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	27.73
0	0	28.95
0	0	28.05
1	0	29.25
1	0	30.58
2	0	28.97
2	0	29.18
0	1	32.60
0	1	33.03
1	1	33.85
1	1	34.09
0	2	32.61
0	2	33.81
1	2	34.95
1	2	35.53
1	2	35.63
2	2	33.01
2	2	34.43
2	2	34.14
1	3	33.54
2	3	32.41
2	3	33.81

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

Answer 1

The point estimate can be found by using Excel<Megastats<Regression

Enter x1 and y1 in independent variable and y in dependent variable.

The output is as follows:

Regression Analysis
	R²	0.617
	Adjusted R²	0.577	n	22
	R	0.785	k	2
	Std. Error	1.635	Dep. Var.	Y
ANOVA table
Source	SS	df	MS	F	p-value
Regression	81.8452	2	40.9226	15.30	.0001
Residual	50.8060	19	2.6740
Total	132.6513	21
Regression output					confidence interval
variables	coefficients	std. error	t (df=19)	p-value	95% lower	95% upper
Intercept	29.9803
(x1)	-0.1371	0.4617	-0.297	.7697	-1.1033	0.8291
(x2)	1.8482	0.3470	5.326	3.86E-05	1.1218	2.5746

The Point estimate is 29.9803

Please do the comment in case of any doubt.

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