Question

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, 1, 2, or 3 units), on gasoline mileage, y. Mileage tests are carried out using equipment that simulates driving under prescribed conditions. The combinations of x₁ and x₂ used in the experiment, along with the corresponding values of y, are given below.

RST Units (x1)	XST Units (x2)	Gas Mileage (y, mpg)
0	0	27.55
0	0	28.53
0	0	28.62
1	0	29.34
1	0	30.55
2	0	28.12
2	0	29.81
0	1	32.81
0	1	33.94
1	1	33.75
1	1	34.98
0	2	32.19
0	2	33.98
1	2	34.81
1	2	35.75
1	2	35.63
2	2	33.61
2	2	34.07
2	2	34.44
1	3	33.94
2	3	32.94
2	3	33.67

Using the model, y = β₀ + β₁x₁ + β₂x₁² + β₃x₂ + β₄x₂² + ε, calculate the point estimate.

(Moreover, consider the mean mileage obtained by all gallons of the gasoline when it is made with one unit of RST and two units of XST (a combination that the data on the page margin indicates would maximize mean mileage). Do not round intermediate calculations. Round your answer to 4 decimal places.)

Point estimate

Answer 1

Using Minitab software

The mean mileage obtained by all gallons of the gasoline when it is made with one unit of RST and two units of XST is

y = 28.4008 + 3.0810*1 - 1.4000 *1^1 + 5.4206*2 - 1.3706*2^2 =35.4406