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. (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. Let x1 represent engine's displacement. Let x2 represent variable Class Midsize. Let x3 represent 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) = 165.7224457 + X1+ X2 + 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. 69.4 % X3 (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. Let x1 represents engine's displacement. Let x2 represents variable ClassMidsize. Let x3 represents variable ClassLarge. Let x4 represents 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) + = 165.7224457 X4 + X1 + X2 + How much of the variation in the sample values of Hwy MPG does this estimated regression equation explain? If required, round your answer to one decimal places. % X3 Car Class Displacement Fuel Type Hwy MPG 1 Compact 3.1 P 25 28 Compact 3.5 P 2 Compact 3.1 P 25 29 Compact 4.2 P 3 Compact 3 P 25 30 Compact 4.6 P 4 Compact 3 P 25 31 Compact 4.6 P Compact 25 32 Compact 4.6 6 Compact 3 25 33 Compact 3.5 P 7 Compact 2.4 25 34 Compact 3.6 P 8 Compact 3.5 P 25 35 Compact 3.2 P Compact P 25 36 Compact 3.2 P 10 Compact 2.4 24 37 Compact 3.5 R 11 Compact 2.8 P 24 38 Compact 2.4 R 12 Compact 2.5 24 39 Compact 3.5 R 222222222222 24 24 24 24 24 24 24 24 24 24 24 24 13 Compact 24 40 Compact 3.5 R 24 14 Compact 2.5 24 41 Compact 3.2 23 15 Compact 2.4 R 24 42 Compact 4.2 P 23 16 Compact 5.3 24 43 Compact 4.8 P 23 17 Compact 24 44 Compact 4.8 P 23 18 Compact 3.5 R 24 45 Compact 3.5 P 23 19 Compact 3.5 R 24 46 Compact 4.6 R 23 20 Compact 3.5 R 24 47 Compact 4.6 R 23 21 Compact 3.5 24 48 Compact 5.7 R 23 22 Compact 3.5 R 24 49 Compact 5.7 R 23 23 Compact 3.8 R 24 50 Compact 4.6 R 23 24 Compact 3.5 R 24 51 Compact 4.6 R 23 25 Compact 3.5 24 52 Compact 4.2 P 23 26 Compact 5.3 24 53 Compact 4.2 P 23 27 Compact 4.6 P 24 54 Compact 4.8 P 23 55 Compact 3.5 P 56 Compact 3 P 57 Compact 4.4 P 58 Compact 3 P 59 Compact 3.9 R 60 Compact 3.5 P 61 Compact 4.2 P 62 Compact 4.2 63 Compact 4.6 64 Compact 4.6 65 Compact 3.5 66 Compact 5.7 67 Compact 5.7 68 Compact 3.5 69 Compact 4.8 70 Compact 3 71 Compact 4.2 72 Compact 5 73 Compact 3.5 74 Compact 5.5 75 Compact 4.2 76 Compact 5.5 77 Compact 5.5 78 Compact 4.5 79 Compact 5.5 80 Compact 4.6 81 Compact 4.2 82 Compact 4.2 PRRRRRR 22222222222222 P P P P P P P P P P 222222222222222222222782 83 Compact 6 P 20 23 84 Compact 4.5 P 20 23 85 Compact 5.5 P 222 112 Midsize 1.8 R 37 113 Midsize 2 R 35 20 114 Midsize 1.6 R 35 23 86 Compact 6 P 19 115 Midsize 1.8 R 35 87 Compact 5.2 P 19 116 Midsize 1.6 R 34 88 Compact 5.2 P 19 117 Midsize 2.4 R 34 89 Compact 4.4 P 19 118 Midsize 2 R 33 90 Compact 5.5 P 19 119 Midsize 1.6 91 Compact 6.2 P 19 120 Midsize 2 92 Compact 6.2 P 18 121 Midsize 2 93 Compact 6.2 P 18 122 Midsize 1.8 94 Compact 6.1 P 18 123 Midsize 2.5 95 Compact 6.1 P 18 124 Midsize 96 Compact 4.6 R 18 125 Midsize 1.6 97 Compact 4.6 R 18 126 Midsize 1.6 98 Compact 6.1 P 18 127 Midsize 1.6 99 Compact 5.5 P 17 128 Midsize 100 Compact 5.5 P 17 129 Midsize 2.4 101 Compact 6.2 P 17 130 Midsize 2066242 102 Compact 6 P 17 131 Midsize 103 Compact 5.5 P 17 132 Midsize 21 104 Compact 5 P 17 133 Midsize 122 1.8 2.5 2.4 21 105 Compact 5 P 17 134 Midsize 2 21 106 Compact 5.5 P 16 135 Midsize 2.4 21 107 Compact 6 P 16 136 Midsize 2 21 108 Compact 5.5 P 16 137 Midsize 2 2 21 109 Compact 6 P 16 138 Midsize 2.4 20 110 Compact 5.7 P 16 20 111 Compact 5.7 15 65 139 Midsize 2.4 140 Midsize 2.4 RRRRRRRRRRRRRRRRRRRRRR 33 33 33 33 33 33 32 32 32 32 32 32 32 32 32 P 31 31 31 31 31 31 31 141 Midsize 2.4 142 Midsize 2.4 143 Midsize 2.2 144 Midsize 2.4 145 Midsize 2.4 146 Midsize 2.5 147 Midsize 1.8 148 Midsize 149 Midsize 2.4 150 Midsize 2.4 151 Midsize 152 Midsize 153 Midsize 2.4 2.4 154 Midsize 155 Midsize 2.4 156 Midsize 2.4 157 Midsize 2.4 158 Midsize 2.4 159 Midsize 160 Midsize 4244582442442444425 22 2.5 161 Midsize 2.4 162 Midsize 163 Midsize 164 Midsize 165 Midsize 166 Midsize 167 Midsize 2.3 168 Midsize 2.3 72222222 RRRRRRRRRRRRRRRRRRRRR222222R 31 169 Midsize 31 170 Midsize 31 171 Midsize 3.5 2254 R 29 2 R R 29 31 172 Midsize 2.5 R 31 173 Midsize 2.5 R 31 174 Midsize 2.5 R 31 175 Midsize 2.5 R 31 176 Midsize 3.5 R 31 177 Midsize 3.5 R 31 178 Midsize 3.5 R P 30 179 Midsize 2.5 P 30 180 Midsize 2 P 30 181 Midsize 30 182 Midsize 30 183 Midsize 30 184 Midsize 185 Midsize 30 186 Midsize 30 187 Midsize 30 188 Midsize 189 Midsize +3335 312222322 3.5 R 1.8 R 29 2.4 R 2.3 R 2.3 R 2.3 R 3.5 R 2.4 2.4 P P P P P 2222222 190 Midsize 191 Midsize 192 Midsize +4233 P P 28 P P 193 Midsize 194 Midsize 195 Midsize 222 2.5 P 2.5 P 2.4 P 196 Midsize 2.4 P 2222222222222222222222222222 197 Midsize 2.4 198 Midsize 2.4 199 Midsize 3.5 200 Midsize 20 201 Midsize 2 202 Midsize 2 203 Midsize 2 204 Midsize 3.9 205 Midsize 3.5 206 Midsize 3.3 207 Midsize 208 Midsize 33 3.5 3.5 209 Midsize 3 210 Midsize 2.3 211 Midsize 2 29 212 Midsize 3.8 213 Midsize 3.5 214 Midsize 2.3 215 Midsize 2.7 216 Midsize 2.3 28 217 Midsize 3.5 218 Midsize 2.3 28 219 Midsize 3.8 28 220 28 221 Midsize Midsize 3.5 2 222 Midsize 28 224 223 Midsize Midsize 322 3.1 2.5 2.5 PPRRRRRRRRRR222RRRRRRRR22222 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 27 27 27 27 225 Midsize 2.5 27 254 Large 2.5 226 Midsize 2.5 P 27 255 Large 2.4 227 Midsize 2.5 R 27 256 Large 2.4 228 Midsize 2.5 R 27 257 Large 2.4 229 Midsize 2.5 R 27 258 Large 3.5 230 Midsize 2.5 R 27 259 Large 3.6 231 Midsize 3.3 R 27 260 Large 3.3 232 Midsize 3.5 27 261 Large 2.7 233 Midsize 3.1 P 27 262 Large 2.7 234 Midsize 3 P 27 263 Large 3.8 235 Midsize 3.5 P 27 264 Large 3.3 236 Midsize 3.5 27 265 Large 3.2 237 Midsize 3.5 P 27 266 Large 3.5 238 Midsize 2.7 R 27 267 Large 3 239 Midsize 2.7 R 27 268 Large 3 240 Midsize 2.7 R 27 269 Large 3 241 Midsize 2 R 27 270 Large 2.3 242 Midsize 2.7 R 27 271 Large 3.5 243 Midsize 2.4 R 27 272 Large 2.3 244 Midsize 3 R 26 273 Large 3.6 245 Midsize 3 R 26 274 Large 3.6 246 Midsize 3.6 247 Large 248 Large 249 Large 250 Large 251 Large 2.8 252 Large 2.5 253 Large 2.5 03332855 R 26 275 Large 3.6 P 26 276 Large 3.6 26 277 Large 3.6 P 26 278 Large 3.6 P 26 279 Large 3.6 P 26 280 Large 3.5 26 281 Large 3.5 P 26 282 Large 69996553 P22RRRRRRRR222222222RRRRRRRRP 26 283 Large 3.5 26 284 Large 2.5 26 285 Large 2.5 26 286 Large 2.5 26 287 Large 2.5 26 288 Large 3.5 26 289 Large 4.2 26 290 Large 4.2 26 291 Large 4.2 26 26 26 26 26 26 26 25 22222222222222222222 26 292 Large 3.8 26 293 Large 3.1 294 Large 3 26 295 Large 3 296 Large 3 26 297 Large 3 26 298 Large 3.5 299 Large 3.5 300 Large 3.8 301 Large 302 Large 303 Large 26 304 Large 26 305 Large 26 306 Large 26 307 Large 3533332 3.5 5.3 3.6 3.6 3.6 3.6 2.4 26 308 Large 26 309 Large 26 310 Large 311 Large 3333 3 3 22222222222222222222RRRRRRRRR P 25 P 25 P 25 25 P 25 25 P 25 P 25 P 25 25 P 25 P 25 P 25 P 25 P 25 P 25 P 25 P 25 P 25 P 25 25 25 25 25 25 25 25 25 25