The U.S. Department of Energys Fuel Economy Guide provides fuel efficiency data for cars and trucks. A portion of the data for 311 compact, midsized, and large cars is contained in the pictures below. The dataset contains the following variables:

Class identifies the size of the car; Compact, Midsize, or Large

Displacement = engine displacement in liters

FuelType shows whether the car uses premium (P) or regular (R) fuel

HwyMPG = fuel efficiency rating for highway driving in miles per gallon

1. Develop an estimated regression equation to predict the fuel efficiency for highway driving given the engines displacement. Plot the residuals from this regression to see if you see any pattern. Conduct a hypothesis test to determine whether the coefficient on Displacement is statistically significantly different from 0 using the 0.05 level of significance. How much of the variation in the sample values of HwyMPG does this estimated regression equation explain?
2. Create a scatter chart with HwyMPG on the y-axis and displacement on the x-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?
3. Add 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. Estimate the new regression equation. What happened to the adjusted R² when these variables were added to the regression? What does this tell you?
4. Use significance level of 0.05 to determine whether the dummy variables added to the model in part c are significant.
5. Finally add the dummy variable FuelPremium, (which is 1 if the car uses premium fuel and 0 if the car uses regular fuel) to the regression. What happened to the adjusted R² when these variables were added to the regression? What does this tell you?
6. For the estimated regression equation developed in part e, test for the significance of the overall regression relationship (using the F-statistic) and for each of the independent variables the 0.05 level of significance for each test.

Please use Regression tool (Data Analysis) to explain the rationale.

A \begin{tabular}{|c|c|c|c|c|} \hline A & B & C & D & E \\ \hline 296 & Large & P & 3 & 25 \\ \hline 297 & Large & P & 3 & 25 \\ \hline \multicolumn{2}{|c|}{ 2! Workbook last saved: Just now } & P & 3.5 & 25 \\ \hline 300YY & Large & P & 3.5 & 25 \\ \hline 300 & Large & P & 3.8 & 25 \\ \hline 301 & Large & P & 3.5 & 25 \\ \hline 302 & Large & P & 5.3 & 25 \\ \hline 303 & Large & R & 3.6 & 25 \\ \hline 304 & Large & R & 3.6 & 25 \\ \hline 305 & Large & R & 3.6 & 25 \\ \hline 306 & Large & R & 3.6 & 25 \\ \hline 307 & Large & R & 2.4 & 25 \\ \hline 308 & Large & R & 3 & 25 \\ \hline 309 & Large & R & 3 & 25 \\ \hline 310 & Large & R & 3 & 25 \\ \hline 311 & Large & R & 3 & 25 \\ \hline \end{tabular} \begin{tabular}{|c|c|c|c|c|c|} \hline 2 & A & B & C & D & E \\ \hline 1 & Car & Class & Fuel Type & Displacement & Hwy MPG \\ \hline 2 & 1 & Compact & P & 3.1 & 25 \\ \hline 3 & 2 & Compact & P & 3.1 & 25 \\ \hline 4 & 3 & Compact & P & 3 & 25 \\ \hline 5 & 4 & Compact & P & 3 & 25 \\ \hline 6 & 5 & Compact & P & 3 & 25 \\ \hline 7 & 6 & Compact & P & 3 & 25 \\ \hline 8 & 7 & Compact & P & 2.4 & 25 \\ \hline 9 & 8 & Compact & P & 3.5 & 25 \\ \hline 10 & 9 & Compact & P & 3 & 25 \\ \hline 11 & 10 & Compact & P & 2.4 & 24 \\ \hline 12 & 11 & Compact & P & 2.8 & 24 \\ \hline 13 & 12 & Compact & P & 2.5 & 24 \\ \hline 14 & 13 & Compact & P & 3 & 24 \\ \hline 15 & 14 & Compact & P & 2.5 & 24 \\ \hline 16 & 15 & Compact & R & 2.4 & 24 \\ \hline 17 & 16 & Compact & P & 5.3 & 24 \\ \hline 18 & 17 & Compact & P & 6 & 24 \\ \hline 19 & 18 & Compact & R & 3.5 & 24 \\ \hline 20 & 19 & Compact & R & 3.5 & 24 \\ \hline 21 & 20 & Compact & R & 3.5 & 24 \\ \hline 22 & 21 & Compact & R & 3.5 & 24 \\ \hline 23 & 22 & Compact & R & 3.5 & 24 \\ \hline 24 & 23 & Compact & R & 3.8 & 24 \\ \hline 25 & 24 & Compact & R & 3.5 & 24 \\ \hline 26 & 25 & Compact & P & 3.5 & 24 \\ \hline 27 & 26 & Compact & P & 5.3 & 24 \\ \hline 28 & 27 & Compact & P & 4.6 & 24 \\ \hline 29 & 28 & Compact & P & 3.5 & 24 \\ \hline 30 & 29 & Compact & P & 4.2 & 24 \\ \hline 31 & 30 & Compact & P & 4.6 & 24 \\ \hline 32 & 31 & Compact & P & 4.6 & 24 \\ \hline 33 & 32 & Compact & P & 4.6 & 24 \\ \hline 34 & 33 & Compact & P & 3.5 & 24 \\ \hline 35 & 34 & Compact & P & 3.6 & 24 \\ \hline 36 & 35 & Compact & P & 3.2 & 24 \\ \hline 37 & 36 & Compact & P & 3.2 & 24 \\ \hline 38 & 37 & Compact & R & 3.5 & 24 \\ \hline 39 & 38 & Compact & R & 2.4 & 24 \\ \hline 40 & 39 & Compact & R & 3.5 & 24 \\ \hline 41 & 40 & Compact & R & 3.5 & 24 \\ \hline 42 & 41 & Compact & P & 3.2 & 23 \\ \hline 43 & 42 & Compact & P & 4.2 & 23 \\ \hline 44 & 43 & Compact & P & 4.8 & 23 \\ \hline 45 & 44 & Compact & P & 4.8 & 23 \\ \hline 46 & 45 & Compact & P & 3.5 & 23 \\ \hline 47 & 46 & Compact & R & 4.6 & 23 \\ \hline 48 & 47 & Compact & R & 4.6 & 23 \\ \hline 49 & 48 & Compact & R & 5.7 & 23 \\ \hline 50 & 49 & Compact & R & 5.7 & 23 \\ \hline 51 & 50 & Compact & R & 4.6 & 23 \\ \hline 52 & 51 & Compact & R & 4.6 & 23 \\ \hline 53 & 52 & Compact & P & 4.2 & 23 \\ \hline 54 & 53 & Compact & P & 4.2 & 23 \\ \hline 55 & 54 & Compact & P & 4.8 & 23 \\ \hline 56 & 55 & Compact & P & 3.5 & 23 \\ \hline 57 & 56 & Compact & P & 3 & 23 \\ \hline 58 & 57 & Compact & P & 4.4 & 23 \\ \hline 59 & 58 & Compact & P & 3 & 22 \\ \hline \end{tabular} \begin{tabular}{|c|c|c|c|c|} \hline A & B & C & D & E \\ \hline 119 & Midsize & R & 1.6 & 33 \\ \hline 120 & Midsize & R & 2 & 33 \\ \hline 121 & Midsize & R & 2 & 33 \\ \hline 122 & Midsize & R & 1.8 & 33 \\ \hline 123 & Midsize & R & 2.5 & 33 \\ \hline 124 & Midsize & R & 2 & 33 \\ \hline 125 & Midsize & R & 1.6 & 32 \\ \hline 126 & Midsize & R & 1.6 & 32 \\ \hline 127 & Midsize & R & 1.6 & 32 \\ \hline 128 & Midsize & R & 2 & 32 \\ \hline 129 & Midsize & R & 2.4 & 32 \\ \hline 130 & Midsize & R & 2 & 32 \\ \hline 131 & Midsize & R & 1.8 & 32 \\ \hline 132 & Midsize & R & 2.5 & 32 \\ \hline 133 & Midsize & R & 2.4 & 32 \\ \hline 134 & Midsize & P & 2 & 31 \\ \hline 135 & Midsize & R & 2.4 & 31 \\ \hline 136 & Midsize & R & 2 & 31 \\ \hline 137 & Midsize & R & 2 & 31 \\ \hline 138 & Midsize & R & 2.4 & 31 \\ \hline 139 & Midsize & R & 2.4 & 31 \\ \hline 140 & Midsize & R & 2.4 & 31 \\ \hline 141 & Midsize & R & 2.4 & 31 \\ \hline 142 & Midsize & R & 2.4 & 31 \\ \hline 143 & Midsize & R & 2.2 & 31 \\ \hline 144 & Midsize & R & 2.4 & 31 \\ \hline 145 & Midsize & R & 2.4 & 31 \\ \hline 146 & Midsize & R & 2.5 & 31 \\ \hline 147 & Midsize & R & 1.8 & 31 \\ \hline 148 & Midsize & R & 2 & 31 \\ \hline 149 & Midsize & R & 2.4 & 31 \\ \hline 150 & Midsize & R & 2.4 & 31 \\ \hline 151 & Midsize & P & 2 & 30 \\ \hline 152 & Midsize & R & 2.4 & 30 \\ \hline 153 & Midsize & R & 2.4 & 30 \\ \hline 154 & Midsize & R & 2 & 30 \\ \hline 155 & Midsize & R & 2.4 & 30 \\ \hline 156 & Midsize & R & 2.4 & 30 \\ \hline 157 & Midsize & R & 2.4 & 30 \\ \hline 158 & Midsize & R & 2.4 & 30 \\ \hline 159 & Midsize & R & 2 & 30 \\ \hline 160 & Midsize & R & 2.5 & 30 \\ \hline 161 & Midsize & R & 2.4 & 30 \\ \hline 162 & Midsize & P & 2 & 29 \\ \hline 163 & Midsize & P & 2 & 29 \\ \hline 164 & Midsize & P & 2 & 29 \\ \hline 165 & Midsize & P & 2 & 29 \\ \hline 166 & Midsize & P & 2 & 29 \\ \hline 167 & Midsize & R & 2.3 & 29 \\ \hline 168 & Midsize & R & 2.3 & 29 \\ \hline 169 & Midsize & R & 2 & 29 \\ \hline 170 & Midsize & R & 2 & 29 \\ \hline 171 & Midsize & R & 3.5 & 29 \\ \hline 172 & Midsize & R & 2.5 & 29 \\ \hline 173 & Midsize & R & 2.5 & 29 \\ \hline 174 & Midsize & R & 2.5 & 29 \\ \hline 175 & Midsize & R & 2.5 & 29 \\ \hline 176 & Midsize & R & 3.5 & 29 \\ \hline 177 & Midsize & R & 3.5 & 29 \\ \hline \end{tabular} \begin{tabular}{|c|c|c|c|c|} \hline A & B & C & D & E \\ \hline 59 & Compact & R & 3.9 & 22 \\ \hline 60 & Compact & P & 3.5 & 22 \\ \hline 61 & Compact & P & 4.2 & 22 \\ \hline 62 & Compact & P & 4.2 & 22 \\ \hline 63 & Compact & R & 4.6 & 22 \\ \hline 64 & Compact & R & 4.6 & 22 \\ \hline 65 & Compact & R & 3.5 & 22 \\ \hline 66 & Compact & R & 5.7 & 22 \\ \hline 67 & Compact & R & 5.7 & 22 \\ \hline 68 & Compact & R & 3.5 & 22 \\ \hline 69 & Compact & P & 4.8 & 22 \\ \hline 70 & Compact & P & 3 & 22 \\ \hline 71 & Compact & P & 4.2 & 22 \\ \hline 72 & Compact & P & 5 & 22 \\ \hline 73 & Compact & P & 3.5 & 22 \\ \hline 74 & Compact & P & 5.5 & 22 \\ \hline 75 & Compact & P & 4.2 & 21 \\ \hline 76 & Compact & P & 5.5 & 21 \\ \hline 77 & Compact & P & 5.5 & 21 \\ \hline 78 & Compact & P & 4.5 & 21 \\ \hline 79 & Compact & P & 5.5 & 21 \\ \hline 80 & Compact & P & 4.6 & 21 \\ \hline 81 & Compact & P & 4.2 & 20 \\ \hline 82 & Compact & P & 4.2 & 20 \\ \hline 83 & Compact & P & 6 & 20 \\ \hline 84 & Compact & P & 4.5 & 20 \\ \hline 85 & Compact & P & 5.5 & 20 \\ \hline 86 & Compact & P & 6 & 19 \\ \hline 87 & Compact & P & 5.2 & 19 \\ \hline 88 & Compact & P & 5.2 & 19 \\ \hline 89 & Compact & P & 4.4 & 19 \\ \hline 90 & Compact & P & 5.5 & 19 \\ \hline 91 & Compact & P & 6.2 & 19 \\ \hline 92 & Compact & P & 6.2 & 18 \\ \hline 93 & Compact & P & 6.2 & 18 \\ \hline 94 & Compact & P & 6.1 & 18 \\ \hline 95 & Compact & P & 6.1 & 18 \\ \hline 96 & Compact & R & 4.6 & 18 \\ \hline 97 & Compact & R & 4.6 & 18 \\ \hline 98 & Compact & P & 6.1 & 18 \\ \hline 99 & Compact & P & 5.5 & 17 \\ \hline 100 & Compact & P & 5.5 & 17 \\ \hline 101 & Compact & P & 6.2 & 17 \\ \hline 102 & Compact & P & 6 & 17 \\ \hline 103 & Compact & P & 5.5 & 17 \\ \hline 104 & Compact & P & 5 & 17 \\ \hline 105 & Compact & P & 5 & 17 \\ \hline 106 & Compact & P & 5.5 & 16 \\ \hline 107 & Compact & P & 6 & 16 \\ \hline 108 & Compact & P & 5.5 & 16 \\ \hline 109 & Compact & P & 6 & 16 \\ \hline 110 & Compact & P & 5.7 & 16 \\ \hline 111 & Compact & P & 5.7 & 15 \\ \hline 112 & Midsize & R & 1.8 & 37 \\ \hline 113 & Midsize & R & 2 & 35 \\ \hline 114 & Midsize & R & 1.6 & 35 \\ \hline 115 & Midsize & R & 1.8 & 35 \\ \hline 116 & Midsize & R & 1.6 & 34 \\ \hline 117 & Midsize & R & 2.4 & 34 \\ \hline \end{tabular}