Nonlinear Regression Preview

Nonlinear regression model:

r = \frac{ks \cdot KCH4 \cdot (PCH4 \cdot {PH2O}^{2} - \frac{PCO2 \cdot {PH2}^{4}}{0.00005051})}{1 + KCH4 \cdot PCH4}

Boundaries

m (ks) = 1

m (KCH4) = 1

Data-Table

	PCH4	PH2O	PCO2	PH2	r
1	0.06298	0.23818	0.0042	0.01669	0.00013717
2	0.03748	0.26315	0.00467	0.01686	0.00015584
3	0.05178	0.29557	0.00542	0.02079	0.00020028
4	0.04978	0.23239	0.00177	0.07865	5.7E-05
5	0.04809	0.29491	0.00655	0.02464	0.0002015
6	0.03849	0.24171	0.00184	0.06873	7.887E-05
7	0.03886	0.26048	0.00381	0.0148	0.00014983
8	0.0523	0.26286	0.05719	0.01635	0.00015988
9	0.05185	0.33529	0.00718	0.0282	0.00026194
10	0.06432	0.24787	0.00509	0.02055	0.00014426
11	0.09609	0.28457	0.00652	0.02627	0.00020195

Program validated. Ready to Solve.

# Example 30 - Nonlinear Regression
# Catalytic Reforming Reac.
# Verified Final Values: ks = 0.002784, KCH4 = 101.999
# Ref: Prob 3.10 in Problem Solving in Chemical...

[
PCH4 PH2O PCO2 PH2 r
0.06298 0.23818 0.0042 0.01669 0.00013717
0.03748 0.26315 0.00467 0.01686 0.00015584
0.05178 0.29557 0.00542 0.02079 0.00020028
0.04978 0.23239 0.00177 0.07865 5.7E-05
0.04809 0.29491 0.00655 0.02464 0.0002015
0.03849 0.24171 0.00184 0.06873 7.887E-05
0.03886 0.26048 0.00381 0.0148 0.00014983
0.0523 0.26286 0.05719 0.01635 0.00015988
0.05185 0.33529 0.00718 0.0282 0.00026194
0.06432 0.24787 0.00509 0.02055 0.00014426
0.09609 0.28457 0.00652 0.02627 0.00020195
]
nlinfit r = ks*KCH4*(PCH4*PH2O^2-PCO2*PH2^4/5.051e-5)/(1+KCH4*PCH4)
m(ks)=1
m(KCH4)=1

Regression Model

r = ks*KCH4*(PCH4*PH2O^2-PCO2*PH2^4/5.051e-5)/(1+KCH4*PCH4)

where ks, KCH4 are the variables to find based on r = f(PCH4, PH2O, PCO2, PH2)

Model Variable	Initial Guess	Value	95% confidence
ks	1	0.0027840696	0.00000384101
KCH4	1	101.99936	0.884321

R²	R²adj	Rmsd	Variance
0.996861	0.996512	9.33109e-7	1.17060e-11

Nonlinear Regression Fit

Nonlinear Regression r Residuals

Data Table

	PCH4	PH2O	PCO2	PH2	r	Calculated r	Residual %
1	0.06298	0.23818	0.0042	0.01669	0.00013717	0.00013641827	0.5480%
2	0.03748	0.26315	0.00467	0.01686	0.00015584	0.00015237736	2.222%
3	0.05178	0.29557	0.00542	0.02079	0.00020028	0.00020359457	-1.655%
4	0.04978	0.23239	0.00177	0.07865	0.000057	0.000062961732	-10.46%
5	0.04809	0.29491	0.00655	0.02464	0.0002015	0.00019883301	1.324%
6	0.03849	0.24171	0.00184	0.06873	0.00007887	0.000082774434	-4.950%
7	0.03886	0.26048	0.00381	0.0148	0.00014983	0.00015063555	-0.5376%
8	0.0523	0.26286	0.05719	0.01635	0.00015988	0.00015837140	0.9436%
9	0.05185	0.33529	0.00718	0.0282	0.00026194	0.00025915455	1.063%
10	0.06432	0.24787	0.00509	0.02055	0.00014426	0.00014775281	-2.421%
11	0.09609	0.28457	0.00652	0.02627	0.00020195	0.00020296468	-0.5024%

Settings and Hints

	Name/Source	Value	Type
1	Algorithm	LM	Setting
2	Sample size	11	Setting
3	Model vars	2	Setting
4	Indep vars	4	Setting
5	Iterations	71	Setting
6	Elapsed time	0.968 ms	Setting
7	#@NLR_SOLUTION_METHOD_INDEX	1	Setting
8	#@NLR_maxiter	128	Setting
9	#@NLR_miniter	1	Setting
10	Version	7.0.73	Setting
11	#@report_fix_digits = 8		Default (integer)
12	#@chart_size = 428,300		Default (array)
13	#@report_show_charts = true		Default (boolean)
14	#@report_show_source = true		Default (boolean)
15	#@report_show_header = false		Default (boolean)
16	#@report_show_settings = true		Default (boolean)
17	#@report_show_data_points = true		Default (boolean)

Messages