United Oil Company is attempting to develop a reasonably priced unleaded gasolin
ID: 3131141 • Letter: U
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 ofy, 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.)
Point estimate: ___________
RST Units (x1) XST Units (x2) Gas Mileage(y, mpg) 0 0 27.03 0 0 28.17 0 0 28.83 1 0 29.5 1 0 30.31 2 0 28 2 0 29.86 0 1 32.79 0 1 33.28 1 1 33.1 1 1 34.77 0 2 32.51 0 2 33.44 1 2 34.48 1 2 35.38 1 2 35.53 2 2 33.45 2 2 34.08 2 2 34.12 1 3 33.77 2 3 32.07 2 3 33.68Explanation / Answer
Regression Analysis
R²
0.927
Adjusted R²
0.910
n
22
R
0.963
k
4
Std. Error
0.773
Dep. Var.
Gas Mileage(y, mpg)
ANOVA table
Source
SS
df
MS
F
p-value
Regression
128.5656
4
32.1414
53.81
1.98E-09
Residual
10.1542
17
0.5973
Total
138.7199
21
Regression output
confidence interval
variables
coefficients
std. error
t (df=17)
p-value
95% lower
95% upper
Intercept
28.2321
0.3557
79.377
2.72E-23
27.4817
28.9825
RST Units (x1)
3.0749
0.7227
4.255
.0005
1.5501
4.5997
x1^2
-1.3804
0.3451
-4.000
.0009
-2.1085
-0.6523
XST Units (x2)
5.3397
0.5061
10.551
7.01E-09
4.2719
6.4074
x2^2
-1.3612
0.1849
-7.362
1.11E-06
-1.7513
-0.9711
Predicted values for: Gas Mileage(y, mpg)
95% Confidence Interval
95% Prediction Interval
RST Units (x1)
x1^2
XST Units (x2)
x2^2
Predicted
lower
upper
lower
upper
Leverage
1
1
2
4
35.16089
34.51573
35.80604
33.40731
36.91446
0.157
(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: 35.1609
Regression Analysis
R²
0.927
Adjusted R²
0.910
n
22
R
0.963
k
4
Std. Error
0.773
Dep. Var.
Gas Mileage(y, mpg)
ANOVA table
Source
SS
df
MS
F
p-value
Regression
128.5656
4
32.1414
53.81
1.98E-09
Residual
10.1542
17
0.5973
Total
138.7199
21
Regression output
confidence interval
variables
coefficients
std. error
t (df=17)
p-value
95% lower
95% upper
Intercept
28.2321
0.3557
79.377
2.72E-23
27.4817
28.9825
RST Units (x1)
3.0749
0.7227
4.255
.0005
1.5501
4.5997
x1^2
-1.3804
0.3451
-4.000
.0009
-2.1085
-0.6523
XST Units (x2)
5.3397
0.5061
10.551
7.01E-09
4.2719
6.4074
x2^2
-1.3612
0.1849
-7.362
1.11E-06
-1.7513
-0.9711
Predicted values for: Gas Mileage(y, mpg)
95% Confidence Interval
95% Prediction Interval
RST Units (x1)
x1^2
XST Units (x2)
x2^2
Predicted
lower
upper
lower
upper
Leverage
1
1
2
4
35.16089
34.51573
35.80604
33.40731
36.91446
0.157
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.