United Oil Company is attempting to develop a reasonably priced unleaded gasolin

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.

  

Using the model, y = 0 + 1x1 + 2x12 + 3x2 + 4x22 + , 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.)

RST
Units
(x1) XST
Units
(x2) Gas Mileage
(y, mpg) 0 0 27.51 0 0 28.47 0 0 28.35 1 0 29.83 1 0 30.40 2 0 28.25 2 0 29.42 0 1 32.22 0 1 33.89 1 1 33.55 1 1 34.21 0 2 32.94 0 2 33.06 1 2 34.76 1 2 35.63 1 2 35.71 2 2 33.25 2 2 34.52 2 2 34.25 1 3 33.75 2 3 32.35 2 3 33.51

Explanation / Answer

The point estimate is 29.9573.

Having one unit of RST (X1) and two unit of XST(X2)

Y = 29.9573 - 0.1475*1 + 1.8625*2

Y = 33.5348.

SUMMARY OUTPUT Regression Statistics Multiple R 0.7744349 R Square 0.599749414 Adjusted R Square 0.557617774 Standard Error 1.706867798 Observations 22 ANOVA df SS MS F Significance F Regression 2 82.94519406 41.4726 14.23513 0.000166784 Residual 19 55.35455594 2.913398 Total 21 138.29975 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 29.95735449 0.666618698 44.93927 9.3E-21 28.56210552 31.35260346 28.56210552 31.35260346 RST Units (x1) -0.147515355 0.481874104 -0.30613 0.762836 -1.156089444 0.861058734 -1.156089444 0.861058734 XST Units (x2) 1.862535829 0.362251919 5.141549 5.8E-05 1.10433385 2.620737808 1.10433385 2.620737808

Related Questions

Navigate

• Browse (All)
• Browse U
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.