Orthogonal Polynomial multipliers (equally spaced X)
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levels = 3 |
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levels = 4 |
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X |
l |
q |
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X |
l |
q |
c |
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1 |
-1 |
1 |
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1 |
-3 |
1 |
-1 |
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2 |
0 |
-2 |
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2 |
-1 |
-1 |
3 |
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3 |
1 |
1 |
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3 |
1 |
-1 |
-3 |
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4 |
3 |
1 |
1 |
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levels = 5 |
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X |
l |
q |
c |
q |
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1 |
-2 |
2 |
-1 |
1 |
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2 |
-1 |
-1 |
2 |
-4 |
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3 |
0 |
-2 |
0 |
6 |
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4 |
1 |
-1 |
-2 |
-4 |
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5 |
2 |
2 |
1 |
1 |
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levels = 6 |
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1 |
-5 |
5 |
-5 |
1 |
-1 |
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2 |
-3 |
-1 |
7 |
-3 |
5 |
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3 |
-1 |
-4 |
4 |
2 |
-10 |
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4 |
1 |
-4 |
-4 |
2 |
10 |
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5 |
3 |
-1 |
-7 |
-3 |
-5 |
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6 |
5 |
5 |
5 |
1 |
1 |
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levels = 7 |
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1 |
-3 |
5 |
-1 |
3 |
-1 |
1 |
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2 |
-2 |
0 |
1 |
-7 |
4 |
-6 |
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3 |
-1 |
-3 |
1 |
1 |
-5 |
15 |
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4 |
0 |
-4 |
0 |
6 |
0 |
-20 |
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5 |
1 |
-3 |
-1 |
1 |
5 |
15 |
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6 |
2 |
0 |
-1 |
-7 |
-4 |
-6 |
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7 |
3 |
5 |
1 |
3 |
1 |
1 |
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levels = 8 |
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1 |
-7 |
7 |
-7 |
7 |
-7 |
1 |
-1 |
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2 |
-5 |
1 |
5 |
-13 |
23 |
-5 |
7 |
|
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3 |
-3 |
-3 |
7 |
-3 |
-17 |
9 |
-21 |
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4 |
-1 |
-5 |
3 |
9 |
-15 |
-5 |
35 |
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|
5 |
1 |
-5 |
-3 |
9 |
15 |
-5 |
-35 |
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|
6 |
3 |
-3 |
-7 |
-3 |
17 |
9 |
21 |
|
|
7 |
5 |
1 |
-5 |
-13 |
-23 |
-5 |
-7 |
|
|
8 |
7 |
7 |
7 |
7 |
7 |
1 |
1 |
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levels = 9 |
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|
1 |
-4 |
28 |
-14 |
14 |
-4 |
4 |
-1 |
1 |
|
2 |
-3 |
7 |
7 |
-21 |
11 |
-17 |
6 |
-8 |
|
3 |
-2 |
-8 |
13 |
-11 |
-4 |
22 |
-14 |
28 |
|
4 |
-1 |
-17 |
9 |
9 |
-9 |
1 |
14 |
-56 |
|
5 |
0 |
-20 |
0 |
18 |
0 |
-20 |
0 |
70 |
|
6 |
1 |
-17 |
-9 |
9 |
9 |
1 |
-14 |
-56 |
|
7 |
2 |
-8 |
-13 |
-11 |
4 |
22 |
14 |
28 |
|
8 |
3 |
7 |
-7 |
-21 |
-11 |
-17 |
-6 |
-8 |
|
9 |
4 |
28 |
14 |
14 |
4 |
4 |
1 |
1 |
For levels of X that are not equally spaced there is a SAS IML instruction that will produce the orthogonal polynomial multipliers. The following statements will do this if you have SAS IML available.
OPTIONS PS=60 LS=78;
where the X vector gives the levels of the quantitative variable.
The orpol function needs one parameter specifying the name of the quantitative variable vector and a second parameter specifying the number of orthogonal polynomials levels desired.