More with Forbes’s data (Data files: Forbes and Hooker) An alternative approach to the analysis of Forbes’s experiments comes from the Clausius–Clapeyron formula of classical thermodynamics, which...

More with Forbes’s data (Data files: Forbes and Hooker) An alternative approach to the analysis of Forbes’s experiments comes from the Clausius–Clapeyron formula of classical thermodynamics, which dates to Clausius (1850). According to this theory, we should find that

where bpKelvin is boiling point in kelvin, which equals 255.37 + (5/9) × bp. If we were to graph this mean function on a plot of pres versus bpKelvin, we would get a curve, not a straight line. However, we can estimate the parameters β₀
and β₁
using simple linear regression methods by defining u₁
to be the inverse of temperature in kelvin,

The mean function (2.22) can be rewritten as

for which simple linear regression is suitable. The notation we have used in (2.23) is a little different, as the left side of the equation says we are conditioning on bp, but the variable bp does not appear explicitly on the right side of the equation, although of course the regressor u₁
depends on bp.