Multiple Discriminant Analysis in Excel with Unistat

Multiple Discriminant Analysis: Stepwise Statistics

Summary Table

Tolerance: 0.001
F-to-Enter: 3.8416 (5.0%)
F-to-Remove: 2.7056 (10.0%)

Variable	Entered at Step	F-to-Enter	Significance	Wilks' Lambda
Var3	1	16.9426	0.0000	0.5649
Var1	2	4.7660	0.0046	0.4631
Var5	3	4.2502	0.0085	0.3861

Step 0

Variable	Entered at Step	Tolerance	F-to-Enter/Remove	Wilks' Lambda
Var1		1.0000	6.4644	0.7729
Var2		1.0000	1.1458	0.9505
Var3		1.0000	16.9426	0.5649
Var4		1.0000	0.1583	0.9929
Var5		1.0000	8.5882	0.7192
Var6		1.0000	0.3047	0.9863
Var7		1.0000	1.5744	0.9332

Step 1

Variable	Entered at Step	Tolerance	F-to-Enter/Remove	Wilks' Lambda
Var1		0.8445	4.7660	0.4631
Var2		0.8974	1.8542	0.5204
Var3	1	-1.0000	16.9426	1.0000
Var4		0.9654	0.4390	0.5537
Var5		0.9656	3.6752	0.4830
Var6		0.9947	0.2616	0.5582
Var7		0.9233	3.2327	0.4916

Step 2

Variable	Entered at Step	Tolerance	F-to-Enter/Remove	Wilks' Lambda
Var1	2	-1.0000	4.7660	0.5649
Var2		0.6657	2.6896	0.4112
Var3	1	-1.0000	14.4963	0.7729
Var4		0.8601	1.3557	0.4354
Var5		0.8532	4.2502	0.3861
Var6		0.8707	0.0898	0.4611
Var7		0.8817	2.4184	0.4159

Step 3

Variable	Entered at Step	Tolerance	F-to-Enter/Remove	Wilks' Lambda
Var1	2	-1.0000	5.3514	0.4830
Var2		0.9691	2.7738	0.3411
Var3	1	-1.0000	11.5667	0.5955
Var4		0.9379	1.6458	0.3581
Var5	3	-1.0000	4.2502	0.4631
Var6		0.9992	0.0983	0.3843
Var7		0.9988	1.9661	0.3531

Linear Discriminant Analysis

Group Means

	Var1	Var2	Var3	Var4	Var5	Var6	Var7
1	92.8235	42.5294	34.7647	14.6471	25.0000	9.4118	9.4706
2	99.8889	43.2778	35.9444	14.3889	26.2222	9.7222	9.9444
3	98.8824	42.6471	40.1765	14.5294	29.4706	9.5882	9.2353
4	99.7778	44.7778	38.5000	14.7778	30.5000	9.7222	9.5000

Group Standard Deviations

	Var1	Var2	Var3	Var4	Var5	Var6	Var7
1	4.7728	2.8748	2.4375	2.0292	2.1213	1.0641	1.0676
2	5.8600	2.6303	1.8302	1.6852	2.7344	0.7519	0.6391
3	6.7443	6.6327	2.8556	2.0346	4.4458	1.3720	1.0914
4	4.3999	2.7982	2.6402	1.2154	4.8416	1.1785	1.0981

Within-Groups Covariance Matrix

	Var1	Var2	Var3	Var4	Var5	Var6	Var7
Var1	30.3807	14.0841	5.3566	3.9983	8.5968	2.1931	2.2541
Var2	14.0841	16.4673	3.2039	3.0382	5.8744	1.0167	0.8402
Var3	5.3566	3.2039	6.0754	0.8089	1.7017	0.1986	0.6761
Var4	3.9983	3.0382	0.8089	3.1137	2.4880	0.2880	0.2439
Var5	8.5968	5.8744	1.7017	2.4880	13.8462	0.5137	0.5430
Var6	2.1931	1.0167	0.1986	0.2880	0.5137	1.2342	0.9178
Var7	2.2541	0.8402	0.6761	0.2439	0.5430	0.9178	0.9809

Within-Groups Correlation Matrix

	Var1	Var2	Var3	Var4	Var5	Var6	Var7
Var1	1.0000	0.6297	0.3943	0.4111	0.4192	0.3582	0.4129
Var2	0.6297	1.0000	0.3203	0.4243	0.3890	0.2255	0.2091
Var3	0.3943	0.3203	1.0000	0.1860	0.1855	0.0725	0.2769
Var4	0.4111	0.4243	0.1860	1.0000	0.3789	0.1469	0.1395
Var5	0.4192	0.3890	0.1855	0.3789	1.0000	0.1243	0.1473
Var6	0.3582	0.2255	0.0725	0.1469	0.1243	1.0000	0.8342
Var7	0.4129	0.2091	0.2769	0.1395	0.1473	0.8342	1.0000

Total Covariance Matrix

	Var1	Var2	Var3	Var4	Var5	Var6	Var7
Var1	37.5986	14.9899	8.8754	3.7261	12.6333	2.4536	2.3594
Var2	14.9899	16.5716	3.5524	2.9787	6.9315	1.0561	0.8480
Var3	8.8754	3.5524	10.2865	0.8253	5.9631	0.2936	0.3184
Var4	3.7261	2.9787	0.8253	2.9998	2.5306	0.2727	0.2137
Var5	12.6333	6.9315	5.9631	2.5306	18.4143	0.6520	0.2472
Var6	2.4536	1.0561	0.2936	0.2727	0.6520	1.1969	0.8936
Var7	2.3594	0.8480	0.3184	0.2137	0.2472	0.8936	1.0054

Univariate Statistics

	Lambda	F-Statistic	Significance
Var1	0.7729	6.4644	0.0007
Var2	0.9505	1.1458	0.3372
Var3	0.5649	16.9426	0.0000
Var4	0.9929	0.1583	0.9239
Var5	0.7192	8.5882	0.0001
Var6	0.9863	0.3047	0.8219
Var7	0.9332	1.5744	0.2039

Linear Discriminant Functions

	1	2	3	4
Var1	2.4700	2.7236	2.4571	2.5292
Var3	3.5919	3.5815	4.4302	4.0700
Var5	-0.1694	-0.2374	0.0584	0.1322
Constant	-176.3697	-198.6425	-212.7547	-207.9029

Canonical Discriminant Analysis

Eigenvalues

	Eigenvalue	Percent	Cumulative	Correlation
1	0.9930	77.6%	77.6%	0.7059
2	0.2269	17.7%	95.4%	0.4300
3	0.0591	4.6%	100.0%	0.2363

Canonical Statistics

	Wilks' Lambda	Chi-Square	DoF	Significance
1	0.3861	62.3265	9	0.0000
2	0.7696	17.1552	4	0.0018
3	0.9442	3.7618	1	0.0524

Standardised Coefficients

	Function 1	Function 2	Function 3
Var1	-0.2772	1.1368	-0.1364
Var3	0.8791	-0.2564	-0.5884
Var5	0.5402	-0.1929	0.9407

Structure Matrix

	Function 1	Function 2	Function 3
Var1	0.2959	0.9549	0.0259
Var3	0.8700	0.1560	-0.4676
Var5	0.5871	0.2360	0.7743

Unstandardised Coefficients

	Function 1	Function 2	Function 3
Var1	-0.0503	0.2063	-0.0247
Var3	0.3567	-0.1040	-0.2387
Var5	0.1452	-0.0518	0.2528
Constant	-12.4335	-14.8654	4.3051

Canonical Discriminant Functions

	Function 1	Function 2	Function 3
1	-1.0728	-0.6329	0.0296
2	-0.8299	0.6382	-0.1178
3	1.2017	-0.1780	-0.2820
4	0.7082	0.1277	0.3562

Canonical Discriminant Scores

	Function 1	Function 2	Function 3
1	-2.0221	-1.8549	1.1219
2	-2.2015	-1.3909	0.0753
3	-0.4010	-0.6225	0.2112
4	-1.5819	-0.6707	1.4683
5	-1.0034	-0.0541	0.1476
6	-0.6857	-1.0857	-0.4730
7	-0.3451	-1.3956	0.0574
8	-0.4456	-0.9831	0.0079
9	-0.8309	-1.0339	-0.7258
10	-0.8412	-1.8067	-0.1353
11	0.5181	-0.3158	-0.5792
12	-0.8755	-1.3945	-0.9291
13	-0.1896	-0.6747	-0.2803
14	-0.5805	-0.1585	-0.8354
15	-2.1316	1.8551	-1.3142
16	-2.3295	-0.0505	1.1520
17	-2.2906	0.8771	1.5339
18	-2.5535	0.0529	-0.0979
19	-0.1896	-0.6747	-0.2803
20	0.5077	-1.0886	0.0113
21	-0.0947	-0.5202	-0.0523
22	0.6187	-0.7283	-0.5297
23	-0.2901	-0.2622	-0.3298
24	-1.7121	1.4937	0.2132
25	-1.0387	2.2647	-0.8795
26	-0.4363	1.6963	-0.8159
27	-1.0868	1.6470	1.4277
28	-2.1476	1.6492	-0.5452
29	-1.4949	0.8746	-0.4569
30	-1.1553	2.4713	-0.1599
31	-0.4684	1.2845	0.7222
32	-1.3887	-0.1048	-0.5860
33	-1.3269	1.5444	0.9468
34	-0.5691	-1.2923	-1.1925
35	-0.1117	1.1805	0.4835
36	0.0676	-2.2728	-0.3352
37	0.8930	-1.0379	0.7449
38	1.0874	0.6107	0.7892
39	-0.4446	-2.8898	0.2412
40	2.0122	0.3504	-0.1798
41	0.3833	0.5089	-1.4224
42	2.2900	0.2979	-1.4156
43	1.3046	-0.0084	0.1191
44	2.0682	-0.4228	-0.3336
45	2.8100	-0.4761	0.1613
46	3.1440	1.6876	0.6369
47	0.4300	0.0455	1.1128
48	1.7618	-0.5250	-0.0702
49	0.9514	0.3527	-2.1527
50	-0.1506	0.2529	0.1016
51	0.9835	0.7645	-3.6907
52	0.8370	-0.2647	0.8988
53	-0.6079	0.7694	0.2908
54	1.3994	0.1460	0.3471
55	1.3388	-0.4206	0.9129
56	2.2133	-0.4746	-0.0808
57	2.4855	0.0398	-1.1381
58	0.5306	-0.3670	1.1622
59	-0.0912	-0.2632	-2.5627
60	-2.2358	-0.9787	-0.7185
61	0.9319	-0.1103	1.1268
62	1.8842	1.6908	0.8969
63	-0.4284	0.3054	1.3374
64	0.5856	0.7665	0.7751
65	0.1294	-0.6236	1.1976
66	1.4120	0.0948	2.0885
67	1.2989	0.5585	0.2976
68	-0.8765	0.5121	-1.1624
69	1.3435	0.9191	0.5010
70	1.4337	-0.2662	1.1409

Classification by Case

	Actual Group	Misclassified	Estimated Group	Probability
1	1		1	0.3096
2	1		1	0.6040
3	1		1	0.9223
4	1		1	0.5067
5	1		1	0.9496
6	1		1	0.8947
7	1		1	0.7742
8	1		1	0.9153
9	1		1	0.8519
10	1		1	0.6919
11	1	*	3	0.9022
12	1		1	0.6735
13	1		1	0.8308
14	1	*	2	0.7502
15	1	*	2	0.2030
16	1		1	0.3649
17	1	*	2	0.1778
18	2	*	1	0.4438
19	2	*	1	0.8308
20	2	*	3	0.7063
21	2	*	1	0.8070
22	2	*	3	0.8722
23	2	*	1	0.8304
24	2		2	0.6549
25	2		2	0.3520
26	2		2	0.6233
27	2		2	0.3244
28	2		2	0.4008
29	2		2	0.8934
30	2		2	0.3250
31	2		2	0.7401
32	2	*	1	0.8596
33	2		2	0.5316
34	2	*	1	0.5355
35	2		2	0.7599
36	3	*	1	0.2485
37	3	*	4	0.6722
38	3	*	4	0.9045
39	3	*	1	0.1367
40	3		3	0.8142
41	3		3	0.4858
42	3		3	0.4409
43	3		3	0.9776
44	3		3	0.8463
45	3		3	0.4117
46	3		3	0.0440
47	3	*	4	0.8834
48	3		3	0.9235
49	3		3	0.2789
50	3	*	2	0.8830
51	3		3	0.0057
52	3	*	4	0.9265
53	4	*	2	0.9720
54	4		4	0.9236
55	4		4	0.7993
56	4	*	3	0.7646
57	4	*	3	0.4884
58	4		4	0.8192
59	4	*	3	0.0758
60	4	*	1	0.5658
61	4		4	0.8731
62	4		4	0.2489
63	4		4	0.5152
64	4		4	0.8968
65	4		4	0.6577
66	4		4	0.3211
67	4		4	0.9105
68	4	*	2	0.7749
69	4		4	0.7889
70	4		4	0.7298

Classification by Group

	1	2	3	4
1	13	3	1	0
	76.47%	17.65%	5.88%	0.00%
2	6	10	2	0
	33.33%	55.56%	11.11%	0.00%
3	2	1	10	4
	11.76%	5.88%	58.82%	23.53%
4	1	2	3	12
	5.56%	11.11%	16.67%	66.67%

Correctly Classified: 64.29%

Distance Between Centroids

Clusters	Distance
3 - 4	0.8628
1 - 2	1.3025
2 - 4	1.6885
1 - 4	1.9639
2 - 3	2.1956
1 - 3	2.3404