# Chwirut1: Ultrasonic calibration study 1 In NISTnls: Nonlinear least squares examples from NIST

## Description

The `Chwirut1` data frame has 214 rows and 2 columns giving

## Format

This data frame contains the following columns:

y

A numeric vector of ultrasonic response values

x

A numeric vector or metal distance values

## Details

These data are the result of a NIST study involving ultrasonic calibration. The response variable is ultrasonic response, and the predictor variable is metal distance.

## Source

Chwirut, D., NIST (197?). Ultrasonic Reference Block Study.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14``` ```Try <- function(expr) if (!inherits(val <- try(expr), "try-error")) val plot(y ~ x, data = Chwirut1) Try(fm1 <- nls(y ~ exp(-b1*x)/(b2+b3*x), data = Chwirut1, trace = TRUE, start = c(b1 = 0.1, b2 = 0.01, b3 = 0.02))) Try(fm1a <- nls(y ~ exp(-b1*x)/(b2+b3*x), data = Chwirut1, trace = TRUE, start = c(b1 = 0.1, b2 = 0.01, b3 = 0.02), alg = "port")) Try(fm2 <- nls(y ~ exp(-b1*x)/(b2+b3*x), data = Chwirut1, trace = TRUE, start = c(b1 = 0.15, b2 = 0.008, b3 = 0.010))) Try(fm2a <- nls(y ~ exp(-b1*x)/(b2+b3*x), data = Chwirut1, trace = TRUE, start = c(b1 = 0.15, b2 = 0.008, b3 = 0.010), alg = "port")) Try(fm3 <- nls(y ~ exp(-b1*x)/(1+p3*x), data = Chwirut1, trace = TRUE, start = c(b1 = 0.1, p3 = 0.02/0.01), algorithm = "plinear")) Try(fm4 <- nls(y ~ exp(-b1*x)/(1+p3*x), data = Chwirut1, trace = TRUE, start = c(b1 = 0.15, p3 = 0.01/0.008), algorithm = "plinear")) ```

### Example output

```50068.65 :  0.10 0.01 0.02
4258.757 :  0.157558936 0.006560689 0.012122015
2416.907 :  0.188633917 0.006055854 0.010471023
2384.48 :  0.190182706 0.006129919 0.010532848
2384.477 :  0.190274347 0.006131376 0.010531006
2384.477 :  0.190277961 0.006131398 0.010530915
Nonlinear regression model
model: y ~ exp(-b1 * x)/(b2 + b3 * x)
data: Chwirut1
b1       b2       b3
0.190278 0.006131 0.010531
residual sum-of-squares: 2384

Number of iterations to convergence: 5
Achieved convergence tolerance: 7.253e-07
0:     25034.324: 0.100000 0.0100000 0.0200000
1:     8737.6270: -0.00932540 0.00859407 0.0163344
2:     4303.8923: 0.123635 0.00344250 0.0129733
3:     1506.1509: 0.123276 0.00479593 0.0127332
4:     1194.5816: 0.181822 0.00608072 0.0107060
5:     1192.2446: 0.189616 0.00612504 0.0105501
6:     1192.2386: 0.190250 0.00613121 0.0105316
7:     1192.2386: 0.190277 0.00613139 0.0105310
8:     1192.2386: 0.190278 0.00613140 0.0105309
Nonlinear regression model
model: y ~ exp(-b1 * x)/(b2 + b3 * x)
data: Chwirut1
b1       b2       b3
0.190278 0.006131 0.010531
residual sum-of-squares: 2384

Algorithm "port", convergence message: relative convergence (4)
4575.709 :  0.150 0.008 0.010
2431.842 :  0.16786093 0.00560620 0.01143976
2384.679 :  0.189567762 0.006141611 0.010523876
2384.477 :  0.190155384 0.006129649 0.010535289
2384.477 :  0.190275830 0.006131414 0.010530932
2384.477 :  0.190277917 0.006131397 0.010530918
Nonlinear regression model
model: y ~ exp(-b1 * x)/(b2 + b3 * x)
data: Chwirut1
b1       b2       b3
0.190278 0.006131 0.010531
residual sum-of-squares: 2384

Number of iterations to convergence: 5
Achieved convergence tolerance: 8.277e-07
0:     2287.8543: 0.150000 0.00800000 0.0100000
1:     1279.1851: 0.202001 0.00699164 0.00930359
2:     1192.7291: 0.184867 0.00606749 0.0106907
3:     1192.2399: 0.190045 0.00613038 0.0105360
4:     1192.2386: 0.190262 0.00613123 0.0105314
5:     1192.2386: 0.190278 0.00613140 0.0105309
6:     1192.2386: 0.190278 0.00613140 0.0105309
Nonlinear regression model
model: y ~ exp(-b1 * x)/(b2 + b3 * x)
data: Chwirut1
b1       b2       b3
0.190278 0.006131 0.010531
residual sum-of-squares: 2384

Algorithm "port", convergence message: relative convergence (4)
3144.225 :    0.100   2.000 163.305
2395.405 :    0.1703262   1.8778966 168.5821864
2384.695 :    0.1890125   1.7177557 162.9130044
2384.478 :    0.1901318   1.7188861 163.1455743
2384.477 :    0.1902745   1.7175465 163.0948220
2384.477 :    0.1902779   1.7175401 163.0949849
Nonlinear regression model
model: y ~ exp(-b1 * x)/(1 + p3 * x)
data: Chwirut1
b1       p3     .lin
0.1903   1.7175 163.0950
residual sum-of-squares: 2384

Number of iterations to convergence: 5
Achieved convergence tolerance: 4.167e-06
3769.524 :    0.1500   1.2500 131.6984
2434.583 :    0.166877   1.773483 162.479146
2384.697 :    0.1872659   1.7424999 163.9832256
2384.478 :    0.1901634   1.7179373 163.0989871
2384.477 :    0.1902689   1.7176164 163.0977463
2384.477 :    0.1902779   1.7175385 163.0949021
2384.477 :    0.1902782   1.7175373 163.0948815
Nonlinear regression model
model: y ~ exp(-b1 * x)/(1 + p3 * x)
data: Chwirut1
b1       p3     .lin
0.1903   1.7175 163.0949
residual sum-of-squares: 2384

Number of iterations to convergence: 6
Achieved convergence tolerance: 3.066e-07
```

NISTnls documentation built on May 29, 2017, 3:49 p.m.