Example for Discriminant Analysis

A high school administrator wants to create a model to classify future students into one of three educational tracks. The administrator randomly selects 180 students and records an achievement test score, a motivation score, and the current track for each.

Open the sample data set, EducationPlacement.MTW.
Choose Stat > Multivariate > Discriminant Analysis.
In Groups, enter Track.
In Predictors, enter Test Score and Motivation.
Under Discriminant Function, ensure that Linear is selected.
Click OK.

Interpret the results

The Summary of Classification table shows the proportion of observations correctly placed into their true groups by the model. The school administrator uses the results to see how accurately the model classifies the students. Overall, 93.9% of students were placed into the correct educational track. Group 2 had the lowest proportion of correct placement, with only 53 of 60 students, or 88.3%, correctly placed into that educational track.

The Summary of Misclassified Observations table indicates into which group an observation should have been placed. The school administrator uses the results to see which individual students were misclassified. For example, student 4 should have been placed into group 2, but was incorrectly placed into group 1.

Linear Method for Response: Track

Predictors: Test Score, Motivation

Groups

Group	1	2	3
Count	60	60	60

Summary of Classification

	True Group
Put into Group	1	2	3
1	59	5	0
2	1	53	3
3	0	2	57
Total N	60	60	60
N correct	59	53	57
Proportion	0.983	0.883	0.950

Correct Classifications

N	Correct	Proportion
180	169	0.939

Squared Distance Between Groups

	1	2	3
1	0.0000	12.9853	48.0911
2	12.9853	0.0000	11.3197
3	48.0911	11.3197	0.0000

Linear Discriminant Function for Groups

	1	2	3
Constant	-9707.5	-9269.0	-8921.1
Test Score	17.4	17.0	16.7
Motivation	-3.2	-3.7	-4.3

Summary of Misclassified Observations

Observation	True Group	Pred Group	Group	Squared Distance	Probability
4**	1	2	1	3.524	0.438
			2	3.028	0.562
			3	25.579	0.000
65**	2	1	1	2.764	0.677
			2	4.244	0.323
			3	29.419	0.000
71**	2	1	1	3.357	0.592
			2	4.101	0.408
			3	27.097	0.000
78**	2	1	1	2.327	0.775
			2	4.801	0.225
			3	29.695	0.000
79**	2	1	1	1.528	0.891
			2	5.732	0.109
			3	32.524	0.000
100**	2	1	1	5.016	0.878
			2	8.962	0.122
			3	38.213	0.000
107**	2	3	1	39.0226	0.000
			2	7.3604	0.032
			3	0.5249	0.968
116**	2	3	1	31.898	0.000
			2	7.913	0.285
			3	6.070	0.715
123**	3	2	1	30.164	0.000
			2	5.662	0.823
			3	8.738	0.177
124**	3	2	1	26.328	0.000
			2	4.054	0.918
			3	8.887	0.082
125**	3	2	1	28.542	0.000
			2	3.059	0.521
			3	3.230	0.479