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.)

=

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

We fail to rejectH₀. We cannot 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.)

=

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 parameter₂is equal to zero.Find thep-value. (Round your answer to four decimal places.)

p-value =

State your conclusion.

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.

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.

(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.)

=

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 parameter₁is equal to zero.Find thep-value. (Round your answer to four decimal places.)p-value =

State your conclusion.

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.

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.

Test whether the regression parameter₂is 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 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.

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

Test whether the regression parameter₃is 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 large automobiles and compact automobiles.

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

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.

Test whether the regression parameter₄is equal to zero.Find thep-value. (Round your answer to four decimal places.)p

-value =

State your conclusion.

We fail to 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 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.

(g)An automobile manufacturer is designing a new compact model with a displacement of2.7literswith the objective of creating a model that will achieve at least25estimatedhighway MPG. The manufacturer must now decide if the car can be designed to use premium fuel and still achieve the objective of25MPGon 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 have MPGon the highway and a new model that is designed to use premium fuel would have MPGon the highway. Therefore, the new model should be designed to use ---Select--- regular premium fuel.

Car	Class	Displacement	Fuel Type	Hwy MPG
1	Compact	3.1	P	25
2	Compact	3.1	P	25
3	Compact	3	P	25
4	Compact	3	P	25
5	Compact	3	P	25
6	Compact	3	P	25
7	Compact	2.4	P	25
8	Compact	3.5	P	25
9	Compact	3	P	25
10	Compact	2.4	P	24
11	Compact	2.8	P	24
12	Compact	2.5	P	24
13	Compact	3	P	24
14	Compact	2.5	P	24
15	Compact	2.4	R	24
16	Compact	5.3	P	24
17	Compact	6	P	24
18	Compact	3.5	R	24
19	Compact	3.5	R	24
20	Compact	3.5	R	24
21	Compact	3.5	R	24
22	Compact	3.5	R	24
23	Compact	3.8	R	24
24	Compact	3.5	R	24
25	Compact	3.5	P	24
26	Compact	5.3	P	24
27	Compact	4.6	P	24
28	Compact	3.5	P	24
29	Compact	4.2	P	24
30	Compact	4.6	P	24
31	Compact	4.6	P	24
32	Compact	4.6	P	24
33	Compact	3.5	P	24
34	Compact	3.6	P	24
35	Compact	3.2	P	24
36	Compact	3.2	P	24
37	Compact	3.5	R	24
38	Compact	2.4	R	24
39	Compact	3.5	R	24
40	Compact	3.5	R	24
41	Compact	3.2	P	23
42	Compact	4.2	P	23
43	Compact	4.8	P	23
44	Compact	4.8	P	23
45	Compact	3.5	P	23
46	Compact	4.6	R	23
47	Compact	4.6	R	23
48	Compact	5.7	R	23
49	Compact	5.7	R	23
50	Compact	4.6	R	23
51	Compact	4.6	R	23
52	Compact	4.2	P	23
53	Compact	4.2	P	23
54	Compact	4.8	P	23
55	Compact	3.5	P	23
56	Compact	3	P	23
57	Compact	4.4	P	23
58	Compact	3	P	22
59	Compact	3.9	R	22
60	Compact	3.5	P	22
61	Compact	4.2	P	22
62	Compact	4.2	P	22
63	Compact	4.6	R	22
64	Compact	4.6	R	22
65	Compact	3.5	R	22
66	Compact	5.7	R	22
67	Compact	5.7	R	22
68	Compact	3.5	R	22
69	Compact	4.8	P	22
70	Compact	3	P	22
71	Compact	4.2	P	22
72	Compact	5	P	22
73	Compact	3.5	P	22
74	Compact	5.5	P	22
75	Compact	4.2	P	21
76	Compact	5.5	P	21
77	Compact	5.5	P	21
78	Compact	4.5	P	21
79	Compact	5.5	P	21
80	Compact	4.6	P	21
81	Compact	4.2	P	20
82	Compact	4.2	P	20
83	Compact	6	P	20
84	Compact	4.5	P	20
85	Compact	5.5	P	20
86	Compact	6	P	19
87	Compact	5.2	P	19
88	Compact	5.2	P	19
89	Compact	4.4	P	19
90	Compact	5.5	P	19
91	Compact	6.2	P	19
92	Compact	6.2	P	18
93	Compact	6.2	P	18
94	Compact	6.1	P	18
95	Compact	6.1	P	18
96	Compact	4.6	R	18
97	Compact	4.6	R	18
98	Compact	6.1	P	18
99	Compact	5.5	P	17
100	Compact	5.5	P	17
101	Compact	6.2	P	17
102	Compact	6	P	17
103	Compact	5.5	P	17
104	Compact	5	P	17
105	Compact	5	P	17
106	Compact	5.5	P	16
107	Compact	6	P	16
108	Compact	5.5	P	16
109	Compact	6	P	16
110	Compact	5.7	P	16
111	Compact	5.7	P	15
112	Midsize	1.8	R	37
113	Midsize	2	R	35
114	Midsize	1.6	R	35
115	Midsize	1.8	R	35
116	Midsize	1.6	R	34
117	Midsize	2.4	R	34
118	Midsize	2	R	33
119	Midsize	1.6	R	33
120	Midsize	2	R	33
121	Midsize	2	R	33
122	Midsize	1.8	R	33
123	Midsize	2.5	R	33
124	Midsize	2	R	33
125	Midsize	1.6	R	32
126	Midsize	1.6	R	32
127	Midsize	1.6	R	32
128	Midsize	2	R	32
129	Midsize	2.4	R	32
130	Midsize	2	R	32
131	Midsize	1.8	R	32
132	Midsize	2.5	R	32
133	Midsize	2.4	R	32
134	Midsize	2	P	31
135	Midsize	2.4	R	31
136	Midsize	2	R	31
137	Midsize	2	R	31
138	Midsize	2.4	R	31
139	Midsize	2.4	R	31
140	Midsize	2.4	R	31
141	Midsize	2.4	R	31
142	Midsize	2.4	R	31
143	Midsize	2.2	R	31
144	Midsize	2.4	R	31
145	Midsize	2.4	R	31
146	Midsize	2.5	R	31
147	Midsize	1.8	R	31
148	Midsize	2	R	31
149	Midsize	2.4	R	31
150	Midsize	2.4	R	31
151	Midsize	2	P	30
152	Midsize	2.4	R	30
153	Midsize	2.4	R	30
154	Midsize	2	R	30
155	Midsize	2.4	R	30
156	Midsize	2.4	R	30
157	Midsize	2.4	R	30
158	Midsize	2.4	R	30
159	Midsize	2	R	30
160	Midsize	2.5	R	30
161	Midsize	2.4	R	30
162	Midsize	2	P	29
163	Midsize	2	P	29
164	Midsize	2	P	29
165	Midsize	2	P	29
166	Midsize	2	P	29
167	Midsize	2.3	R	29
168	Midsize	2.3	R	29
169	Midsize	2	R	29
170	Midsize	2	R	29
171	Midsize	3.5	R	29
172	Midsize	2.5	R	29
173	Midsize	2.5	R	29
174	Midsize	2.5	R	29
175	Midsize	2.5	R	29
176	Midsize	3.5	R	29
177	Midsize	3.5	R	29
178	Midsize	3.5	R	29
179	Midsize	2.5	P	29
180	Midsize	2	P	29
181	Midsize	3.5	R	29
182	Midsize	1.8	R	29
183	Midsize	2.4	R	29
184	Midsize	2.3	R	29
185	Midsize	2.3	R	29
186	Midsize	2.3	R	29
187	Midsize	3.5	R	29
188	Midsize	2.4	P	28
189	Midsize	2.4	P	28
190	Midsize	2	P	28
191	Midsize	3	P	28
192	Midsize	3	P	28
193	Midsize	2.5	P	28
194	Midsize	2.5	P	28
195	Midsize	2.4	P	28
196	Midsize	2.4	P	28
197	Midsize	2.4	P	28
198	Midsize	2.4	P	28
199	Midsize	3.5	R	28
200	Midsize	2	R	28
201	Midsize	2	R	28
202	Midsize	2	R	28
203	Midsize	2	R	28
204	Midsize	3.9	R	28
205	Midsize	3.5	R	28
206	Midsize	3.3	R	28
207	Midsize	3.5	R	28
208	Midsize	3.5	R	28
209	Midsize	3	P	28
210	Midsize	2.3	P	28
211	Midsize	2	P	28
212	Midsize	3.8	R	28
213	Midsize	3.5	R	28
214	Midsize	2.3	R	28
215	Midsize	2.7	R	28
216	Midsize	2.3	R	28
217	Midsize	3.5	R	28
218	Midsize	2.3	R	28
219	Midsize	3.8	R	28
220	Midsize	3.5	R	28
221	Midsize	2	P	27
222	Midsize	3.1	P	27
223	Midsize	2.5	P	27
224	Midsize	2.5	P	27
225	Midsize	2.5	P	27
226	Midsize	2.5	P	27
227	Midsize	2.5	R	27
228	Midsize	2.5	R	27
229	Midsize	2.5	R	27
230	Midsize	2.5	R	27
231	Midsize	3.3	R	27
232	Midsize	3.5	P	27
233	Midsize	3.1	P	27
234	Midsize	3	P	27
235	Midsize	3.5	P	27
236	Midsize	3.5	P	27
237	Midsize	3.5	P	27
238	Midsize	2.7	R	27
239	Midsize	2.7	R	27
240	Midsize	2.7	R	27
241	Midsize	2	R	27
242	Midsize	2.7	R	27
243	Midsize	2.4	R	27
244	Midsize	3	R	26
245	Midsize	3	R	26
246	Midsize	3.6	R	26
247	Large	3	P	26
248	Large	3	P	26
249	Large	3	P	26
250	Large	2	P	26
251	Large	2.8	P	26
252	Large	2.5	P	26
253	Large	2.5	P	26
254	Large	2.5	P	26
255	Large	2.4	P	26
256	Large	2.4	P	26
257	Large	2.4	R	26
258	Large	3.5	R	26
259	Large	3.6	R	26
260	Large	3.3	R	26
261	Large	2.7	R	26
262	Large	2.7	R	26
263	Large	3.8	R	26
264	Large	3.3	R	26
265	Large	3.2	P	26
266	Large	3.5	P	26
267	Large	3	P	26
268	Large	3	P	26
269	Large	3	P	26
270	Large	2.3	P	26
271	Large	3.5	P	26
272	Large	2.3	P	26
273	Large	3.6	P	26
274	Large	3.6	R	26
275	Large	3.6	R	26
276	Large	3.6	R	26
277	Large	3.6	R	26
278	Large	3.6	R	26
279	Large	3.6	R	26
280	Large	3.5	R	26
281	Large	3.5	R	26
282	Large	3	P	25
283	Large	3.5	P	25
284	Large	2.5	P	25
285	Large	2.5	P	25
286	Large	2.5	P	25
287	Large	2.5	P	25
288	Large	3.5	R	25
289	Large	4.2	P	25
290	Large	4.2	P	25
291	Large	4.2	P	25
292	Large	3.8	R	25
293	Large	3.1	P	25
294	Large	3	P	25
295	Large	3	P	25
296	Large	3	P	25
297	Large	3	P	25
298	Large	3.5	P	25
299	Large	3.5	P	25
300	Large	3.8	P	25
301	Large	3.5	P	25
302	Large	5.3	P	25
303	Large	3.6	R	25
304	Large	3.6	R	25
305	Large	3.6	R	25
306	Large	3.6	R	25
307	Large	2.4	R	25
308	Large	3	R	25
309	Large	3	R	25
310	Large	3	R	25
311	Large	3	R	25