Regression Model
logP = A-B/(C+TC)
where A, B, C are the variables to find based on logP = f(TC)
| Model Variable | Initial Guess | Value | 95% confidence |
|---|---|---|---|
| A | 8.752 | 5.7673466 | 0.152084 |
| B | 2035 | 677.09404 | 48.1591 |
| C | 273 | 153.88537 | 5.68709 |
| R² | R²adj | Rmsd | Variance |
|---|---|---|---|
| 0.999688 | 0.999599 | 0.00472281 | 0.000318642 |
Nonlinear Regression Fit
Nonlinear Regression logP Residuals
Data Table
| TC | logP | Calculated logP | Residual % | |
|---|---|---|---|---|
| 1 | -36.7 | 0 | -0.010627326 | Infinity% |
| 2 | -19.6 | 0.69897 | 0.72514420 | -3.745% |
| 3 | -11.5 | 1 | 1.0119843 | -1.198% |
| 4 | -2.6 | 1.30103 | 1.2917386 | 0.7142% |
| 5 | 7.6 | 1.60206 | 1.5744341 | 1.724% |
| 6 | 15.4 | 1.7781513 | 1.7676270 | 0.5919% |
| 7 | 26.1 | 2 | 2.0054074 | -0.2704% |
| 8 | 42.2 | 2.30103 | 2.3142893 | -0.5762% |
| 9 | 60.6 | 2.60206 | 2.6105158 | -0.3250% |
| 10 | 80.1 | 2.8808136 | 2.8736015 | 0.2504% |
Settings and Hints
| Name/Source | Value | Type | |
|---|---|---|---|
| 1 | Algorithm | LM | Setting |
| 2 | Sample size | 10 | Setting |
| 3 | Model vars | 3 | Setting |
| 4 | Indep vars | 1 | Setting |
| 5 | Iterations | 24 | Setting |
| 6 | Elapsed time | 0.152 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
| Severity | Description | |
|---|---|---|
| 1 | Info | -Infor- 2 Known vectors variables (TC, P) |
| 2 | Info | -Infor- 1 Explicit expressions (logP) |
| 3 | Info | -Infor- 3 Model Variables (, A, B, C) |
| 4 | Info | -Infor- Regression command: nlinfit logP = A-B/(C+TC) |
Source
# Example 29 - Nonlinear Regression
# Pressure Data
# Verified Solution: A=5.76735, B=677.094, C=153.885
# Ref.: Comput. Appl. Eng. Educ. 6: 173, 1998
[
TC P
-36.7 1
-19.6 5
-11.5 10
-2.6 20
7.6 40
15.4 60
26.1 100
42.2 200
60.6 400
80.1 760
]
logP=log(P)
# nlinfit =
nlinfit logP = A-B/(C+TC)
# Initial guess of the regression model variables
m(A)= 8.752
m(B)= 2035
m(C)=273
# Pressure Data
# Verified Solution: A=5.76735, B=677.094, C=153.885
# Ref.: Comput. Appl. Eng. Educ. 6: 173, 1998
[
TC P
-36.7 1
-19.6 5
-11.5 10
-2.6 20
7.6 40
15.4 60
26.1 100
42.2 200
60.6 400
80.1 760
]
logP=log(P)
# nlinfit
nlinfit logP = A-B/(C+TC)
# Initial guess of the regression model variables
m(A)= 8.752
m(B)= 2035
m(C)=273