Description Format Details Source Examples
The Chwirut2
data frame has nr rows and nc columns giving
This data frame contains the following columns:
A numeric vector of ultrasonic response values.
A numeric vector of 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 = Chwirut2)
Try(fm1 <- nls(y ~ exp(-b1*x)/(b2+b3*x), data = Chwirut2, trace = TRUE,
start = c(b1 = 0.1 , b2 = 0.01, b3 = 0.02)))
Try(fm1a <- nls(y ~ exp(-b1*x)/(b2+b3*x), data = Chwirut2, 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 = Chwirut2, trace = TRUE,
start = c(b1 = 0.15 , b2 = 0.008, b3 = 0.01)))
Try(fm2a <- nls(y ~ exp(-b1*x)/(b2+b3*x), data = Chwirut2, trace = TRUE,
start = c(b1 = 0.15 , b2 = 0.008, b3 = 0.01), alg = "port"))
Try(fm3 <- nls(y ~ exp(-b1*x)/(1+p3*x), data = Chwirut2, trace = TRUE,
start = c(b1 = 0.1, p3 = 2.), alg = "plinear"))
Try(fm4 <- nls(y ~ exp(-b1*x)/(1+p3*x), data = Chwirut2, trace = TRUE,
start = c(b1 = 0.15, p3 = 0.01/0.008), alg = "plinear"))
|
14794.79 : 0.10 0.01 0.02
1127.464 : 0.139981133 0.005210818 0.014326137
524.0564 : 0.166842519 0.005181954 0.011911595
513.0496 : 0.166542926 0.005165775 0.012147521
513.048 : 0.166574406 0.005165294 0.012150094
Nonlinear regression model
model: y ~ exp(-b1 * x)/(b2 + b3 * x)
data: Chwirut2
b1 b2 b3
0.166574 0.005165 0.012150
residual sum-of-squares: 513
Number of iterations to convergence: 4
Achieved convergence tolerance: 7.922e-06
0: 7397.3951: 0.100000 0.0100000 0.0200000
1: 1318.1367: -0.00677752 0.00677865 0.0132968
2: 296.40201: 0.0845867 0.00400387 0.0149317
3: 257.65300: 0.154787 0.00508727 0.0124167
4: 256.52629: 0.165797 0.00515591 0.0121755
5: 256.52402: 0.166540 0.00516483 0.0121513
6: 256.52401: 0.166575 0.00516531 0.0121501
7: 256.52401: 0.166577 0.00516533 0.0121500
Nonlinear regression model
model: y ~ exp(-b1 * x)/(b2 + b3 * x)
data: Chwirut2
b1 b2 b3
0.166577 0.005165 0.012150
residual sum-of-squares: 513
Algorithm "port", convergence message: relative convergence (4)
1486.959 : 0.150 0.008 0.010
534.4129 : 0.141831871 0.004586793 0.013138455
513.091 : 0.164508979 0.005143257 0.012210244
513.0481 : 0.166473992 0.005163946 0.012153654
513.048 : 0.166571991 0.005165264 0.012150177
513.048 : 0.166576454 0.005165326 0.012150015
Nonlinear regression model
model: y ~ exp(-b1 * x)/(b2 + b3 * x)
data: Chwirut2
b1 b2 b3
0.166576 0.005165 0.012150
residual sum-of-squares: 513
Number of iterations to convergence: 5
Achieved convergence tolerance: 7.256e-07
0: 743.47941: 0.150000 0.00800000 0.0100000
1: 329.49026: 0.204207 0.00693095 0.00924971
2: 257.91707: 0.158797 0.00517442 0.0122070
3: 256.52510: 0.166019 0.00515822 0.0121690
4: 256.52402: 0.166551 0.00516497 0.0121509
5: 256.52401: 0.166575 0.00516531 0.0121500
6: 256.52401: 0.166577 0.00516533 0.0121500
Nonlinear regression model
model: y ~ exp(-b1 * x)/(b2 + b3 * x)
data: Chwirut2
b1 b2 b3
0.166577 0.005165 0.012150
residual sum-of-squares: 513
Algorithm "port", convergence message: relative convergence (4)
852.0762 : 0.1000 2.0000 165.1199
518.4111 : 0.1482451 2.4711552 196.6031152
513.0639 : 0.1652067 2.3665484 194.1067356
513.0481 : 0.166510 2.353067 193.630750
513.048 : 0.1665736 2.3522640 193.6000916
513.048 : 0.1665765 2.3522251 193.5985809
Nonlinear regression model
model: y ~ exp(-b1 * x)/(1 + p3 * x)
data: Chwirut2
b1 p3 .lin
0.1666 2.3522 193.5986
residual sum-of-squares: 513
Number of iterations to convergence: 5
Achieved convergence tolerance: 1.012e-06
1098.89 : 0.1500 1.2500 133.8166
574.2242 : 0.1424199 2.1089886 177.3429804
513.3576 : 0.162387 2.374994 194.076385
513.0484 : 0.1663405 2.3552654 193.7154889
513.048 : 0.1665658 2.3523655 193.6040115
513.048 : 0.1665762 2.3522300 193.5987704
Nonlinear regression model
model: y ~ exp(-b1 * x)/(1 + p3 * x)
data: Chwirut2
b1 p3 .lin
0.1666 2.3522 193.5988
residual sum-of-squares: 513
Number of iterations to convergence: 5
Achieved convergence tolerance: 3.705e-06
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