Multidimensional Scaling in Excel with UNISTAT
The UNISTAT statistics add-in extends Excel with Multidimensional Scaling capabilities.
For further information visit UNISTAT User's Guide section 8.3. Multidimensional Scaling.
Here we provide a sample output from the UNISTAT Excel statistics add-in for data analysis.
Multidimensional Scaling
Initial Coordinates
Dimension 1 | Dimension 2 | |
---|---|---|
Birmingham | -0.2697 | 0.1254 |
Cardiff | -0.6086 | 0.4951 |
Edinburgh | 1.0632 | -0.0496 |
Glasgow | 1.0835 | 0.1760 |
Leeds | 0.1573 | -0.1427 |
Liverpool | 0.1103 | 0.2274 |
London | -0.6829 | -0.1886 |
Manchester | 0.0846 | 0.0714 |
Newcastle | 0.5795 | -0.2002 |
Norwich | -0.5143 | -0.5670 |
Nottingham | -0.1579 | -0.1035 |
Southampton | -0.8451 | 0.1564 |
Multidimensional Scaling
Convergence History
Terminated at iteration 1: Stress < 0.0005
Iteration | Stress | Reduction | %Reduction |
---|---|---|---|
1 | 0.0003 | 0.0002 | 48.18% |
Final Coordinates
Dimension 1 | Dimension 2 | |
---|---|---|
Birmingham | -0.1263 | 0.0486 |
Cardiff | -0.2484 | 0.2156 |
Edinburgh | 0.4462 | -0.0230 |
Glasgow | 0.4691 | 0.0754 |
Leeds | 0.0641 | -0.0582 |
Liverpool | 0.0448 | 0.1018 |
London | -0.2972 | -0.0738 |
Manchester | 0.0372 | 0.0279 |
Newcastle | 0.2607 | -0.0888 |
Norwich | -0.2118 | -0.2477 |
Nottingham | -0.0632 | -0.0404 |
Southampton | -0.3750 | 0.0626 |
Estimated Coefficients
Observed | Distances | Disparities | Differences | |
---|---|---|---|---|
1 | 35.0000 | 0.0743 | 0.0743 | 0.0000 |
2 | 40.0000 | 0.0902 | 0.0902 | 0.0000 |
3 | 44.0000 | 0.1011 | 0.1011 | 0.0000 |
4 | 50.0000 | 0.1091 | 0.1091 | 0.0000 |
5 | 63.0000 | 0.1215 | 0.1215 | 0.0000 |
6 | 70.0000 | 0.1286 | 0.1286 | 0.0000 |
7 | 75.0000 | 0.1612 | 0.1591 | 0.0020 |
8 | 77.0000 | 0.1571 | 0.1591 | -0.0020 |
9 | 80.0000 | 0.1648 | 0.1648 | 0.0000 |
10 | 92.0000 | 0.1990 | 0.1855 | 0.0134 |
11 | 93.0000 | 0.1791 | 0.1855 | -0.0064 |
12 | 98.0000 | 0.1786 | 0.1855 | -0.0070 |
13 | 103.0000 | 0.2069 | 0.2041 | 0.0028 |
14 | 106.0000 | 0.2103 | 0.2041 | 0.0062 |
15 | 110.0000 | 0.2183 | 0.2041 | 0.0142 |
16 | 110.0000 | 0.1969 | 0.2041 | -0.0072 |
17 | 114.0000 | 0.1937 | 0.2041 | -0.0104 |
18 | 119.0000 | 0.1985 | 0.2041 | -0.0055 |
19 | 122.0000 | 0.2551 | 0.2457 | 0.0093 |
20 | 122.0000 | 0.2364 | 0.2457 | -0.0093 |
21 | 128.0000 | 0.2491 | 0.2491 | 0.0000 |
22 | 132.0000 | 0.2521 | 0.2521 | 0.0000 |
23 | 148.0000 | 0.2654 | 0.2654 | 0.0000 |
24 | 153.0000 | 0.3159 | 0.3020 | 0.0139 |
25 | 155.0000 | 0.2880 | 0.3020 | -0.0139 |
26 | 157.0000 | 0.3275 | 0.3098 | 0.0177 |
27 | 158.0000 | 0.3084 | 0.3098 | -0.0014 |
28 | 159.0000 | 0.2935 | 0.3098 | -0.0163 |
29 | 162.0000 | 0.3284 | 0.3214 | 0.0069 |
30 | 165.0000 | 0.3145 | 0.3214 | -0.0069 |
31 | 172.0000 | 0.3418 | 0.3382 | 0.0035 |
32 | 176.0000 | 0.3347 | 0.3382 | -0.0035 |
33 | 185.0000 | 0.3714 | 0.3583 | 0.0131 |
34 | 185.0000 | 0.3496 | 0.3583 | -0.0088 |
35 | 189.0000 | 0.3616 | 0.3583 | 0.0033 |
36 | 193.0000 | 0.3506 | 0.3583 | -0.0077 |
37 | 202.0000 | 0.3844 | 0.3841 | 0.0003 |
38 | 202.0000 | 0.3838 | 0.3841 | -0.0003 |
39 | 205.0000 | 0.4106 | 0.4106 | 0.0000 |
40 | 208.0000 | 0.4137 | 0.4129 | 0.0007 |
41 | 215.0000 | 0.4122 | 0.4129 | -0.0007 |
42 | 215.0000 | 0.4345 | 0.4244 | 0.0101 |
43 | 215.0000 | 0.4265 | 0.4244 | 0.0021 |
44 | 216.0000 | 0.4204 | 0.4244 | -0.0040 |
45 | 216.0000 | 0.4252 | 0.4244 | 0.0008 |
46 | 219.0000 | 0.4155 | 0.4244 | -0.0090 |
47 | 220.0000 | 0.4336 | 0.4276 | 0.0060 |
48 | 221.0000 | 0.4216 | 0.4276 | -0.0060 |
49 | 232.0000 | 0.4554 | 0.4554 | 0.0000 |
50 | 236.0000 | 0.4647 | 0.4647 | 0.0000 |
51 | 262.0000 | 0.5098 | 0.5041 | 0.0056 |
52 | 264.0000 | 0.4985 | 0.5041 | -0.0056 |
53 | 274.0000 | 0.5581 | 0.5515 | 0.0066 |
54 | 277.0000 | 0.5448 | 0.5515 | -0.0066 |
55 | 289.0000 | 0.5770 | 0.5770 | 0.0000 |
56 | 290.0000 | 0.5960 | 0.5946 | 0.0014 |
57 | 301.0000 | 0.5932 | 0.5946 | -0.0014 |
58 | 324.0000 | 0.6535 | 0.6535 | 0.0000 |
59 | 366.0000 | 0.6954 | 0.6954 | 0.0000 |
60 | 378.0000 | 0.7452 | 0.7369 | 0.0083 |
61 | 379.0000 | 0.7311 | 0.7369 | -0.0058 |
62 | 385.0000 | 0.7345 | 0.7369 | -0.0024 |
63 | 385.0000 | 0.7537 | 0.7537 | 0.0000 |
64 | 397.0000 | 0.7807 | 0.7807 | 0.0000 |
65 | 420.0000 | 0.8442 | 0.8350 | 0.0093 |
66 | 421.0000 | 0.8257 | 0.8350 | -0.0093 |