b Consider the addition of the dummy variable FuelPremium wh

b. Consider the addition of the dummy variable FuelPremium, where the value of FuelPremium is 1 if the required or recommended type of fuel is premium gasoline and 0 if the type of fuel is regular gasoline. 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 variable FuelPremium.

Round your answers to four decimal places. Enter negative values as negative numbers.

c. Use = .05 to determine whether the dummy variable added in part (b) is significant.

Solution

Regression Analysis: Hwy MPG versus Displacement, Fuel

The regression equation is
Hwy MPG = 40.6 - 3.19 Displacement - 2.72 Fuel

Predictor Coef SE Coef T P
Constant 40.5946 0.4906 82.74 0.000
Displacement -3.1944 0.1701 -18.77 0.000
Fuel -2.7230 0.4222 -6.45 0.000

S = 3.20680 R-Sq = 68.5% R-Sq(adj) = 68.3%

Analysis of Variance

Source DF SS MS F P
Regression 2 6841.1 3420.5 332.62 0.000
Residual Error 306 3146.8 10.3
Total 308 9987.9

Source DF Seq SS
Displacement 1 6413.3
Fuel 1 427.8

Unusual Observations

Obs Displacement Hwy MPG Fit SE Fit Residual St Resid
34 1.50 44.000 35.803 0.295 8.197 2.57R
35 1.30 44.000 36.442 0.316 7.558 2.37R
36 1.30 44.000 36.442 0.316 7.558 2.37R
64 2.00 25.000 31.483 0.406 -6.483 -2.04R
65 2.00 22.000 31.483 0.406 -9.483 -2.98R
66 2.00 23.000 31.483 0.406 -8.483 -2.67R
75 2.50 23.000 29.886 0.350 -6.886 -2.16R
92 1.50 46.000 35.803 0.295 10.197 3.19R
122 6.20 18.000 20.789 0.670 -2.789 -0.89 X
123 6.20 24.000 20.789 0.670 3.211 1.02 X
124 6.20 24.000 20.789 0.670 3.211 1.02 X
204 2.00 27.000 34.206 0.255 -7.206 -2.25R
206 2.00 27.000 34.206 0.255 -7.206 -2.25R
221 2.40 40.000 32.928 0.240 7.072 2.21R
230 2.40 40.000 32.928 0.240 7.072 2.21R
247 1.80 48.000 34.845 0.268 13.155 4.12R

R denotes an observation with a large standardized residual.
X denotes an observation whose X value gives it large leverage.

Summary of Regression Statistics:

The regression equation is
Hwy MPG = 40.6 - 3.19 Displacement - 2.72 Fuel

Multiple R:0.827647

R Square:68.5%

Adjusted R Square:68.3%

Standard error=10.3

Observations=309

c) the observed value of the test statistic is t=-6.45 and p-value=0<0.05,so we can conclude that the coefficient of the dummy variable Fuel is significantly different from 0.