groups, a pretest, and used in previous studies, 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 $1$

$\backslash$table$[[$Factor$,$Initial Eigenvalues$],[,$Total,$\%$ of Variance,Cumulative $\%],[1,3,751,31,257,31,257],[2,2,492,20,768,52,025],[3,1,115,9,293,61,318],[4,0,851,7,088,68,407],[5,0,77,6,413,74,819],[6,0,605,5,043,79,862],[7,0,577,4,808,84,67],[8,0,497,4,144,88,814],[9,0,444,3,696,92,51]]$

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b$.$ Interpret the following factor matrix:

$(8)$

$\backslash$table$[[$VARIMAX$-$ROTATED LOADINGS$],[$Variable$,$Factor,Community$],[1,2,3,4],[x_9$ Complaint Resolution,$0,943,,,,0,918],[x^{28}$ Delivery Speed,$0,935,,,,0,884],[x^{40}$ Order & Billing,$0,876,,,,0,807],[x_{12}$ Salestorce Imagine,,$0,902,,,0,886],[x,E-$Commerce,,$0,89,,,0,841],[x_{10}$ Advertising,,$0,711,,,0,584],[x_B$ Technical Support,,,$0,958,,0,932],[x_{16}$ Warranty & Claims,,,$0,951,,0,916],[x_6$ Product Quality,,,,$0,889,0,804],[x_{13}$ Competitive Pricing,,,,$-0,72,0,699]]$