The U.S. Department of Energy's Fuel Economy Guide provides fuel efficiency data for cars and trucks (U.S. Department of Energy website, February 22, 2008). A portion of the data for 311 compact, midsize, and large cars follows. The column labeled Class identifies the size of the car: Compact, Midsize, or Large. The column labeled Displacement shows the engine's displacement in liters. The column labeled Fuel Type shows whether the car uses premium (P) or regular (R) fuel, and the column labeled HwyMPG shows the fuel efficiency rating for highway driving in terms of miles per gallon. The complete data set is contained in the DATAfile namedFuelData.

Click on the datafile logo to reference the data.

(a)

Develop an estimated regression equation that can be used to predict the fuel efficiency for highway driving, given the engine's displacement.

Letxrepresent the engine's displacement.

If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)

= + x

Is there a relationship between HwyMPG and displacement at the 0.05 level of significance?

- Select your answer -YesNoItem 3

How much of the variation in the sample values of HwyMPG is is explained by this estimated regression equation?

If required, round your answer to one decimal places.

%

(b)

Create a scatter chart in Excel 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. Choose the correct chart below.

(i)
(ii)
(iii)
(iv)

- Select your answer -Chart (i)Chart (ii)Chart (iii)Chart (iv)Item 5

What does this chart suggest about the relationship between the class of automobile (compact, midsize, and large) and HwyMPG?

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(c)

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.

Letx₁represent engine's displacement.

Letx₂represent variable ClassMidsize.

Letx₃represent variable ClassLarge.

If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)

= + x₁+ x₂+ x₃

How much of the variation in the sample values of HwyMPG does this estimated regression equation explain?

If required, round your answer to one decimal places.

%

(d)

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

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(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.

Letx₁represents engine's displacement.

Letx₂represents variable ClassMidsize.

Letx₃represents variable ClassLarge.

Letx₄represents variable FuelPremium.

If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)

= + x₁+ x₂+ x₃+ x₄

How much of the variation in the sample values of HwyMPG does this estimated regression equation explain?

If required, round your answer to one 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. Explain

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Question 2 of 2

Problem 07-15 (Categorical Independent Variables)