Re: No linear-curve fitting

Prabin_1988 · Posted 08-22-2018 11:20 AM

Hi,

I would like to fit the data (see attached .csv file for the data) in following equation and want to get the parameters, i.e., a, b, c, d, e, and f.

Could you please help me out for finding correct code or resources for non-linear curve fitting. thank you very much in advance!

y = a + b*[1-exp(-x/c)] + d*[1-exp(-x/e)] + f*x

PeterClemmensen · Posted 08-22-2018 11:35 AM

For non linear regression in SAS, see PROC NLIN and PROC TRANSREG. PROC NLIN is probably the best choice here.

Provide sample data in the form of a data step to get a code answer.

The DATA to DATA Step Macro
Blog: SASnrd

Prabin_1988 · Posted 08-22-2018 11:49 AM

x	y
0.000544	1.77E-06
0.001568	5.41E-06
0.002592	0.00001251
0.003616	0.000021935
0.00464	0.000032702
0.005664	0.000045242
0.006688	0.000056652
0.007712	0.000068892
0.008736	0.000078402
0.00976	0.000084212
0.010784	0.000086692
0.011808	0.000085242
0.012832	0.000080972
0.013856	0.000075862
0.01488	0.000070702
0.015904	0.000065842
0.016928	0.000061162
0.017952	0.000056582
0.018976	0.000051312
0.02	0.000046122
0.021024	0.000041682
0.022048	0.000040732
0.023072	0.000043332
0.024096	0.000049972
0.02512	0.000059102
0.026144	0.000068202
0.027168	0.000075832
0.028192	0.000080132
0.029216	0.000081402
0.03024	0.000080242
0.031264	0.000078402
0.032288	0.000075612
0.033312	0.000074082
0.034336	0.000071932
0.03536	0.000069362
0.036384	0.000066432
0.037408	0.000062822
0.038432	0.000060242
0.039456	0.000059732
0.04048	0.000061132
0.042016	0.000065252
0.044064	0.000068292
0.046112	0.000068362
0.04816	0.000071012
0.050208	0.000077392
0.052256	0.000081422
0.054304	0.000076572
0.056352	0.000069772
0.0584	0.000069022
0.060448	0.000071172
0.062496	0.000070592
0.064544	0.000071202
0.066592	0.000075272
0.06864	0.000079322
0.070688	0.000077832
0.072736	0.000075482
0.074784	0.000078272
0.076832	0.000080132
0.07888	0.000077202
0.080928	0.000072302
0.082976	0.000073572
0.085024	0.000078672
0.087072	0.000079742
0.08912	0.000078102
0.091168	0.000078472
0.093216	0.000079952
0.095264	0.000079412
0.097312	0.000078062
0.09936	0.000079762
0.10141	0.000080032
0.10346	0.000076942
0.1055	0.000074652
0.10755	0.000078492
0.1096	0.000085122
0.11165	0.000084732
0.1137	0.000078792
0.11574	0.000076922
0.11779	0.000080562
0.11984	0.000084202
0.12189	0.000083262
0.12496	0.000082642
0.12906	0.000077202
0.13315	0.000082932
0.13725	0.000086932
0.14134	0.000081562
0.14544	0.000085862
0.14954	0.000081752
0.15363	0.000081392
0.15773	0.000087072
0.16182	0.000087272
0.16592	0.000082582
0.17002	0.000086862
0.17411	0.000084882
0.17821	0.000087592
0.1823	0.000087392
0.1864	0.000089822
0.1905	0.000086152
0.19459	0.000087862
0.19869	0.000085832
0.20278	0.000091062
0.20688	0.000088662
0.21098	0.000089182
0.21507	0.000087422
0.21917	0.000091372
0.22326	0.000087312
0.22736	0.000094712
0.23146	0.000088022
0.23555	0.000088682
0.23965	0.000089042
0.24374	0.000092282
0.24784	0.000090032
0.25194	0.000094222
0.25603	0.000090522
0.26013	0.000091502
0.26422	0.000087922
0.26832	0.000096702
0.27242	0.000091192
0.27651	0.000092922
0.28061	0.000090502
0.2847	0.000092792
0.29085	0.000094512
0.29904	0.000093502
0.30723	0.000094392
0.31542	0.000094582
0.32362	0.000093462
0.33181	0.000094742
0.34	0.000095712
0.34819	0.000095682
0.35638	0.000096302
0.36458	0.000096282
0.37277	0.000096722
0.38096	0.000096522
0.38915	0.000096972
0.39734	0.000096552
0.40554	0.000098702
0.41373	0.000097962
0.42192	0.000097612
0.43011	0.000098242
0.4383	0.000098482
0.4465	0.000099662
0.45469	0.000099382
0.46288	0.000098382
0.47107	0.000100032
0.47926	0.000099772
0.48746	0.000100682
0.49565	0.000100282
0.50384	0.000100412
0.51203	0.000101322
0.52022	0.000101802
0.52842	0.000100842
0.53661	0.000103092
0.5448	0.000102142
0.55299	0.000099552
0.56118	0.000102622
0.56938	0.000103752
0.57757	0.000102222
0.58576	0.000102702
0.59395	0.000102662
0.60214	0.000103722
0.61034	0.000103612
0.62262	0.000104152
0.63901	0.000104492
0.65539	0.000104882
0.67178	0.000105672
0.68816	0.000104752
0.70454	0.000106292
0.72093	0.000107302
0.73731	0.000106522
0.7537	0.000106302
0.77008	0.000108072
0.78646	0.000108382
0.80285	0.000108142
0.81923	0.000108642
0.83562	0.000108572
0.852	0.000110432
0.86838	0.000109772
0.88477	0.000108712
0.90115	0.000109762
0.91754	0.000109892
0.93392	0.000110412
0.9503	0.000110252
0.96669	0.000111092
0.98307	0.000112322
0.99946	0.000112052
1.0158	0.000112892
1.0322	0.000112802
1.0486	0.000112482
1.065	0.000112842
1.0814	0.000113412
1.0978	0.000114352
1.1141	0.000114152
1.1305	0.000113232
1.1469	0.000115172
1.1633	0.000115862
1.1797	0.000115372
1.1961	0.000114532
1.2124	0.000115262
1.2288	0.000116192
1.2452	0.000116232
1.2616	0.000116362
1.2862	0.000116162
1.3189	0.000116562
1.3517	0.000117522
1.3845	0.000117852
1.4172	0.000118772
1.45	0.000118512
1.4828	0.000119712
1.5156	0.000119062
1.5483	0.000120662
1.5811	0.000120522
1.6139	0.000121442
1.6466	0.000121732
1.6794	0.000121312
1.7122	0.000122972
1.7449	0.000122142
1.7777	0.000123552
1.8105	0.000123252
1.8432	0.000123882
1.876	0.000124512
1.9088	0.000124852
1.9415	0.000125722
1.9743	0.000125602
2.0071	0.000125792
2.0398	0.000125462
2.0726	0.000126252
2.1054	0.000125902
2.1381	0.000126922
2.1709	0.000127042
2.2037	0.000127962
2.2364	0.000127472
2.2692	0.000128242
2.302	0.000128652
2.3348	0.000129092
2.3675	0.000128582
2.4003	0.000129982
2.4331	0.000129642
2.4658	0.000130732
2.4986	0.000130092
2.5314	0.000130902
2.5641	0.000130442
2.6133	0.000131182
2.6788	0.000131442
2.7444	0.000132332
2.8099	0.000132922
2.8754	0.000133242
2.941	0.000134022
3.0065	0.000134222
3.072	0.000134972
3.1376	0.000135802
3.2031	0.000136732
3.2686	0.000136852
3.3342	0.000137082
3.3997	0.000137332
3.4652	0.000137432
3.5308	0.000138002
3.5963	0.000138832
3.6619	0.000139542
3.7274	0.000139722
3.7929	0.000140222
3.8585	0.000140082
3.924	0.000140672
3.9895	0.000140812
4.0551	0.000141492
4.1206	0.000141742
4.1861	0.000142162
4.2517	0.000142812
4.3172	0.000143412
4.3828	0.000143332
4.4483	0.000143962
4.5138	0.000144252
4.5794	0.000145062
4.6449	0.000145252
4.7104	0.000145522
4.776	0.000145562
4.8415	0.000145862
4.907	0.000146352
4.9726	0.000146852
5.0381	0.000147302
5.1036	0.000147442
5.1692	0.000147412
5.2675	0.000147772
5.3986	0.000148852
5.5296	0.000149202
5.6607	0.000149562
5.7918	0.000150212
5.9228	0.000150772
6.0539	0.000151702
6.185	0.000152362
6.3161	0.000152902
6.4471	0.000153962
6.5782	0.000154482
6.7093	0.000155302
6.8404	0.000155992
6.9714	0.000156382
7.1025	0.000156912
7.2336	0.000157812
7.3646	0.000157812
7.4957	0.000158322
7.6268	0.000158672
7.7579	0.000159542
7.8889	0.000160032
8.02	0.000160452
8.1511	0.000160762
8.2821	0.000161172
8.4132	0.000161612
8.5443	0.000162522
8.6754	0.000163232
8.8064	0.000163652
8.9375	0.000164692
9.0686	0.000164442
9.1996	0.000165192
9.3307	0.000165422
9.4618	0.000166042
9.5929	0.000166552
9.7239	0.000166922
9.855	0.000167672
9.9861	0.000168052
10.117	0.000168142
10.248	0.000168782
10.379	0.000169182
10.576	0.000169402
10.838	0.000170732
11.1	0.000171432
11.362	0.000172402
11.624	0.000172982
11.887	0.000174122
12.149	0.000175252
12.411	0.000176212
12.673	0.000176622
12.935	0.000177632
13.197	0.000178142
13.459	0.000179092
13.722	0.000180022
13.984	0.000180822
14.246	0.000181232
14.508	0.000182482
14.77	0.000183502
15.032	0.000183952
15.294	0.000184232
15.557	0.000184812
15.819	0.000185742
16.081	0.000186482
16.343	0.000187632
16.605	0.000187862
16.867	0.000188532
17.13	0.000189542
17.392	0.000189912
17.654	0.000190542
17.916	0.000191252
18.178	0.000192012
18.44	0.000192412
18.702	0.000193522
18.965	0.000194182
19.227	0.000194602
19.489	0.000195212
19.751	0.000195542
20.013	0.000196232
20.275	0.000197042
20.537	0.000197822
20.8	0.000198622
21.193	0.000199112
21.717	0.000200422
22.241	0.000201362
22.766	0.000202302
23.29	0.000203182
23.814	0.000204352
24.338	0.000205152
24.863	0.000206302
25.387	0.000207342
25.911	0.000208472
26.436	0.000209302
26.96	0.000210492
27.484	0.000211472
28.008	0.000212252
28.533	0.000213092
29.057	0.000214092
29.581	0.000214902
30.106	0.000215752
30.63	0.000216782
31.154	0.000217222
31.678	0.000218512
32.203	0.000219112
32.727	0.000219912
33.251	0.000221092
33.776	0.000221572
34.3	0.000222252
34.824	0.000222642
35.349	0.000223532
35.873	0.000224582
36.397	0.000224982
36.921	0.000225902
37.446	0.000226352
37.97	0.000227212
38.494	0.000228032
39.019	0.000228482
39.543	0.000229422
40.067	0.000229702
40.591	0.000230762
41.116	0.000231772
41.64	0.000232482
42.426	0.000233302
43.475	0.000234632
44.524	0.000235912
45.572	0.000237822
46.621	0.000239482
47.669	0.000240812
48.718	0.000242072
49.766	0.000243562
50.815	0.000245142
51.864	0.000246362
52.912	0.000247272
53.961	0.000248652
55.009	0.000250042
56.058	0.000251122
57.106	0.000252522
58.155	0.000253602
59.204	0.000254502
60.252	0.000255732
61.301	0.000256822
62.349	0.000258162
63.398	0.000258982
64.446	0.000260202
65.495	0.000261162
66.544	0.000262312
67.592	0.000263522
68.641	0.000264442
69.689	0.000265182
70.738	0.000266372
71.787	0.000267342
72.835	0.000268222
73.884	0.000269232
74.932	0.000270142
75.981	0.000271652
77.029	0.000272442
78.078	0.000273402
79.127	0.000274682
80.175	0.000275302
81.224	0.000276292
82.272	0.000277062
83.321	0.000277972
84.894	0.000279472
86.991	0.000281492
89.088	0.000282762
91.185	0.000284712
93.282	0.000286262
95.379	0.000287832
97.477	0.000290132
99.574	0.000291762
101.67	0.000293202
103.77	0.000294772
105.87	0.000296532
107.96	0.000298432
110.06	0.000299902
112.16	0.000301182
114.25	0.000302792
116.35	0.000303942
118.45	0.000305392
120.55	0.000306842
122.64	0.000308512
124.74	0.000310802
126.84	0.000312682
128.93	0.000314502
131.03	0.000316192
133.13	0.000317592
135.23	0.000318682
137.32	0.000319772
139.42	0.000321362
141.52	0.000323072
143.61	0.000324872
145.71	0.000326172
147.81	0.000327602
149.91	0.000328942
152	0.000330632
154.1	0.000331762
156.2	0.000333352
158.29	0.000334452
160.39	0.000335872
162.49	0.000337132
164.59	0.000338042
166.68	0.000339132
169.83	0.000340852
174.02	0.000343242
178.22	0.000346512
182.41	0.000349862
186.61	0.000352962
190.8	0.000355142
194.99	0.000357902
199.19	0.000359802
203.38	0.000362052
207.58	0.000364642
211.77	0.000366472
215.97	0.000368322
220.16	0.000370292
224.35	0.000372702
228.55	0.000374762
232.74	0.000376552
236.94	0.000378322
241.13	0.000380132
245.33	0.000382192
249.52	0.000384632
253.71	0.000386622
257.91	0.000388572
262.1	0.000390492
266.3	0.000392202
270.49	0.000394932
274.69	0.000397562
278.88	0.000399472
283.07	0.000400902
287.27	0.000403152
291.46	0.000404792
295.66	0.000406292
299.85	0.000408122
304.05	0.000410002
308.24	0.000411872
312.43	0.000413952
316.63	0.000415832
320.82	0.000417942
325.02	0.000419562
329.21	0.000421632
333.41	0.000424302
339.7	0.000426592
348.09	0.000429652
356.47	0.000433322
364.86	0.000436712
373.25	0.000439882
381.64	0.000443852
390.03	0.000447302
398.42	0.000450252
406.81	0.000452952
415.2	0.000455762
423.58	0.000457312
431.97	0.000460302
440.36	0.000463662
448.75	0.000466432
457.14	0.000470232
465.53	0.000473722
473.92	0.000477042
482.3	0.000479922
490.69	0.000482332
499.08	0.000485322
507.47	0.000486972
515.86	0.000489302
524.25	0.000492742
532.64	0.000495012
541.02	0.000497332
549.41	0.000500812
557.8	0.000503172
566.19	0.000505812
574.58	0.000508142
582.97	0.000510362
591.36	0.000513092
591.36	0.000513592

Thank you very much for quick response! please see above for data

ballardw · Posted 08-22-2018 11:43 AM

A csv is not a SAS data set. Choices need to be made to get a SAS data set and mine may not match yours. So a solution I develop that works for MY version of your data may not work for you.

Instructions here: https://communities.sas.com/t5/SAS-Communities-Library/How-to-create-a-data-step-version-of-your-dat... will show how to turn an existing SAS data set into data step code that can be pasted into a forum code box using the {i} icon or attached as text to show exactly what you have and that we can test code against.

Prabin_1988 · Posted 08-22-2018 11:51 AM

x	y
0.000544	1.77E-06
0.001568	5.41E-06
0.002592	0.00001251
0.003616	0.000021935
0.00464	0.000032702
0.005664	0.000045242
0.006688	0.000056652
0.007712	0.000068892
0.008736	0.000078402
0.00976	0.000084212
0.010784	0.000086692
0.011808	0.000085242
0.012832	0.000080972
0.013856	0.000075862
0.01488	0.000070702
0.015904	0.000065842
0.016928	0.000061162
0.017952	0.000056582
0.018976	0.000051312
0.02	0.000046122
0.021024	0.000041682
0.022048	0.000040732
0.023072	0.000043332
0.024096	0.000049972
0.02512	0.000059102
0.026144	0.000068202
0.027168	0.000075832
0.028192	0.000080132
0.029216	0.000081402
0.03024	0.000080242
0.031264	0.000078402
0.032288	0.000075612
0.033312	0.000074082
0.034336	0.000071932
0.03536	0.000069362
0.036384	0.000066432
0.037408	0.000062822
0.038432	0.000060242
0.039456	0.000059732
0.04048	0.000061132
0.042016	0.000065252
0.044064	0.000068292
0.046112	0.000068362
0.04816	0.000071012
0.050208	0.000077392
0.052256	0.000081422
0.054304	0.000076572
0.056352	0.000069772
0.0584	0.000069022
0.060448	0.000071172
0.062496	0.000070592
0.064544	0.000071202
0.066592	0.000075272
0.06864	0.000079322
0.070688	0.000077832
0.072736	0.000075482
0.074784	0.000078272
0.076832	0.000080132
0.07888	0.000077202
0.080928	0.000072302
0.082976	0.000073572
0.085024	0.000078672
0.087072	0.000079742
0.08912	0.000078102
0.091168	0.000078472
0.093216	0.000079952
0.095264	0.000079412
0.097312	0.000078062
0.09936	0.000079762
0.10141	0.000080032
0.10346	0.000076942
0.1055	0.000074652
0.10755	0.000078492
0.1096	0.000085122
0.11165	0.000084732
0.1137	0.000078792
0.11574	0.000076922
0.11779	0.000080562
0.11984	0.000084202
0.12189	0.000083262
0.12496	0.000082642
0.12906	0.000077202
0.13315	0.000082932
0.13725	0.000086932
0.14134	0.000081562
0.14544	0.000085862
0.14954	0.000081752
0.15363	0.000081392
0.15773	0.000087072
0.16182	0.000087272
0.16592	0.000082582
0.17002	0.000086862
0.17411	0.000084882
0.17821	0.000087592
0.1823	0.000087392
0.1864	0.000089822
0.1905	0.000086152
0.19459	0.000087862
0.19869	0.000085832
0.20278	0.000091062
0.20688	0.000088662
0.21098	0.000089182
0.21507	0.000087422
0.21917	0.000091372
0.22326	0.000087312
0.22736	0.000094712
0.23146	0.000088022
0.23555	0.000088682
0.23965	0.000089042
0.24374	0.000092282
0.24784	0.000090032
0.25194	0.000094222
0.25603	0.000090522
0.26013	0.000091502
0.26422	0.000087922
0.26832	0.000096702
0.27242	0.000091192
0.27651	0.000092922
0.28061	0.000090502
0.2847	0.000092792
0.29085	0.000094512
0.29904	0.000093502
0.30723	0.000094392
0.31542	0.000094582
0.32362	0.000093462
0.33181	0.000094742
0.34	0.000095712
0.34819	0.000095682
0.35638	0.000096302
0.36458	0.000096282
0.37277	0.000096722
0.38096	0.000096522
0.38915	0.000096972
0.39734	0.000096552
0.40554	0.000098702
0.41373	0.000097962
0.42192	0.000097612
0.43011	0.000098242
0.4383	0.000098482
0.4465	0.000099662
0.45469	0.000099382
0.46288	0.000098382
0.47107	0.000100032
0.47926	0.000099772
0.48746	0.000100682
0.49565	0.000100282
0.50384	0.000100412
0.51203	0.000101322
0.52022	0.000101802
0.52842	0.000100842
0.53661	0.000103092
0.5448	0.000102142
0.55299	0.000099552
0.56118	0.000102622
0.56938	0.000103752
0.57757	0.000102222
0.58576	0.000102702
0.59395	0.000102662
0.60214	0.000103722
0.61034	0.000103612
0.62262	0.000104152
0.63901	0.000104492
0.65539	0.000104882
0.67178	0.000105672
0.68816	0.000104752
0.70454	0.000106292
0.72093	0.000107302
0.73731	0.000106522
0.7537	0.000106302
0.77008	0.000108072
0.78646	0.000108382
0.80285	0.000108142
0.81923	0.000108642
0.83562	0.000108572
0.852	0.000110432
0.86838	0.000109772
0.88477	0.000108712
0.90115	0.000109762
0.91754	0.000109892
0.93392	0.000110412
0.9503	0.000110252
0.96669	0.000111092
0.98307	0.000112322
0.99946	0.000112052
1.0158	0.000112892
1.0322	0.000112802
1.0486	0.000112482
1.065	0.000112842
1.0814	0.000113412
1.0978	0.000114352
1.1141	0.000114152
1.1305	0.000113232
1.1469	0.000115172
1.1633	0.000115862
1.1797	0.000115372
1.1961	0.000114532
1.2124	0.000115262
1.2288	0.000116192
1.2452	0.000116232
1.2616	0.000116362
1.2862	0.000116162
1.3189	0.000116562
1.3517	0.000117522
1.3845	0.000117852
1.4172	0.000118772
1.45	0.000118512
1.4828	0.000119712
1.5156	0.000119062
1.5483	0.000120662
1.5811	0.000120522
1.6139	0.000121442
1.6466	0.000121732
1.6794	0.000121312
1.7122	0.000122972
1.7449	0.000122142
1.7777	0.000123552
1.8105	0.000123252
1.8432	0.000123882
1.876	0.000124512
1.9088	0.000124852
1.9415	0.000125722
1.9743	0.000125602
2.0071	0.000125792
2.0398	0.000125462
2.0726	0.000126252
2.1054	0.000125902
2.1381	0.000126922
2.1709	0.000127042
2.2037	0.000127962
2.2364	0.000127472
2.2692	0.000128242
2.302	0.000128652
2.3348	0.000129092
2.3675	0.000128582
2.4003	0.000129982
2.4331	0.000129642
2.4658	0.000130732
2.4986	0.000130092
2.5314	0.000130902
2.5641	0.000130442
2.6133	0.000131182
2.6788	0.000131442
2.7444	0.000132332
2.8099	0.000132922
2.8754	0.000133242
2.941	0.000134022
3.0065	0.000134222
3.072	0.000134972
3.1376	0.000135802
3.2031	0.000136732
3.2686	0.000136852
3.3342	0.000137082
3.3997	0.000137332
3.4652	0.000137432
3.5308	0.000138002
3.5963	0.000138832
3.6619	0.000139542
3.7274	0.000139722
3.7929	0.000140222
3.8585	0.000140082
3.924	0.000140672
3.9895	0.000140812
4.0551	0.000141492
4.1206	0.000141742
4.1861	0.000142162
4.2517	0.000142812
4.3172	0.000143412
4.3828	0.000143332
4.4483	0.000143962
4.5138	0.000144252
4.5794	0.000145062
4.6449	0.000145252
4.7104	0.000145522
4.776	0.000145562
4.8415	0.000145862
4.907	0.000146352
4.9726	0.000146852
5.0381	0.000147302
5.1036	0.000147442
5.1692	0.000147412
5.2675	0.000147772
5.3986	0.000148852
5.5296	0.000149202
5.6607	0.000149562
5.7918	0.000150212
5.9228	0.000150772
6.0539	0.000151702
6.185	0.000152362
6.3161	0.000152902
6.4471	0.000153962
6.5782	0.000154482
6.7093	0.000155302
6.8404	0.000155992
6.9714	0.000156382
7.1025	0.000156912
7.2336	0.000157812
7.3646	0.000157812
7.4957	0.000158322
7.6268	0.000158672
7.7579	0.000159542
7.8889	0.000160032
8.02	0.000160452
8.1511	0.000160762
8.2821	0.000161172
8.4132	0.000161612
8.5443	0.000162522
8.6754	0.000163232
8.8064	0.000163652
8.9375	0.000164692
9.0686	0.000164442
9.1996	0.000165192
9.3307	0.000165422
9.4618	0.000166042
9.5929	0.000166552
9.7239	0.000166922
9.855	0.000167672
9.9861	0.000168052
10.117	0.000168142
10.248	0.000168782
10.379	0.000169182
10.576	0.000169402
10.838	0.000170732
11.1	0.000171432
11.362	0.000172402
11.624	0.000172982
11.887	0.000174122
12.149	0.000175252
12.411	0.000176212
12.673	0.000176622
12.935	0.000177632
13.197	0.000178142
13.459	0.000179092
13.722	0.000180022
13.984	0.000180822
14.246	0.000181232
14.508	0.000182482
14.77	0.000183502
15.032	0.000183952
15.294	0.000184232
15.557	0.000184812
15.819	0.000185742
16.081	0.000186482
16.343	0.000187632
16.605	0.000187862
16.867	0.000188532
17.13	0.000189542
17.392	0.000189912
17.654	0.000190542
17.916	0.000191252
18.178	0.000192012
18.44	0.000192412
18.702	0.000193522
18.965	0.000194182
19.227	0.000194602
19.489	0.000195212
19.751	0.000195542
20.013	0.000196232
20.275	0.000197042
20.537	0.000197822
20.8	0.000198622
21.193	0.000199112
21.717	0.000200422
22.241	0.000201362
22.766	0.000202302
23.29	0.000203182
23.814	0.000204352
24.338	0.000205152
24.863	0.000206302
25.387	0.000207342
25.911	0.000208472
26.436	0.000209302
26.96	0.000210492
27.484	0.000211472
28.008	0.000212252
28.533	0.000213092
29.057	0.000214092
29.581	0.000214902
30.106	0.000215752
30.63	0.000216782
31.154	0.000217222
31.678	0.000218512
32.203	0.000219112
32.727	0.000219912
33.251	0.000221092
33.776	0.000221572
34.3	0.000222252
34.824	0.000222642
35.349	0.000223532
35.873	0.000224582
36.397	0.000224982
36.921	0.000225902
37.446	0.000226352
37.97	0.000227212
38.494	0.000228032
39.019	0.000228482
39.543	0.000229422
40.067	0.000229702
40.591	0.000230762
41.116	0.000231772
41.64	0.000232482
42.426	0.000233302
43.475	0.000234632
44.524	0.000235912
45.572	0.000237822
46.621	0.000239482
47.669	0.000240812
48.718	0.000242072
49.766	0.000243562
50.815	0.000245142
51.864	0.000246362
52.912	0.000247272
53.961	0.000248652
55.009	0.000250042
56.058	0.000251122
57.106	0.000252522
58.155	0.000253602
59.204	0.000254502
60.252	0.000255732
61.301	0.000256822
62.349	0.000258162
63.398	0.000258982
64.446	0.000260202
65.495	0.000261162
66.544	0.000262312
67.592	0.000263522
68.641	0.000264442
69.689	0.000265182
70.738	0.000266372
71.787	0.000267342
72.835	0.000268222
73.884	0.000269232
74.932	0.000270142
75.981	0.000271652
77.029	0.000272442
78.078	0.000273402
79.127	0.000274682
80.175	0.000275302
81.224	0.000276292
82.272	0.000277062
83.321	0.000277972
84.894	0.000279472
86.991	0.000281492
89.088	0.000282762
91.185	0.000284712
93.282	0.000286262
95.379	0.000287832
97.477	0.000290132
99.574	0.000291762
101.67	0.000293202
103.77	0.000294772
105.87	0.000296532
107.96	0.000298432
110.06	0.000299902
112.16	0.000301182
114.25	0.000302792
116.35	0.000303942
118.45	0.000305392
120.55	0.000306842
122.64	0.000308512
124.74	0.000310802
126.84	0.000312682
128.93	0.000314502
131.03	0.000316192
133.13	0.000317592
135.23	0.000318682
137.32	0.000319772
139.42	0.000321362
141.52	0.000323072
143.61	0.000324872
145.71	0.000326172
147.81	0.000327602
149.91	0.000328942
152	0.000330632
154.1	0.000331762
156.2	0.000333352
158.29	0.000334452
160.39	0.000335872
162.49	0.000337132
164.59	0.000338042
166.68	0.000339132
169.83	0.000340852
174.02	0.000343242
178.22	0.000346512
182.41	0.000349862
186.61	0.000352962
190.8	0.000355142
194.99	0.000357902
199.19	0.000359802
203.38	0.000362052
207.58	0.000364642
211.77	0.000366472
215.97	0.000368322
220.16	0.000370292
224.35	0.000372702
228.55	0.000374762
232.74	0.000376552
236.94	0.000378322
241.13	0.000380132
245.33	0.000382192
249.52	0.000384632
253.71	0.000386622
257.91	0.000388572
262.1	0.000390492
266.3	0.000392202
270.49	0.000394932
274.69	0.000397562
278.88	0.000399472
283.07	0.000400902
287.27	0.000403152
291.46	0.000404792
295.66	0.000406292
299.85	0.000408122
304.05	0.000410002
308.24	0.000411872
312.43	0.000413952
316.63	0.000415832
320.82	0.000417942
325.02	0.000419562
329.21	0.000421632
333.41	0.000424302
339.7	0.000426592
348.09	0.000429652
356.47	0.000433322
364.86	0.000436712
373.25	0.000439882
381.64	0.000443852
390.03	0.000447302
398.42	0.000450252
406.81	0.000452952
415.2	0.000455762
423.58	0.000457312
431.97	0.000460302
440.36	0.000463662
448.75	0.000466432
457.14	0.000470232
465.53	0.000473722
473.92	0.000477042
482.3	0.000479922
490.69	0.000482332
499.08	0.000485322
507.47	0.000486972
515.86	0.000489302
524.25	0.000492742
532.64	0.000495012
541.02	0.000497332
549.41	0.000500812
557.8	0.000503172
566.19	0.000505812
574.58	0.000508142
582.97	0.000510362
591.36	0.000513092
591.36	0.000513592

Thank you very much for quick response! Please see above for the data

Prabin_1988 · Posted 08-22-2018 11:53 AM

Thank you very much for quick response! please see above chat history for the data.

Ksharp · Posted 08-22-2018 11:43 AM

Calling @Rick_SAS

Rick_SAS · Posted 08-22-2018 04:42 PM

Did you mistype the third term in the model? The function form of b*[1-exp(-x/c)] is the same as for d*[1-exp(-x/e)], so it doesn't make sense to include the expression twice.

Here is the code to model the data using PROC NLIN. You can easily modify the code to include additional terms, if necessary:

/* least squares fit of parameters */
proc nlin data=Have /* sometimes the NOHALVE option is useful */
          outest=Want(where=(_TYPE_="FINAL"));
   parms a 0 b 1 c 1 f 1;
   bounds c > 0;
   model y = a + b*(1-exp(-x/c)) + f*x;
   output out=Out P=Pred;
run;

proc print data=Want;run;

title "Data and Fitted Curve";
proc sgplot data=Out;
   scatter x=x y=y;
   series x=x y=Pred;
run;

Prabin_1988 · Posted 08-28-2018 07:26 AM

Thank you very much for this, much appreciated!

PGStats · Posted 08-22-2018 05:02 PM

This is a bit hard to fit (expand the Taylor series, and you will see why) You need to proceed with pretty good starting values. Do it in stages:

/* Get starting values for a and f */
proc reg data=have;
model y = x;
run;

/* Get starting values for a, f, b and c */
proc nlin data=have;
parms a = 1.34e-4 f = 8.5e-7 b = 0 c = 1; 
model y = a + b*(1-exp(-x/c)) + f*x;
run;

/* Fit whole model */
proc nlin data=have plots=fitplot;
parms a = 8.8e-5 f = 5.3e-7 b = 1.5e-4 d = 0 c = 14.1 e = 1; 
model y = a + b*(1-exp(-x/c)) + d*(1-exp(-x/e)) + f*x;
run;

PG

Prabin_1988 · Posted 08-28-2018 07:28 AM

Thank you very much for this!

How to fit a non-linear curve