Hahn1_opt: Thermal expansion data

In NISTopt: Nonlinear least squares examples from NIST in form of functions for optim() and optimx()

Description

The Hahn1 data frame has 236 rows and 2 columns of data from a study on the thermal expansion of copper.

Format

This data frame contains the following columns:

y

A numeric vector of values of the coefficient of thermal expansion.

x

A numeric vector of temperatures (K).

Details

These data are the result of a NIST study involving the thermal expansion of copper. The response variable is the coefficient of thermal expansion, and the predictor variable is temperature in degrees Kelvin.

Source

Hahn, T., NIST (197?). Copper Thermal Expansion Study.

Examples

Try <- function(expr) if (!inherits(val <- try(expr), "try-error")) val
plot(y ~ x, data = Hahn1)
Try(fm1 <- nls(y ~ (b1+b2*x+b3*x**2+b4*x**3) / (1+b5*x+b6*x**2+b7*x**3),
           data = Hahn1, trace = TRUE,
           start = c(b1 = 10, b2 = -1, b3 = 0.05,
             b4 = -0.00001, b5 = -0.05, b6 = 0.001, b7 = -0.000001)))
Try(fm1a <- nls(y ~ (b1+b2*x+b3*x**2+b4*x**3) / (1+b5*x+b6*x**2+b7*x**3),
           data = Hahn1, trace = TRUE, alg = "port",
           start = c(b1 = 10, b2 = -1, b3 = 0.05,
             b4 = -0.00001, b5 = -0.05, b6 = 0.001, b7 = -0.000001)))
Try(fm2 <- nls(y ~ (b1+b2*x+b3*x**2+b4*x**3) / (1+b5*x+b6*x**2+b7*x**3),
           data = Hahn1, trace = TRUE,
           start = c(b1 = 1, b2 = -0.1, b3 = 0.005, b4 = -0.000001,
              b5 = -0.005, b6 = 0.0001, b7 = -0.0000001)))
Try(fm2a <- nls(y ~ (b1+b2*x+b3*x**2+b4*x**3) / (1+b5*x+b6*x**2+b7*x**3),
             data = Hahn1, trace = TRUE, alg = "port",
           start = c(b1 = 1, b2 = -0.1, b3 = 0.005, b4 = -0.000001,
              b5 = -0.005, b6 = 0.0001, b7 = -0.0000001)))
Try(fm3 <- nls(y ~ cbind(1, x, x^2, x^3)/(1+x*(b5+x*(b6+x*b7))),
           data = Hahn1, trace = TRUE, algorithm = "plinear",
           start = c(b5 = -0.05, b6 = 0.001, b7 = -0.000001)))
Try(fm4 <- nls(y ~ cbind(1, x, x^2, x^3)/(1+x*(b5+x*(b6+x*b7))),
           data = Hahn1, trace = TRUE, algorithm = "plinear",
           start = c(b5 = -0.005, b6 = 0.0001, b7 = -0.0000001)))

NISTopt documentation built on July 25, 2017, 3:01 p.m.