titanium: titanium heat data
In DierckxSpline: R companion to "Curve and Surface Fitting with Splines"

Description Usage Format Details Source Examples

49 values expressing a thermal property of titanium.

1	data(titanium)

a data.frame with the following columns:

x Temperature (in unknown units. The primary source, de Boor and Rice (1968), does not say. However, standard practice with these kinds of experimens would be to record data like this in degrees Kelvin, and the numbers seem consistent with that practice.)
yphysical property
yhatpredictions from some method
residual100*(y-yhat)

Famous example used by de Boor and Rice (1968), Jupp (1978), Dierckx (1993) and perhaps others. (de Boor and Rice do not mention the source nor provide other information on the units or how the data were collected.)

de Boor, C., and Rice, J. R. (1986), Least-squares cubic spline approximation. II: variable knots. Report CSD TR 21, Purdue U., Lafayette, IN. (available from http:// citeseer.ist.psu.edu/cache/papers/cs/24666/ ftp:zSzzSzftp.cs.wisc.eduzSzApproxzSztr21.pdf/ deboor68least.pdf; accessed 2008.07.22)

Dierckx, Paul (1993), Curve and Surface Fitting with Splines, Springer.

Jupp, D. L. B. (1975), Approximation to data by splines with free knots, SIAM Journal on Numerical Analysis, 15: 328-343.

data(titanium)
# Skip this test on CRAN,
# because it may exeed their 5 second limit
if(!CRAN()){

r <- curfit.free.knot(titanium$x2,
   titanium$y, g = 10, eps = 5e-4)
xyplot(r, show.knots = TRUE)
}