As part of a nuclear safeguards program, the contents of a

Chapter , Problem 39

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As part of a nuclear safeguards program, the contents of a tank are routinely measured. The determination of volume is made indirectly by measuring the difference in pressure at the top and at the bottom of the tank. The tank is cylindrical in shape, but its internal geometry is complicated by various pipes and agitator paddles. Without these complications, pressure and volume should have a linear relationship. To calibrate pressure with respect to volume, known quantities (x) of liquid are placed in the tank and pressure readings (y) are taken. The data in the file tankvolume are from Knafl et al. (1984). The units of volume are kiloliters and those of pressure are pascals.

a. Plot pressure versus volume. Does the relationship appear linear?

b. Calculate the linear regression of pressure on volume, and plot the residuals versus volume. What does the residual plot show?

c. Try fitting pressure as a quadratic function of volume. What do you think of the fit?