A synthetic yarn manufacturer wants information on the possible commercial acceptance of new yarn. He wants to know the characteristic of the fibers that differentiate between prospective buyers /non-buyers of the product. He is interested primarily in ascertaining the relative importance of the following yarn characteristics.

• Durability
• Lightness in weight
• Low investment in conversion facilities
• Rot resistance

The above-stated points affect a potential buyer’s overall evaluation of the yarn’s desirability. The ratings in the Table 1 pertain to the product being considered and represent the judgment of 18 potential buyers regarding the individual characteristic ratings and ‘buy’ versus ‘not buy’ response. Thus each respondent rates the product according to each of the four characters and then indicates whether he would be the prospective buyer of the product or not. The rating is done on an 11-point scale (where 0 represents very poor and 10 excellent).

The data obtained is given in Table 1. The SPSS output file is from Table 2 to Table 10. Answer the following questions.

1. What is meant by the statistical significance of the discriminant function?
2. Mention the percentage of customers that it is able to classify correctly or how good is the discriminant model.
3. Which of the independent variable are relatively better in discriminating between ‘buyer’ and ‘Non-buyer’ customers?
4. How to classify a new customer into one of those two groups – buyer/nonbuyer.

Table 1

Resp No.	buy_non	durab	light_Weight	low_investment	rot_resistance
1	1	9	8	7	6
2	1	7	6	6	5
3	1	10	7	8	2
4	1	8	4	5	4
5	1	9	9	3	3
6	1	8	6	7	2
7	1	7	5	6	2
8	1	5	4	2	3
9	1	4	3	3	4
10	2	4	4	4	6
11	2	3	6	6	3
12	2	6	3	3	4
13	2	2	4	5	2
14	2	1	2	2	1
15	2	4	6	5	6
16	2	6	7	5	6
17	2	7	5	6	2
18	2	3	2	3	3

Summary of Canonical Discriminant Functions

Table 2

Eigenvalues
Function		Eigenvalue	% of Variance	Cumulative %	Canonical Correlation
1		1.033a	100.0	100.0	.713
a. First 1 canonical discriminant functions were used in the analysis.

Wilks' Lambda
Test of Function(s)		Wilks' Lambda	Chi-square	df	Sig.
dimension0	1	.492	9.936	4	.042

Standardized Canonical Discriminant Function Coefficients
	Function
	1
Durability	1.219
Light Weight	-.104
Low Investment	-.338
Rot Resistance	-.268

Structure Matrix
	Function
	1
Durability	.911
Light Weight	.397
Low Investment	.258
Rot Resistance	-.068
Pooled within-groups correlations between discriminating variables and standardized canonical discriminant functions Variables ordered by the absolute size of correlation within the function.

Canonical Discriminant Function Coefficients
	Function
	1
Durability	.618
Light Weight	-.055
Low Investment	-.188
Rot Resistance	-.157
(Constant)	-1.800
Unstandardized coefficients

Functions at Group Centroids
Buyer / Non-Buyer		Function
		1
dimension0	Buyer	.958
	Non Buyer	-.958
Unstandardized canonical discriminant functions evaluated at group means

Prior Probabilities for Groups
Buyer / Non-Buyer		Prior	Cases Used in Analysis
			Unweighted	Weighted
dimension0	Buyer	.500	9	9.000
	Non Buyer	.500	9	9.000
Total	1.000	18	18.000

Table 9

Classification Resultsare
		Buyer / Non-Buyer		Predicted Group Membership		Total
				Buyer	2
Original	Count	dimension2	Buyer	8	1	9
			Non Buyer	2	7	9
	%	dimension2	Buyer	88.9	11.1	100.0
			Non Buyer	22.2	77.8	100.0

Answer rating: 100% (QA)

SOLUTION The statistical significance of the discriminant function refers to whether the discriminant function is able to significantly differentiate ... View the full answer