When gasoline is pumped into the tank of an automobile,

Chapter , Problem 55

(choose chapter or problem)

When gasoline is pumped into the tank of an automobile, hydrocarbon vapors in the tank are forced out and into the atmosphere, producing a significant amount of air pollution. For this reason, vapor-recovery devices are often installed on gasoline pumps. It is difficult to test a recovery device in actual operation, because all that can be measured is the amount of vapor actually recovered and, by means of a "sniffer," whether any vapor escaped into the atmosphere. To estimate the efficiency of the device, it is thus necessary to estimate the total amount of vapor in the tank by using its relation to the values of variables that can actually be measured. In this exercise, you will try to develop such a predictive relationship using data that were obtained in a laboratory experiment. The file gasvapor contains recordings of the following variables: initial tank temperature \(\left({ }^{\circ} \mathrm{F}\right)\), temperature of the dispensed gasoline \(\left({ }^{\circ} \mathrm{F}\right)\), initial vapor pressure in the tank (psi), vapor pressure of the dispensed gasoline ( psi), and emitted hydrocarbons (g). A prediction of emitted hydrocarbons is desired.

First, randomly select 40 observations and set them aside. You will develop a predictive relationship based on the remaining observations and then test its strength on the observations you have held out. (It is instructive to have each student in the class hold out the same 40 observations and then compare results.)

a. Look at the relationships among the variables by scatterplots. Comment on which relationships look strong. Based on this information, what variables would you conjecture will be important in the model? Do the plots suggest that transformations will be helpful? Do there appear to be any outliers?

b. Try fitting a few different models and select two that you think are the best.

c. Using these two models, predict the responses for the 40 observations you have held out and compare the predictions to the observed values by plotting predicted versus observed values, and by plotting prediction errors versus each of the independent variables. Summarize the strength of the prediction by the root mean square prediction error:

                                    \(\mathrm{RMSPE}=\sqrt{\frac{1}{40} \sum_{i=1}^{40}\left(Y_i-\hat{Y}_i\right)^2}\)

where \(Y_i\) is the i th observed value and \(\hat{Y}_i\) is the predicted value.