Class Displacement Fuel Type Hwy MPG Compact 3.1 P 25 Compact 3.1 P 25 Compact 3 P 25 Compact 3 P 25 Compact 3 P 25 Compact 3 P 25 Compact 2.4 P 25 Compact 3.5 P 25 Compact 3 P 25 Compact 2.4 P 24 Compact 2.8 P 24 Compact 2.5 P 24 Compact 3 P 24 Compact 2.5 P 24 Compact 2.4 R 24 Compact 5.3 P 24 Compact 6 P 24 Compact 3.5 R 24 Compact 3.5 R 24 Compact 3.5 R 24 Compact 3.5 R 24 Compact 3.5 R 24 Compact 3.8 R 24 Compact 3.5 R 24 Compact 3.5 P 24 Compact 5.3 P 24 Compact 4.6 P 24 Compact 3.5 P 24 Compact 4.2 P 24 Compact 4.6 P 24 Compact 4.6 P 24 Compact 4.6 P 24 Compact 3.5 P 24 Compact 3.6 P 24 Compact 3.2 P 24 Compact 3.2 P 24 Compact 3.5 R 24 Compact 2.4 R 24 Compact 3.5 R 24 Compact 3.5 R 24 Compact 3.2 P 23 Compact 4.2 P 23 Compact 4.8 P 23 Compact 4.8 P 23 Compact 3.5 P 23 Compact 4.6 R 23 Compact 4.6 R 23 Compact 5.7 R 23 Compact 5.7 R 23 Compact 4.6 R 23 Compact 4.6 R 23 Compact 4.2 P 23 Compact 4.2 P 23 Compact 4.8 P 23 Compact 3.5 P 23 Compact 3 P 23 Compact 4.4 P 23 Compact 3 P 22 Compact 3.9 R 22 Compact 3.5 P 22 Compact 4.2 P 22 Compact 4.2 P 22 Compact 4.6 R 22 Compact 4.6 R 22 Compact 3.5 R 22 Compact 5.7 R 22 Compact 5.7 R 22 Compact 3.5 R 22 Compact 4.8 P 22 Compact 3 P 22 Compact 4.2 P 22 Compact 5 P 22 Compact 3.5 P 22 Compact 5.5 P 22 Compact 4.2 P 21 Compact 5.5 P 21 Compact 5.5 P 21 Compact 4.5 P 21 Compact 5.5 P 21 Compact 4.6 P 21 Compact 4.2 P 20 Compact 4.2 P 20 Compact 6 P 20 Compact 4.5 P 20 Compact 5.5 P 20 Compact 6 P 19 Compact 5.2 P 19 Compact 5.2 P 19 Compact 4.4 P 19 Compact 5.5 P 19 Compact 6.2 P 19 Compact 6.2 P 18 Compact 6.2 P 18 Compact 6.1 P 18 Compact 6.1 P 18 Compact 4.6 R 18 Compact 4.6 R 18 Compact 6.1 P 18 Compact 5.5 P 17 Compact 5.5 P 17 Compact 6.2 P 17 Compact 6 P 17 Compact 5.5 P 17 Compact 5 P 17 Compact 5 P 17 Compact 5.5 P 16 Compact 6 P 16 Compact 5.5 P 16 Compact 6 P 16 Compact 5.7 P 16 Compact 5.7 P 15 Midsize 1.8 R 37 Midsize 2 R 35 Midsize 1.6 R 35 Midsize 1.8 R 35 Midsize 1.6 R 34 Midsize 2.4 R 34 Midsize 2 R 33 Midsize 1.6 R 33 Midsize 2 R 33 Midsize 2 R 33 Midsize 1.8 R 33 Midsize 2.5 R 33 Midsize 2 R 33 Midsize 1.6 R 32 Midsize 1.6 R 32 Midsize 1.6 R 32 Midsize 2 R 32 Midsize 2.4 R 32 Midsize 2 R 32 Midsize 1.8 R 32 Midsize 2.5 R 32 Midsize 2.4 R 32 Midsize 2 P 31 Midsize 2.4 R 31 Midsize 2 R 31 Midsize 2 R 31 Midsize 2.4 R 31 Midsize 2.4 R 31 Midsize 2.4 R 31 Midsize 2.4 R 31 Midsize 2.4 R 31 Midsize 2.2 R 31 Midsize 2.4 R 31 Midsize 2.4 R 31 Midsize 2.5 R 31 Midsize 1.8 R 31 Midsize 2 R 31 Midsize 2.4 R 31 Midsize 2.4 R 31 Midsize 2 P 30 Midsize 2.4 R 30 Midsize 2.4 R 30 Midsize 2 R 30 Midsize 2.4 R 30 Midsize 2.4 R 30 Midsize 2.4 R 30 Midsize 2.4 R 30 Midsize 2 R 30 Midsize 2.5 R 30 Midsize 2.4 R 30 Midsize 2 P 29 Midsize 2 P 29 Midsize 2 P 29 Midsize 2 P 29 Midsize 2 P 29 Midsize 2.3 R 29 Midsize 2.3 R 29 Midsize 2 R 29 Midsize 2 R 29 Midsize 3.5 R 29 Midsize 2.5 R 29 Midsize 2.5 R 29 Midsize 2.5 R 29 Midsize 2.5 R 29 Midsize 3.5 R 29 Midsize 3.5 R 29 Midsize 3.5 R 29 Midsize 2.5 P 29 Midsize 2 P 29 Midsize 3.5 R 29 Midsize 1.8 R 29 Midsize 2.4 R 29 Midsize 2.3 R 29 Midsize 2.3 R 29 Midsize 2.3 R 29 Midsize 3.5 R 29 Midsize 2.4 P 28 Midsize 2.4 P 28 Midsize 2 P 28 Midsize 3 P 28 Midsize 3 P 28 Midsize 2.5 P 28 Midsize 2.5 P 28 Midsize 2.4 P 28 Midsize 2.4 P 28 Midsize 2.4 P 28 Midsize 2.4 P 28 Midsize 3.5 R 28 Midsize 2 R 28 Midsize 2 R 28 Midsize 2 R 28 Midsize 2 R 28 Midsize 3.9 R 28 Midsize 3.5 R 28 Midsize 3.3 R 28 Midsize 3.5 R 28 Midsize 3.5 R 28 Midsize 3 P 28 Midsize 2.3 P 28 Midsize 2 P 28 Midsize 3.8 R 28 Midsize 3.5 R 28 Midsize 2.3 R 28 Midsize 2.7 R 28 Midsize 2.3 R 28 Midsize 3.5 R 28 Midsize 2.3 R 28 Midsize 3.8 R 28 Midsize 3.5 R 28 Midsize 2 P 27 Midsize 3.1 P 27 Midsize 2.5 P 27 Midsize 2.5 P 27 Midsize 2.5 P 27 Midsize 2.5 P 27 Midsize 2.5 R 27 Midsize 2.5 R 27 Midsize 2.5 R 27 Midsize 2.5 R 27 Midsize 3.3 R 27 Midsize 3.5 P 27 Midsize 3.1 P 27 Midsize 3 P 27 Midsize 3.5 P 27 Midsize 3.5 P 27 Midsize 3.5 P 27 Midsize 2.7 R 27 Midsize 2.7 R 27 Midsize 2.7 R 27 Midsize 2 R 27 Midsize 2.7 R 27 Midsize 2.4 R 27 Midsize 3 R 26 Midsize 3 R 26 Midsize 3.6 R 26 Large 3 P 26 Large 3 P 26 Large 3 P 26 Large 2 P 26 Large 2.8 P 26 Large 2.5 P 26 Large 2.5 P 26 Large 2.5 P 26 Large 2.4 P 26 Large 2.4 P 26 Large 2.4 R 26 Large 3.5 R 26 Large 3.6 R 26 Large 3.3 R 26 Large 2.7 R 26 Large 2.7 R 26 Large 3.8 R 26 Large 3.3 R 26 Large 3.2 P 26 Large 3.5 P 26 Large 3 P 26 Large 3 P 26 Large 3 P 26 Large 2.3 P 26 Large 3.5 P 26 Large 2.3 P 26 Large 3.6 P 26 Large 3.6 R 26 Large 3.6 R 26 Large 3.6 R 26 Large 3.6 R 26 Large 3.6 R 26 Large 3.6 R 26 Large 3.5 R 26 Large 3.5 R 26 Large 3 P 25 Large 3.5 P 25 Large 2.5 P 25 Large 2.5 P 25 Large 2.5 P 25 Large 2.5 P 25 Large 3.5 R 25 Large 4.2 P 25 Large 4.2 P 25 Large 4.2 P 25 Large 3.8 R 25 Large 3.1 P 25 Large 3 P 25 Large 3 P 25 Large 3 P 25 Large 3 P 25 Large 3.5 P 25 Large 3.5 P 25 Large 3.8 P 25 Large 3.5 P 25 Large 5.3 P 25 Large 3.6 R 25 Large 3.6 R 25 Large 3.6 R 25 Large 3.6 R 25 Large 2.4 R 25 Large 3 R 25 Large 3 R 25 Large 3 R 25 Large 3 R 25

DATAFile:FuelData

You may need to use the appropriatetechnologyto answer this question.

The U.S. Department of Energy's Fuel Economy Guide provides fuel efficiency data for cars and trucks. A portion of the data for 311 compact, midsized, and large cars follows. The Class column identifies the size of the car: Compact, Midsize, or Large. The Displacement column shows the engine's displacement in liters. The Fuel Type column shows whether the car uses premium (P) or regular (R) fuel, and the Hwy MPG column shows the fuel efficiency rating for highway driving in terms of miles per gallon. The complete data set is contained in the file FuelData. (Letx₁represent the engine's displacement,x₂represent ClassMidsize,x₃represent ClassLarge,x₄represent FuelPremium, andyrepresent HwyMPG.)

(a)

Develop an estimated regression equation that can be used to predict the fuel efficiency for highway driving given the engine's displacement. (Round your numerical values to four decimal places.)

=35.39502.8821x

Test for significance using the 0.05 level of significance. (Use thettest.)

Find thep-value. (Round your answer to four decimal places.)

p-value =

State your conclusion.

We fail to rejectH₀. We cannot conclude that there is a relationship between HwyMPG and displacement.

We fail to rejectH₀. We can conclude that there is a relationship between HwyMPG and displacement.

We rejectH₀. We cannot conclude that there is a relationship between HwyMPG and displacement.

We rejectH₀. We can conclude that there is a relationship between HwyMPG and displacement.

How much of the variation in the sample values of HwyMPG (in %) does this estimated regression equation explain? (Round your answers to two decimal places.)

%

(b)

Make a scatter chart with HwyMPG on they-axis and displacement on thex-axis for which the points representing compact, midsize, and large automobiles are shown in different shapes and/or colors. What does this chart suggest about the relationship between the class of automobile (compact, midsize, and large) and HwyMPG?

This chart suggests that for each class of automobile (compact, midsize, and large) HwyMPG

---Select---

increases

decreases

as displacement increases. The chart also suggests that

---Select---

compact

midsize

large

automobiles generally have the highest HwyMPG while

---Select---

compact

midsize

large

automobiles generally have the lowest HwyMPG.

(c)

Now consider the addition of the dummy variables ClassMidsize and ClassLarge to the simple linear regression model in part (a). The value of ClassMidsize is 1 if the car is a midsize car and 0 otherwise; the value of ClassLarge is 1 if the car is a large car and 0 otherwise. Thus, for a compact car, the value of ClassMidsize and the value of ClassLarge are both 0. Develop the estimated regression equation that can be used to predict the fuel efficiency for highway driving, given the engine's displacement and the dummy variables ClassMidsize and ClassLarge. (Round your numerical values to four decimal places.)

=29.0359+1.6625x1

+4.4686x2

+1.8047x3

How much of the variation in the sample values of HwyMPG (in %) is explained by this estimated regression equation? (Round your answer to two decimal places.)

%

(d)

Use significance level of 0.05 to determine whether the dummy variables added to the model in part (c) are significant.

Test whether the regression parameter?₂is equal to zero.

Find thep-value. (Round your answer to four decimal places.)

p-value =

State your conclusion.

We rejectH₀. We can conclude that there is a difference in HwyMPG between midsized automobiles and compact automobiles.

We fail to rejectH₀. We cannot conclude that there is a difference in HwyMPG between midsized automobiles and compact automobiles.

We fail to rejectH₀. We can conclude that there is a difference in HwyMPG between midsized automobiles and compact automobiles.

We rejectH₀. We cannot conclude that there is a difference in HwyMPG between midsized automobiles and compact automobiles.

Test whether the regression parameter?₃is equal to zero.

Find thep-value. (Round your answer to four decimal places.)

p-value =

State your conclusion.

We fail to rejectH₀. We cannot conclude that there is a difference in HwyMPG between large automobiles and compact automobiles.

We fail to rejectH₀. We can conclude that there is a difference in HwyMPG between large automobiles and compact automobiles.

We rejectH₀. We cannot conclude that there is a difference in HwyMPG between large automobiles and compact automobiles.

We rejectH₀. We can conclude that there is a difference in HwyMPG between large automobiles and compact automobiles.

(e)

Consider the addition of the dummy variable FuelPremium, where the value of FuelPremium is 1 if the car uses premium fuel and 0 if the car uses regular fuel. Develop the estimated regression equation that can be used to predict the fuel efficiency for highway driving given the engine's displacement, the dummy variables ClassMidsize and ClassLarge, and the dummy variable FuelPremium. (Round your numerical values to four decimal places.)

=29.7624+1.6347x1

+3.9634x2

+1.6450x3

+1.1210x4

How much of the variation in the sample values of HwyMPG (in %) does this estimated regression equation explain? (Round your answer to two decimal places.)

%

(f)

For the estimated regression equation developed in part (e), test for the significance of the relationship between each of the independent variables and the dependent variable using the 0.05 level of significance for each test.

Test whether the regression parameter?₁is equal to zero.

Find thep-value. (Round your answer to four decimal places.)

p-value =

State your conclusion.

We fail to rejectH₀. We cannot conclude that there is a relationship between HwyMPG and displacement.

We fail to rejectH₀. We can conclude that there is a relationship between HwyMPG and displacement.

We rejectH₀. We can conclude that there is a relationship between HwyMPG and displacement.

We rejectH₀. We cannot conclude that there is a relationship between HwyMPG and displacement.

Test whether the regression parameter?₂is equal to zero.

Find thep-value. (Round your answer to four decimal places.)

p-value =

State your conclusion.

We rejectH₀. We can conclude that there is a difference in HwyMPG between midsized automobiles and compact automobiles.

We fail to rejectH₀. We cannot conclude that there is a difference in HwyMPG between midsized automobiles and compact automobiles.

We fail to rejectH₀. We can conclude that there is a difference in HwyMPG between midsized automobiles and compact automobiles.

We rejectH₀. We cannot conclude that there is a difference in HwyMPG between midsized automobiles and compact automobiles.

Test whether the regression parameter?₃is equal to zero.

Find thep-value. (Round your answer to four decimal places.)

p-value =

State your conclusion.

We fail to rejectH₀. We cannot conclude that there is a difference in HwyMPG between large automobiles and compact automobiles.

We fail to rejectH₀. We can conclude that there is a difference in HwyMPG between large automobiles and compact automobiles.

We rejectH₀. We can conclude that there is a difference in HwyMPG between large automobiles and compact automobiles.

We rejectH₀. We cannot conclude that there is a difference in HwyMPG between large automobiles and compact automobiles.

Test whether the regression parameter?₄is equal to zero.

Find thep-value. (Round your answer to four decimal places.)

p-value =

State your conclusion.

We fail to rejectH₀. We cannot conclude that there is a difference in HwyMPG between premium fuel and regular fuel.

We rejectH₀. We can conclude that there is a difference in HwyMPG between premium fuel and regular fuel.

We rejectH₀. We cannot conclude that there is a difference in HwyMPG between premium fuel and regular fuel.

We fail to rejectH₀. We can conclude that there is a difference in HwyMPG between premium fuel and regular fuel.

(g)

An automobile manufacturer is designing a new compact model with a displacement of3.1literswith the objective of creating a model that will achieve at least24estimatedhighway MPG. The manufacturer must now decide if the car can be designed to use premium fuel and still achieve the objective of24MPGon the highway. Use the model developed in part (e) to recommend a decision to this manufacturer. (Round your answers to one decimal place.)

Using the estimated multiple linear regression equation developed in part (e), a new model that is designed to use regular fuel would haveMPGon the highway and a new model that is designed to use premium fuel would haveMPGon the highway. Therefore, the new model should be designed to use

---Select---

regular

premium

fuel.