Description Format Details Source Examples
The Chwirut1
data frame has 214 rows and 2 columns giving
This data frame contains the following columns:
A numeric vector of ultrasonic response values
A numeric vector or metal distance values
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.
Chwirut, D., NIST (197?). Ultrasonic Reference Block Study.
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"))
|
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
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