How the PTV data was created

Suppose a fixed quantity of gas is
examined at a varying pressures and temperatures.
Its volume is measured in most cases, and we have to
develop an empirical rule for other cases.

We take a known relationship (Boyle's Law)

pressure * volume = constant * temperature

so we can illustrate the effect of a priori
knowledge in the development of a rule.

Monotonicities present:

volume decreases as pressure increases if temperature is unchanged.
We say volume is monotonically decreasing with pressure (\).

Volume increases as temperature increases if pressure is unchanged.
We say volume is monotonically increasing with pressure (/).

In both cases it is understood: "all other inputs being equal" --
mathematically we are referring to a partial derivative.

Standard atmospheric pressure is 1013.2 millibars, so in our samples
we vary the pressure around this using the MS Excel formula

Pressure = 400+1226.4*RAND().

We let the temperature vary between very cold and very hot days (say
from -30 to +100 degrees Fahrenheit),so we generate temperatures this way

Temperature (Fahrenheit) = TempF = -30 +130*RAND().

There is a relationship between TempF and the temperature in
degrees Celsius = TempC = (TempF - 32) * 5/9,
however, let's assume that due to inaccuratcies of
both thermometers, the relationship is

TempC = (TempF - 32) * 5/9 -1 + 2 * rand().

Finally volume is going to be a function of TempC but with an
error from -3 to +3 degrees C.  Since Boyle's law uses absolute
temperature (add 273 to TempC), we get for the volume, after
errors are introduced:

Volume = 7*(TempC+270 + 6 * RAND())/Pressure