Air pressure (psi) and temperature (°F) were measured for a compression process in a certain piston-cylinder device, resulting in the following data (from Introduction to Engineering Experimentation, Prentice-Hall, Inc., 1996, p. 153):

Pressure 20.0 40.4 60.8 80.2 100.4 Temperature 44.9 102.4 142.3 164.8 192.2 Pressure 120.3 141.1 161.4 181.9 201.4 Temperature 221.4 228.4 249.5 269.4 270.8 Pressure 220.8 241.8 261.1 280.4 300.1 Temperature 291.5 287.3 313.3 322.3 325.8 Pressure 320.6 341.1 360.8 Temperature 337.0 332.6 342.9

a. Would you fit the simple linear regression model to the data and use it as a basis for predicting temperature from pressure? Why or why not?

b. Find a suitable probabilistic model and use it as a basis for predicting the value of temperature that would result from a pressure of 200 in the most informative way possible.