Problem 10    Due 2/10/99
This problem illustrates the uses of QR
factorization to do linear regression problems.
Much research has been done in France on
the fast neutron breeder reactor which uses
the Uranium - Plutonium fuel cycle to generate
more fuel than it consumes.  One idiosyncracy
of this process is that it requires fast neutrons -
neutrons which have not been thermalized by
interacting with light nuclei such as water.  As
a consequence, this reactor must be cooled by
liquid sodium.  In this problem we use the following
table of data to develop a correlation for the
viscosity of sodium as a function of temperature.

T (deg C)   viscosity (centipoise)
100         .705
200         .450
300         .345
400         .284
500         .234
600         .210
700         .186
800         .165
900         .150

It is usual to develop the correlation for the inverse
of the viscosity rather than viscosity itself, thus:
1/visc = a + b*t + c*t^2

a). Write a script which calculates the coefficients
in the correlation using the normal equations.
Plot the data and the correlation to show how well the
correlation does in describing the data.

b). Use the qr factorization command and the back
substitution command you wrote for the previous
assignment to get the coefficients as well.  Show that
the two answers are the same.