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 XST Gas Mileage Units Units (y, mpg) X1 X2 Y 0 0 27.43 0 0 28.07 0 0 28.46 1 0 29.38 1 0 30 2 0 28.14 2 0 29.5 0 1 32.43 0 1 33.95 1 1 33.96 1 1 34.77 0 2 32.68 0 2 33.84 1 2 34.64 1 2 35.46 1 2 35.96 2 2 33.76 2 2 34.57 2 2 34.79 1 3 33.2 2 3 32.7 2 3 33.41 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.)

Units	Units	(y, mpg)
X1	X2	Y
0	0	27.43
0	0	28.07
0	0	28.46
1	0	29.38
1	0	30
2	0	28.14
2	0	29.5
0	1	32.43
0	1	33.95
1	1	33.96
1	1	34.77
0	2	32.68
0	2	33.84
1	2	34.64
1	2	35.46
1	2	35.96
2	2	33.76
2	2	34.57
2	2	34.79
1	3	33.2
2	3	32.7
2	3	33.41

Answer 1

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.9749
R Square	0.9504
Adjusted R Square	0.9388
Standard Error	0.6701
Observations	22
ANOVA
	df	SS	MS	F	Significance F
Regression	4	146.3280	36.5820	81.4697	0.0000
Residual	17	7.6334	0.4490
Total	21	153.9614
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	28.0953	0.3084	91.1065	0.0000	27.4446	28.7459
x1	2.8451	0.6266	4.5404	0.0003	1.5231	4.1672
x12	-1.2171	0.2992	-4.0674	0.0008	-1.8484	-0.5858
x2	6.0217	0.4388	13.7235	0.0000	5.0959	6.9475
x22	-1.5937	0.1603	-9.9412	0.0000	-1.9319	-1.2555

The point estimate or the regression equation is

y^=28.0953+2.8451 (x1) -1.2171 (x12)+ 6.0217 (x2) - 1.5937 (x22)

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