United Oil Company is attempting to develop a reasonably priced unleaded gasoline that will deliver higher gasoline mileages than can be achieved by its current unleaded gasolines. As part of its development process. United Oil wishes to study the effect of two independent variables-x1, amount of gasoline additive RST (0. 1. or 2 units), and x2, amount of gasoline additive XST (0, I, 2. or 3 units), on gasoline mileage, y. Mileage tests are carried out using equipment that simulates driving under prescribed conditions. The combinations of A, and AS used in the experiment, along with the corresponding values of y, are given in Table 15.3.
a. Discuss why the data plots given on the page margin indicate that the model
y = β0 + β1x1 + β2x21 + β3x2 + β4x22 + ε
might appropriately relate y to x1 and x2.
b. If we use Excel to analyze the data in Table 15.3 by using the model in part a, we obtain the output in Figure 15.6. Noting from Table 15.3 that the combination of one unit of gasoline additive RST and two units of gasoline additive XST seems to maximize gasoline mileage, assume that United Oil Company will use this combination to make its unleaded gasoline. The estimation and prediction results at the bottom of the output are for the combinational = 1 and. x2 = 2.
(1) Use the computer output to find and report a point estimate of and a 95 percent confidence interval for the mean mileage obtained by all gallons of the gasoline when it is made using one unit of RST and two units of XST.
(2) Use the computer output to find and report a point prediction of and a 95 percent prediction interval for the mileage that would be obtained by an individual gallon of the gasoline when it is made using one unit of RST and two units of XST.